# Heterogeneous Domain Adaptation with Adversarial Neural Representation
Learning: Experiments on E-Commerce and Cybersecurity

Mohammadreza Ebrahimi, Yidong Chai, Hao Helen Zhang, and Hsinchun Chen, M.
Ebrahimi is with the School of Information Systems and Management, University
of South Florida, 4202 E. Fowler Avenue, Tampa, FL 33620. E-mail:
<EMAIL_ADDRESS>Chai is with the School of Management, Hefei University
of Technology. Corresspondence to: Y. Chai. Email<EMAIL_ADDRESS>Hao
Helen Zhang is with the Department of Mathematics, University of Arizona.
E-mail<EMAIL_ADDRESS>Hsinchun Chen is with the Aritificial
Intelligence Lab, University of Arizona. Email<EMAIL_ADDRESS>
###### Abstract

Learning predictive models in new domains with scarce training data is a
growing challenge in modern supervised learning scenarios. This incentivizes
developing domain adaptation methods that leverage the knowledge in known
domains (source) and adapt to new domains (target) with a different
probability distribution. This becomes more challenging when the source and
target domains are in heterogeneous feature spaces, known as heterogeneous
domain adaptation (HDA). While most HDA methods utilize mathematical
optimization to map source and target data to a common space, they suffer from
low transferability. Neural representations have proven to be more
transferable; however, they are mainly designed for homogeneous environments.
Drawing on the theory of domain adaptation, we propose a novel framework,
Heterogeneous Adversarial Neural Domain Adaptation (HANDA), to effectively
maximize the transferability in heterogeneous environments. HANDA conducts
feature and distribution alignment in a unified neural network architecture
and achieves domain invariance through adversarial kernel learning. Three
experiments were conducted to evaluate the performance against the state-of-
the-art HDA methods on major image and text e-commerce benchmarks. HANDA shows
statistically significant improvement in predictive performance. The practical
utility of HANDA was shown in real-world dark web online markets. HANDA is an
important step towards successful domain adaptation in e-commerce
applications.

###### Index Terms:

Domain adaptation, adversarial kernel learning, dictionary learning, maximum
mean discrepancy, transfer learning.

##  1 Introduction

Learning predictive models in new domains that lack enough training data has
arisen as a challenge in supervised learning. This forms a strong motivation
for transferring knowledge from common domains (source) to unknown domains
(target), often known as Domain Adaptation (DA) [1, 2, 3]. DA requires less
supervision since it often operates with few labeled samples in the target
domain. A practical example would be utilizing labeled user-generated content
in legal e-commerce platforms (e.g., Amazon, eBay) to recognize unseen content
in a new market and improve product search and indexing [4]. The same scenario
applies to dark web e-commerce platforms (e.g., Dream Market and Russian Silk
Road) in cybersecurity applications.
DA is a branch of transfer learning (TL) addressing two major issues:
distribution divergence and feature discrepancy [5]. The former arises because
source domain samples admit a different distribution than that of the target
domain. The latter occurs when source and target samples are expressed in
different feature spaces. Most studies focus on the first issue, in which data
distributions of source and target are different while samples are in the same
feature space. Also known as homogeneous domain adaptation, this approach is
not sufficient to address real-world scenarios. Addressing both issues is
significantly challenging and has emerged as a new field called Heterogeneous
Domain Adaptation (HDA). In most HDA scenarios, labeled datasets are available
from a known source, while the target domain suffers from a lack of labeled
data (Figure 1) [6, 7].

Figure 1: Illustrating HDA with Distribution Divergence and Feature
Discrepancy. Three product categories are represented by different features
and distributions in the source and target domains.

Most HDA methods use mathematical optimization (e.g., convex optimization) or
linear methods (e.g., linear discriminant analysis) to find common underlying
representations from source and target [8, 5, 9]. These representations could
be less transferable for DA [10]. Neural representations have shown promise in
DA due to their ability to automatically extract transferable features [11].
Transferable features are intermediate representations that are domain
invariant [12, 13] and, thus, instrumental to successful DA [7]. Adversarial
Neural Domain Adaptation (ANDA) is a promising direction to obtain domain-
invariant representations [13], which leverages a game theory-based learning
scheme [14] to obtain high-quality representations. As a subcategory of DA,
existing ANDA methods often address homogeneous domain adaptation [5].
However, heterogeneous sources of user-generated content are very common on
e-commerce platforms (e.g., multilingual text or product images with different
representations). We present a novel ANDA framework to extract transferable
domain-invariant representations from heterogeneous domains. This framework
extends ANDA to heterogeneous domains by employing an inverse problem-solving
method known as dictionary learning to mitigate the feature discrepancy. It
also alleviates the distribution divergence between source and target in an
adversarial manner. Our proposed method significantly improves the performance
of text classification and image recognition in e-commerce applications.

##  2 Related Work

DA is a special case of TL. The goal of TL is to use the knowledge obtained
from a resource-rich domain or task (i.e., source) to help a task or domain
with insufficient training data (i.e., target) [15]. The domain consists of
feature space and data probability distribution [16]. The task is a function
that can be learned on a domain to map the data to a corresponding label
space. In many practical cases, the source and target tasks are often the
same, while the domains vary. Hence, the source domain model often needs to be
adapted to the target domain. For instance, in cybersecurity applications, a
task could be determining if a dark net market product is cybersecurity-
related when the domains are English (source) and Russian (target) product
descriptions in the dark web. DA aims to transfer the knowledge to perform the
same task in different source and target domains [17]. This requires reducing
the distribution divergence and feature discrepancy in the source and target
domains [17, 5]. Most DA methods only focus on alleviating the distribution
divergence (i.e., homogeneous DA) [11, 18, 19, 20]. Homogenous DA does not
apply to heterogeneous domains where the data dimensions and features are
different. In contrast, Heterogeneous DA (HDA) is intended to reduce both
feature discrepancy and distribution divergence.

###  2.1 Heterogeneous Domain Adaptation (HDA)

HDA aims to perform the adaptation when the source and target domains are in
different feature spaces. HDA methods often map features in the source and
target to a common space using mathematical objective function optimization or
a linear projection from source to target domain [8, 21, 5, 9, 22, 23, 24, 25,
26, 27]. These features tend to be less transferable than representations
obtained from neural networks for domain adaptation [28, 29]. A taxonomy of
selected major HDA methods is provided in Table I.

Table I: A Taxonomy of Major HDA Methods Method |  Method Category |  Task |  Testbed
---|---|---|---
Discriminative Joint Distribution Adaptation (DJDA) [9] |  Objective function optimization |  Low-resolution image recognition |  Face images
HDA Network based on Autoencoder (HDANA) [29] |  Stacked autoencoder |  Image recognition |  Newswire articles, product images
Progressive Alignment (PA) [5] |  Objective function optimization |  Multilingual text and image recognition |  Newswire articles, product images
Cross-Domain Mapping (CDM) [8] |  Linear discriminant analysis |  Multilingual text and image recognition |  Newswire articles, product images
Invariant Latent Space (ILS) [22] |  Kernel matching and optimization |  Image and face recognition |  Product and face images
Cross-Domain Landmark Selection (CDLS) [23] |  Objective function optimization |  Image recognition |  Product images
Transfer Neural Trees (TNT) [28] |  Neural decision forest |  Image recognition |  Product images
Generalized Joint Distribution Adaptation (G-JDA) [21] |  Objective function optimization |  Image recognition and multilingual text classification |  Newswire articles, product images
Supervised Kernel Matching (SSKM) [24] |  Kernel matching and optimization |  Text and sentiment classification |  Product reviews, newswire articles
Sparse Heterogeneous Feature Representation (SHFR) [25] |  Objective function optimization |  Text and sentiment classification |  Newswire articles
Semi-supervised Heterogeneous Feature Augmentation (SHFA) [26] |  Convex function optimization |  Text and sentiment classification, Image recognition |  Product reviews, newswire articles
Max-Margin Domain Transforms (MMDT) [27] |  Objective function optimization |  Image recognition |  Product images

As seen in the taxonomy, most HDA approaches obtain feature representations
based on mathematical optimization and linear mapping, and few studies utilize
neural network-based representations to accomplish HDA. Most extant methods
cast the HDA objective into an optimization problem aimed at mapping source
and target to a common feature space without promoting domain invariance
between source and target, resulting in limited improvement in the
transferability of the source model to the target domain. Next, we review the
effective methods to attain domain invariance and position our study within
the body of the related work.

###  2.2 Adversarial Neural Domain Adaptation (ANDA)

One promising direction to achieve domain invariance in DA is to map source
and target samples into a ‘common latent space,’ in which source and target
representations of the same class are close to each other [30, 31]. Recently,
adversarial learning has shown promise in providing domain-invariant
representations without ‘pair alignment,’ eliminating the need for manually
establishing sample correspondence in source and target [6, 10]. Adversarial
learning is a game-theoretic approach for simultaneously training two
competing components, generator and discriminator [32], which yields state-of-
the-art performance in homogeneous DA [11]. When utilized in DA, the generator
is trained to create representations that mimic both source and target
distribution, and the discriminator is tasked to distinguish the source data
from the target data created by the generator. ANDA generates adversarially
learned domain-invariant representations from source and target that are
suitable for domain adaptation [13]. These representations are useful in tasks
such as text classification [12, 33, 34], character recognition [6, 7, 35, 10,
36], or image classification [37, 11, 38, 39, 13] on a variety of datasets
such as English Amazon reviews, handwritten digits, and face images. However,
existing ANDA methods mostly operate on sources and targets with homogeneous
feature spaces and do not address heterogeneous domain adaptation. This
restricts the applicability of DA in real-world applications where the source
and target domains are both relevant to a task but do not share the same
feature representation.

###  2.3 Research Positioning

While ANDA can address the transferability issue, most ANDA frameworks
consider homogeneous feature spaces. Given the heterogeneity of user-generated
content (e.g., multilingual text, diverse image representations), these issues
undermine the applicability of DA to emerging applications such as e-commerece
or cybersecurity. To highlight the position of our proposed method, we
categorize major DA work in two dimensions (Table II). The horizontal
dimension differentiates DA methods supporting heterogeneous features. The
vertical dimension distinguishes between DA methods that generate neural
representations and the others. Among homogeneous studies, methods relying on
mathematical optimization include Support and Model Shift (SMS) [20], Joint
Distribution Adaptation (JDA) [18], and Transfer Component Analysis (TCA)
[19]. Recent homogeneous methods such as Symmetric Networks (SymNets) [39],
Domain Adaptation Network (DAN) [11], Symmetric Bi-directional ADAptive GAN
(SBADA-GAN) [36], Auxiliary Classifier GAN (AC-GAN) [38], Adversarial
Discriminative Domain Adaptation (ADDA), and Cycle Consistent Adversarial
Domain Adaptation (CYCADA) [6] support neural representations (the bottom left
quadrant). Heterogeneous methods (the top right and bottom right quadrants)
were recognized in Section 2.1. Little has been done to provide a solution
that yields neural representations from heterogeneous domains (the bottom
right quadrant).

Table II: Positioning Our Proposed Method in DA Research |  Homogeneous |  Heterogeneous
---|---|---
Mathematical Optimization |  SMS [20], JDA [18], TCA [19] |  PA [5], CDM [8], G-JDA [21], CDLS [23], SHFA [26], MMDT [27]
Neural Representation |  SymNets [39], DAN [11], CYCADA [6], AC-GAN [38], SBADA-GAN [36], ADDA [13] |  HDANA [29], TNT [28], Our proposed model

Two extant neural representation-based HDA methods are recognized as
alternatives for our proposed model: Transfer Neural Trees (TNT) [28] and
Heterogeneous Domain Adaptation Network based on Autoencoder (HDANA) [29]. TNT
is a tree-based neural network architecture focused on conducting HDA via
obtaining corresponding pairs in source and target domains and does not offer
distribution alignment. HDANA is a deep autoencoder architecture addressing
the distribution alignment with a fixed distribution divergence kernel, which
may result in lack of domain invariance. Both these issues can lead to
performance loss. To remedy these issues, our model introduces a novel HDA
framework that enables both feature and distribution alignment in a unified
neural network architecture with enhanced domain invariance. It utilizes
dictionary learning and nonparametric adversarial kernel matching to achieve
these goals without relying on a fixed kernel for distribution matching. Our
model contributes to obtaining high-quality representations from heterogeneous
domains, which are useful in downstream tasks such as multilingual text
classification and image recognition.

##  3 Background for Proposed Model

###  3.1 Model Preliminaries

Let $\mathcal{D}^{s}=\\{\mathcal{X}^{s},P(X^{s},y^{s})\\}$ and
$\mathcal{D}^{t}=\\{\mathcal{X}^{t},Q(X^{t},y^{t})\\}$ denote the source and
target domains, each comprises feature spaces $\mathcal{X}^{s}$ and
$\mathcal{X}^{t}$ and distributions $P$, $Q$ over the source and target
samples, respectively. The source data
$X^{s}=\\{x_{i}^{s},y_{i}^{s}\\}_{i=1}^{n_{s}}$ includes labeled data sampled
from distribution $P$. The target data $X^{t}=\\{x_{i}^{t}\\}_{i=1}^{n_{t}}$
is sampled from distribution $Q$ and contains both labeled data
$\\{(x_{i}^{L},y_{i}^{L})\\}^{n_{L}}_{i=1}\sim{Q}$ and unlabeled data
$\\{(x_{i}^{U})\\}^{n_{U}}_{i=1}\sim{Q}$. HDA aims to help a classification
task in the target domain by using the source domain data when not only is
$P\neq{Q}$, but $\mathcal{X}^{s}\neq{\mathcal{X}^{t}}$. To achieve this, we
present a neural network architecture to approximate a hypothesis $h(x)$ that
not only minimizes the discrepancy between $X^{s}$ and $X^{t}$ as well as the
divergence between distributions $P$ and $Q$, but also minimizes the error of
assigning target labels $\epsilon_{t}(h(x))$, using source domain data and
only a small number of labeled target data. DA models need to be generalizable
to unseen domains in order to reduce the target generalization error
$\epsilon_{t}(h)$ [11]. Accordingly, we draw on the domain adaptation theory
to identify the generalization error bound of the target [40, 41] and inform
the components of our proposed model. For any hypothesis space $\mathcal{H}$
and a fixed representation function the expected target error is bounded by
Theorem 1.

Theorem 1 [41]: Let ${X}^{s}$ and ${X}^{t}$ represent samples drawn from $P$
and $Q$, the source and target domain distributions, respectively. For any
$\delta\in(0,1)$, with probability at least $1-\delta$ (over the choice of the
samples), for every hypothesis $h\in\mathcal{H}$:

$\epsilon_{t}(h)\leq{\hat{\epsilon}}_{s}(h)+\hat{d}_{\mathcal{H}}({X}^{s},{X}^{t})+\epsilon_{s}(h^{*})+\epsilon_{t}(h^{*})+C$
(1)

where ${\hat{\epsilon}}_{s}(h)$ is the empirical source training error,
$\epsilon_{s}(h^{*})+\epsilon_{t}(h^{*})$ is the combined error of the ideal
hypothesis in both domains, and $C$ is a constant given in (2):

$\displaystyle
C=\frac{4}{m}\sqrt{d\log\left(\frac{2em}{d}\right)+\log\left(\frac{4}{\delta}\right)}+4\sqrt{\frac{d\log(2m^{\prime})+log(\frac{4}{\delta})}{m^{\prime}}}$
(2)

where $e$ is the base for the natural logarithm, $d$ is the VC-dimension of
the hypothesis space, $m$ denotes labeled sample size in source, and
$m^{\prime}$ is the unlabeled sample size. As seen in (2), $C$ only depends on
the properties of the hypothesis space (i.e., VC-dimension and sample sizes),
rather than the choice of samples. Assuming that the combined error of the
ideal hypothesis $\epsilon_{s}(h^{*})+\epsilon_{t}(h^{*})$ is small for a
reasonable representation, the bound in Theorem 1 depends on the first and
second terms in the RHS of (1). It is expected that an effective DA model
reduces these two terms and, thus, the target generalization error
$\epsilon_{t}(h)$. The first error term ${\hat{\epsilon}}_{s}(h)$ can be
reduced by learning shared representations from source and target [41], which
requires aligning feature representations when the domains are heterogeneous.
The second term denotes the empirical $\mathcal{H}$-divergence between the
source and target distributions [40]:

$\displaystyle\hat{d}_{\mathcal{H}}({X}^{s},{X}^{t})\triangleq
2(1-\underset{{h\in{\mathcal{H}}}}{\text{min}}\\{\frac{1}{m^{\prime}}\sum_{{x}:h({x})=0}\mathbbm{1}[{x}\in{{X}^{s}}]$
(3)
$\displaystyle+\frac{1}{m^{\prime}}\sum_{{x}:h({x})=1}\mathbbm{1}[{x}\in{{X}^{t}}]\\})$

where $\mathbbm{1}$ is an indicator function that returns 1 when its argument
is true and 0 otherwise. Long et al. [11] show that the minimization term in
(3) is bounded by the Maximum Mean Discrepancy (MMD) distance under kernel $k$
[42]. Thus, (1) can be re-written as:

$\displaystyle\epsilon_{t}(h)\leq{\hat{\epsilon}}_{s}(h)+2(1+D_{k}(X^{s},X^{t}))+\lambda+C$
(4)

where $D_{k}(.)$ denotes the MMD distance in a Reproducing Kernel Hilbert
Space (RKHS) with kernel $k$ [42]. The second term in (4) can be reduced by
distribution kernel matching, aiming to minimize the distance of the source
and target distribution.

To minimize these two terms, next we discuss dictionary learning as a
promising approach to reduce ${\hat{\epsilon}}_{s}(h)$, which addresses
feature discrepancy by translating source and target features to a common
space. Subsequently, to reduce the $\mathcal{H}$-divergence between the source
and target, we discuss distribution kernel matching and adversarial kernel
learning.

###  3.2 Dictionary Learning: Reducing $\bm{{\hat{\epsilon}}_{s}(h)}$

A viable approach to align representations can be devised based on dictionary
learning [5]. Dictionary learning is an inverse problem that aims to decompose
a given data matrix $X$ into a dictionary space $D$ and a coefficient matrix
$R$, which denotes the representation of $X$ under $D$, by optimizing (5):

$\displaystyle\underset{D,R}{\text{min}}\left\|X-DR\right\|_{F}^{2}+\lambda\left\|R\right\|_{1};$
(5) $\displaystyle\text{s.t.}\left\|d_{i}\right\|_{2}\leq 1;\forall i\in
1,\ldots,k$

where $F$ denotes the Frobenius norm measuring reconstruction error and
$d_{i}$ is the $i^{t}h$ column in $D$. Unlike other matrix factorization
methods dictionary learning can promote sparsity in the coefficient matrix,
resulting in extracting only salient features from the input. Dictionary
learning has been successfully applied to signal [43] and image [5]
processing, contributing to reducing the dimensionality of the input data
while preserving the salient features. Sharing the dictionary $D$ between the
source ($X^{s}$) and the target domain ($X^{t}$) forces the new
representations to be projected to ] space [5].

$\displaystyle\underset{D,R^{s},R^{t}}{\text{min}}\left\|X^{s}-DR^{s}\right\|_{F}^{2}+\left\|X^{t}-DR^{t}\right\|_{F}^{2}+\lambda\left\|R\right\|_{1}$
(6) $\displaystyle\text{s.t.}\left\|d_{i}\right\|_{2}\leq 1;\quad
R=[R^{s},R^{t}]$

While this is useful in DA for aligning features, traditional dictionary
learning ignores label information since it is not naturally designed for
classification tasks often encountered in e-commerce applications. We are
motivated to incorporate the dictionary learning objective function in a
neural network architecture that can jointly learn a classification task such
that it is possible to take advantage of labeled data in both the source and
target domains.

###  3.3 Distribution Kernel Matching and Adversarial Kernel Learning:
Reducing $\bm{\hat{d}_{\mathcal{H}}({X}^{s},{X}^{t})$}$

DA requires measuring the distribution divergence between source and target.
This could be successfully achieved by defining a two-sample test statistic on
source and target [44]. Two types of test statistics for DA are parametric and
nonparametric. Parametric statistics measure the similarity of the density
functions in source and target (e.g., Kullback-Leibler divergence) [45, 46].
Nonparametric statistics measure the distance of kernels rather than the
actual densities. This requires the distributions to be treated as functions
in RKHS [42]. Nonparametric distribution kernel matching methods are often
preferred for DA since they circumvent intractable density estimation [11].
Among nonparametric kernel matching methods, Maximum Mean Discrepancy (MMD) is
the most widely used for DA [47, 29]. MMD measures the divergence based on the
distance ${\rm D}$ between source and target domain data $X^{s}\sim{P}$ and
$X^{t}\sim{Q}$.

$\displaystyle{\rm
D}_{k}(X^{s},X^{t})\triangleq\left\|\mathbb{E}_{x^{s}}[\phi_{k}(x^{s})]-\mathbb{E}_{x^{t}}[\phi_{k}(x^{t})]\right\|_{\mathcal{H}_{k}}^{2}$
(7)

where $\phi_{k}(.)$ is a feature mapping from inputs to an embedding in the
Hilbert space $\mathcal{H}_{k}$ characterized by kernel $k$. MMD’s test power
is extremely sensitive to the choice of mapping $\phi_{k}$ [48, 49], which
could negatively affect the distribution alignment performance. Adversarial
kernel learning can address this issue by facilitating finding the proper
kernel that maximizes the test power of MMD [44]. Such a kernel helps align
the distributions in source and target without establishing sample
correspondence. To this end, the mapping $\phi$ in MMD can be optimized via
adversarial kernel learning [44]. However, extant adversarial kernel learning
methods are not designed for heterogeneous domains. Inspired by the recent
advances, we employ adversarial kernel learning for HDA. This enables
benefiting from the nonparametric property of MMD while improving the test
power via adversarial learning.

##  4 Proposed Model: Heterogenous Adversarial Neural Domain Adaptation
(HANDA)

Informed by the effect of ${\hat{\epsilon}}_{s}(h)$ and
$\hat{d}_{\mathcal{H}}(\tilde{X}^{s},\tilde{X}^{t})$ on reducing
$\epsilon_{t}(h)$, we incorporate dictionary learning and adversarial kernel
matching in a unified architecture that reduces the generalization error bound
on any given domain adaptation problem. Accordingly, our proposed model
integrates three components, each targeting an adaptation challenge in HDA.
Figure 2 shows the integration of these three components in our model,
Heterogeneous Adversarial Neural Domain Adaptation (HANDA). The first
component is a shared dictionary learning (SDL) approach that targets
alleviating feature discrepancy via projecting heterogeneous features into a
common latent space and is associated with minimizing a reconstruction loss
$\mathcal{L}_{SDL}$. The second component is a nonparametric adversarial
kernel matching method, which aims to reduce the distribution divergence by
combining the nonparametric benefits of MMD and flexibility of kernel choices
in adversarial learning. This component is associated with minimizing an
adversarial loss denoted by $\mathcal{L}_{Adv}$. Finally, the third HANDA’s
component is a shared classifier in source and target that targets limited
labeled data in the target domain by exploiting labeled samples in both the
source and target domain. This component yields the classifier $h(x)$ as the
ultimate goal of HDA and is associated with minimizing the classification loss
$\mathcal{L}_{C}$.

Figure 2: HANDA Architecture. The Shared Dictionary Learning (left) and
Nonparametric Adversarial Kernel Matching (middle) components operate on the
heterogeneous representations of source and target domain to reduce feature
discrepancy via minimizing $\mathcal{L}_{SDL}$ and to reduce distribution
divergence via minimizing $\mathcal{L}_{Adv}$, simultaneously. The Shared
Classifier (right) component operates on the resultant representations via
minimizing the shared classification loss $\mathcal{L}_{C}$.

While shared dictionary learning aligns heterogeneous features in a common
latent space and yields a new embedding, nonparametric adversarial kernel
matching reduces the distribution divergence in the obtained embedding. After
feature and distribution alignment, a shared classifier conducts the
downstream tasks (e.g., text or image classification). HANDA’s novelty is
threefold. First, it extends ANDA to heterogeneous domains. Second, it
enhances dictionary learning to take advantage of labeled data in the source
and target, and third, it enables joint feature and distribution alignment in
a unified neural network architecture. We describe each HANDA component next.

###  4.1 Component #1: Shared Dictionary Learning (SDL)

To minimize feature discrepancy, the source and target need to be mapped into
the same subspace by domain-specific projections $P^{s}$ and $P^{t}$. This can
be achieved by modifying (6) to get:

$\displaystyle\underset{P^{s},P^{t},D,R^{s},R^{t}}{\text{min}}\left\|P^{s}X^{s}-DR^{s}\right\|_{F}^{2}+$
$\displaystyle\left\|P^{t}X^{t}-DR^{t}\right\|_{F}^{2}$ (8)
$\displaystyle+\lambda\left\|R\right\|_{1};$
$\displaystyle\text{s.t.}\left\|d_{i}\right\|_{2}\leq 1;\quad R=[R^{s},R^{t}]$

where $P_{k\times m_{s}}^{s}$ and $P_{k\times m_{t}}^{t}$ are projections.
$X_{m_{s}\times n_{s}}^{s}$ and $X_{m_{t}\times n_{t}}^{t}$ are the source and
target data. $D_{k\times k}$ is the shared dictionary, and $R_{k\times
n_{s}}^{s}$ and $R_{k\times n_{t}}^{t}$ denote the aligned representations. To
avoid degenerate solutions, $P^{s}$ and $P^{t}$ are often constrained to be
orthogonal [50]. The minimization in (7) yields data representations $R^{s}$
and $R^{t}$ that are in the same feature space.

###  4.2 Component #2: Nonparametric Adversarial Kernel Matching

Even though the obtained representations $R^{s}$ and $R^{t}$ are in the same
space, their distributions are different. Thus, minimizing distribution
divergence is crucial for successful DA. MMD measures the distribution
divergence of source and target via a ‘two-sample test,’ in which the source
and target distributions are the same under the null hypothesis. The
distribution divergence can be minimized by learning a model
$\phi_{\theta}(.)$ parameterized by $\theta$ that minimizes the MMD distance:

$\displaystyle\underset{\theta}{\text{min}}\quad{\rm
D}_{k}(\phi_{k}(\phi_{\theta}(R^{s})),\phi_{k}(\phi_{\theta}(R^{t})))$ (9)

where ${\rm D}_{k}(.)$ is the MMD distance with a mapping function of some
kernel $k$. The explicit computation can be avoided by applying the kernel
trick $k(x,x^{\prime})=\langle\phi(x),\phi(x^{\prime})\rangle_{\mathcal{H}}$
[48], which gives:

$\displaystyle{\rm D}_{k}(X^{s},X^{t})\triangleq\mathbb{E}_{x^{s},x^{\prime
s}}[k(x^{s},x^{\prime s})]$
$\displaystyle-2\mathbb{E}_{x^{s},x^{t}}[k(x^{s},x^{t})]$ (10)
$\displaystyle+\mathbb{E}_{x^{t},x^{\prime t}}[k(x^{t},x^{\prime t})]$

The test power of $D_{k}(.)$ in (9) heavily relies on the choice of the kernel
$k$ [44]. Low test power can preclude correctly distinguishing unlike source
and target domains. To increase the test power in DA, it is natural to search
for the kernel that maximizes the distance between source and target. Thus,
(9) can be re-written as:

$\displaystyle\underset{\theta}{\text{min}}\quad\underset{k}{\text{max}}\quad{\rm
D}_{k}(\phi_{k}(\phi_{\theta}(R^{s})),\phi_{k}(\phi_{\theta}(R^{t})))$ (11)

To cover a wide range of kernels (as opposed to a fixed one), we parameterize
the kernel using neural network $M$ and search for the optimal kernel by
learning the network parameters:

$\displaystyle\underset{\theta}{\text{min}}\quad\underset{\theta_{M}}{\text{max}}\quad{\rm
D}_{\theta_{M}}(\phi_{\theta_{M}}(\phi_{\theta}(R^{s})),\phi_{\theta_{M}}(\phi_{\theta}(R^{t})))$
(12)

Inspired by the idea of adversarial kernel learning [44], we suggest
minimizing (12) via another neural network $N$ in a GAN-like fashion [14].
These two neural networks can be trained in an adversarial manner to solve the
minimax problem in (13).

$\displaystyle\underset{\theta_{N}}{\text{min}}\quad\underset{\theta_{M}}{\text{max}}\quad{\rm
D}_{\theta_{M}}(\phi_{\theta_{M}}(\phi_{\theta_{N}}(R^{s})),\phi_{\theta_{M}}(\phi_{\theta_{N}}(R^{t})))$
(13)

Figure 3 illustrates the abstract view of the adversarial game defined in
(13).

Transformed features obtained from dictionary learning in the source and
target domains participate in an adversarial setup in which they are aligned
via network $N$ to minimize the MMD distance between the domains, while
network $M$ aims to maximize MMD, searching for the kernel with maximal test
power.

###  4.3 Component #3: Shared Classifier for Source and Target

With the aligned features and distributions, a shared neural network $h_{C}$
can be applied to output the class probability of each sample in the source
and target, respectively. Given the suitability of hinge loss [51] in multi-
class problems, the source and target classification losses are defined as
$\mathcal{L}_{s}=L(h_{C}(\phi_{\theta_{N}}(R^{s})),Y^{s})$ and
$\mathcal{L}_{t}=L(h_{C}(\phi_{\theta_{N}}(R^{t})),Y^{t})$, where $L(.)$
denotes the multi-class hinge loss.

We obtain the objective function for the shared classification hypothesis
$h_{C}$ by minimizing a convex combination of $L_{s}$ and $L_{t}$ [40, 11], as
given in (14):

$\displaystyle\underset{\theta_{C}}{\text{min}}\quad\frac{1}{2}(L(h_{C}(\phi_{\theta_{N}}(R^{s})),Y^{s})+L(h_{C}(\phi_{\theta_{N}}(R^{t})),Y^{t}))$
(14)

Finally, the total objective function of HANDA is obtained by aggregating the
three losses in an adversarial manner: shared dictionary loss
$(\mathcal{L}_{SDL})$ obtained from (8), MMD distance loss calculated via
adversarial kernel matching $(\mathcal{L}_{Adv})$ from (13), and combined
classification losses in source and target $(\mathcal{L}_{C})$ from (14).
Thus, the total objective function for our proposed method is given by (15):

$\displaystyle\underset{\theta_{N},\theta_{C},\Theta_{SDL}}{\text{min}}\quad\underset{\theta_{M}}{\text{max}}\quad\beta\mathcal{L}_{SDL}+\gamma\mathcal{L}_{Adv}+\mathcal{L}_{C}$
(15)

where $\Theta_{SDL}=\\{P^{s},P^{t},D,R^{s},R^{t}\\}$ is the set of parameters
for dictionary learning. $\theta_{N}$ and $\theta_{M}$ denote the parameters
of adversarial networks for kernel matching, and $\theta_{C}$ is the
classifier network’s parameters. $\beta$ and $\gamma$ are the trade-off
parameters for the penalty incurred by corresponding losses. In Section 5, we
demonstrate that these trade-off parameters can be empirically tuned via grid
search.

Figure 3: Abstract View of Adversarial Kernel Matching. Network $N$ aligns the
distributions to fool Network $M$ via minimizing MMD between the source and
target representations while network $M$ aims to yield the kernel with maximal
test power between two distributions via maximizing MMD.

###  4.4 Learning Algorithm

Past research has attempted to design DA algorithms that reduce target
generalization error. Li et al. [5] offer a representation learning algorithm
based on objective function optimization with a ‘fixed’ MMD kernel without
kernel learning. Long et al. [11] propose a deep representation learning
algorithm with adversarial kernel learning. However, their algorithm is
designed for homogeneous DA. As shown in model preliminaries, SDL and
adversarial kernel learning can reduce HDA target generalization errors.
Hence, we are motivated to incorporate SDL and nonparametric adversarial
kernel matching in our algorithm to reduce the target error more effectively.
We develop an algorithm to solve the optimization problems for SDL in (8),
nonparametric adversarial kernel matching in (13), and classification in (14)
via a unified architecture. To achieve this, we incorporate SDL into our
model. In the SDL formulation in (8), if $D$ is a low-rank matrix, the
$\ell_{1}$ regularization term can be removed without lack of generalization:

$\displaystyle\underset{P^{s},P^{t},D,R^{s},R^{t}}{\text{min}}\left\|P^{s}X^{s}-DR^{s}\right\|_{F}^{2}+\left\|P^{t}X^{t}-DR^{t}\right\|_{F}^{2}$
(16) $\displaystyle\text{s.t.}\left\|d_{i}\right\|_{2}\leq 1;\quad
P^{s}{P^{s}}^{T}=I;P^{t}{P^{t}}^{T}=I$

where $I$ denotes the identity matrix and the last two constraints ensure
orthogonality. Ideally, the reconstruction errors are reasonably close to 0,
and the source and target representations are expressed as
${\hat{R}}^{s}=D^{-1}P^{s}X^{s}$ and ${\hat{R}}^{t}=D^{-1}P^{t}X^{t}$.
Accordingly, we express $R^{s}$ and $R^{t}$ in the form of products of three
matrices where the first matrix is shared. Specifically, we denote
$R^{s}\approxeq{AB^{s}X^{s}}$ and $R^{t}\approxeq{AB^{t}X^{t}}$, where $B^{s}$
and $B^{t}$ approximate the domain-specific projections and $A$ approximates
the shared projection. To approximate $R^{s}$ and $R^{t}$, we parameterize
$D^{-1}$, $P^{s}$, and $P^{t}$ by fully connected layers $A$, $B^{s}$, and
$B^{t}$, respectively.

Such approximation enables us to integrate shared dictionary learning into our
neural network architecture. As a result, (16) can be written as:

$\displaystyle\underset{P^{s},P^{t},D,A,B^{s},B^{t}}{\text{min}}\left\|P^{s}X^{s}-DAB^{s}X^{s}\right\|_{F}^{2}+$
$\displaystyle\left\|P^{t}X^{t}-DAB^{t}X^{t}\right\|_{F}^{2}$ (17)
$\displaystyle\text{s.t.}\left\|d_{i}\right\|_{2}\leq 1;\quad
P^{s}{P^{s}}^{T}=I;P^{t}{P^{t}}^{T}=I$

To satisfy the orthogonality constraints on $P^{s}$ and $P^{t}$ in (17), we
enforce the weights of $B^{s}$ and $B^{t}$ to be orthogonal after each
gradient update. We also normalize the weights of $D$ and $A$ to the unit
vector. Since $R^{s}$ and $R^{t}$ are restricted to be a function of $X^{s}$
and $X^{t}$, the result of the optimization in (17) is an upper bound for
shared dictionary learning loss:

$\displaystyle\mathcal{L}_{SDL^{up}}=\left\|P^{s}X^{s}-DAB^{s}X^{s}\right\|_{F}^{2}+\left\|P^{t}X^{t}-DAB^{t}X^{t}\right\|_{F}^{2}$
(18)

Given the approximated representations of $R^{s}$ and $R^{t}$, the other loss
functions in objective (15) are re-written as in (19) and (20):

$\displaystyle\mathcal{L}_{Adv}=D_{\theta_{M}}(\phi_{M}(\phi_{N}(AB^{s}X^{s})),\phi_{M}(\phi_{N}(AB^{t}X^{t})))$
(19)

$\displaystyle\mathcal{L}_{C}=\frac{1}{2}(L(h_{C}(\phi_{\theta_{N}}(AB^{s}X^{s})),Y^{s})+$
(20) $\displaystyle L(h_{C}(\phi_{\theta_{N}}(AB^{t}X^{t})),Y^{t}))$

Algorithm 1 HANDA Learning Procedure

1:Input: trade-off parameters $\gamma$ and $\beta$; batch size for source
data, target labeled data, and target unlabeled data: $b_{s}$, $b_{L}$, and
$b_{U}$; # of updates of dictionary learning $n_{d}$; # of updates of
adversarial kernel matching $n_{a}$; # of updates of classification hinge loss
$n_{c}$.

2:Output: Parameters $A$ ,$B^{s}$, $B^{t}$, $D$, $P^{s}$, $P^{t}$,
$\theta_{N}$, $\theta_{M}$, $\theta_{C}$.

3:Initialize parameters $A,B^{s},B^{t},D,P^{s},P^{t},\theta_{N},\theta_{M}$,
$\theta_{C}$.

4:while $\mathcal{L}_{SDL^{up}}$, $\mathcal{L}_{Adv}$, and $\mathcal{L}_{C}$
have not converged do

5: Randomly sample a minibatch of source data
$\\{(x_{i}^{s},y_{i}^{s})\\}^{b_{s}}_{i=1}$.

6: Randomly sample a minibatch of target data
$\\{(x_{i}^{L},y_{i}^{L})\\}^{b_{L}}_{i=1}$ and
$\\{(x_{i}^{U})\\}^{b_{U}}_{i=1}$.

7: Compute $R^{s}=AB^{s}X^{s}$ and $R^{t}=AB^{t}X^{t}$.

8: for $t=1,2,...,n_{d}$ do

9: Compute shared dictionary learning loss $\mathcal{L}_{SDL}$ using (18).

10: Update $A,B^{s},B^{t},D,P^{s},P^{t}$ using stochastic gradient descent to
minimize $\mathcal{L}_{SDL}$.

11: \\\Normalize weights to unit norm

12: $D\leftarrow$clip$(D,1)$, $A\leftarrow$clip$(A,1)$

13: \\\Enforce orthogonality constraint

14: $P^{s},P^{t},B^{s},B^{t}\leftarrow$Orth$(P^{s},P^{t},B^{s},B^{t})$

15: end for

16: for $t=1,2,...,n_{a}$ do

17: Compute adversarial loss for distribution alignment $\mathcal{L}_{Adv}$
using (19).

18: Update parameters $\theta_{M}$ using stochastic gradient descent to
maximize $\mathcal{L}_{Adv}$.

19: Update parameters $\theta_{N},A,B^{s},B^{t}$ via stochastic gradient
descent to minimize $\mathcal{L}_{Adv}$.

20: end for

21: for $t=1,2,...,n_{c}$ do

22: Compute classification loss $\mathcal{L}_{C}$ using (20).

23: Update $\theta_{C},\theta_{N},A,B^{s},B^{t},D,P^{s},P^{t}$ using
stochastic gradient descent to minimize $\mathcal{L}_{C}$.

24: end for

25:end while

26:return $A$ ,$B^{s}$, $B^{t}$, $D$, $P^{s}$, $P^{t}$, $\theta_{N}$,
$\theta_{M}$, $\theta_{C}$.

All three losses can be minimized simultaneously via stochastic gradient
descent [44] in a unified neural network architecture introduced by HANDA.
Algorithm 1 summarizes HANDA’s learning procedure to minimize these losses
simultaneously. Algorithm 1 alternates between minimizing the feature
discrepancy and minimizing the distribution divergence until some convergence
criterion is met or for a number of iterations. Code and datasets are
available at https://github.com/mohammadrezaebrahimi/HANDA. Our algorithm
differs from the heterogeneous method proposed in [5] in two aspects. First,
we incorporate SDL in a unified neural network architecture that allows
utilizing the supervised loss to improve the quality of dictionary learning.
The dictionary learning in [5] is unsupervised and does not account for the
class variable in feature alignment, which could result in lack of
discriminative properties in the projected space. Second, our proposed neural
network architecture offers an effective alternative for the mathematical
optimization based on Lagrange multipliers in [5] via a numerical optimization
(stochastic gradient-based) method that reduces distribution and feature
mismatch simultaneously. Later in the evaluation section we show the
performance benefit gained from this property. Our method also differs from
the homogeneous method offered in [13] in that HANDA does not use GAN. While
GAN implements a minimax setting between a generator and discriminator, the
minimax optimization in our approach is formulated for adversarial kernel
matching between source and target distributions, as given in (19), to achieve
domain invariance.

##  5 Evaluation

For a comprehensive evaluation, we measure both HANDA’s performance and its
practical utility. We construct a large testbed with three e-commerce
datasets. To evaluate the performance, we use two widely used e-commerce
benchmarks for image and multilingual text: Reuters Multilingual Collection
and Office31 – Caltech256. To evaluate the practical utility, we use a real-
world e-commerce dataset from dark web online markets with multilingual
product descriptions. This practical evaluation encompasses a real-world
cybersecurity case study, which is of value for cybersecurity applications.
Reuters Multilingual Collection contains $111,740$ online newswire articles
with commercial themes in five languages: English, French, German, Italian,
and Spanish, across six topics: Economics, Equity Markets, Finance, Industry,
Social, and Performance [52]. Consistent with other studies [8, 23], we used
Spanish as the target language and the other four languages as sources. This
dataset is used for performing multi-class text classification task. Office31
– Caltech256 is an extension of the original dataset created by Gong et al.
[53], and contains two popular heterogeneous image representations: Speeded Up
Robust Features (SURF) with $800$ dimensions [8] and Deep Convolutional
Activation Features (DeCAF) with $4,096$ dimensions [54]. The dataset consists
of $2,533$ online images in 10 categories in four domains: Amazon (A),
downloaded from the Amazon website; Webcam (W), taken by a low-resolution
camera; DSLR (D), taken by a high-resolution DSLR camera; and Caltech(C),
selected from the Caltech-256 dataset. Following other studies [8, 23], three
labeled samples from each category within the source domain were used in
training. This dataset is associated with multi-class product image
recognition task. In addition to widely accepted benchmark e-commerce
datasets, it is useful to evaluate the practical utility of our model in a
real-world setting. To this end, given the recent rise of illegal online
markets on the dark web, we developed crawlers for obtaining data from nine
illegal e-commerce platforms. Our new dark web online markets dataset is an
extension of the dataset proposed in [55], which contains $94,175$ product
descriptions (from seven English markets), $4,600$ Russian, and $1,512$ French
product descriptions (Table III). The dataset has been labeled by three native
speakers and two cybersecurity experts and is publicly available from our
GitHub repository. To construct the training set, we randomly sampled product
descriptions in each language (2,584 products; 706 cyber threats, 1,878 benign
products). Since more English labeled data is available, English markets are
used as the source, and Russian and French markets are used as the targets.
Each language was manually labeled by a cybersecurity expert and a native
speaker. This dataset is used for cyber threat detection, which is viewed as a
binary classification task.

Table III: Testbed for Cybersecurity Case Study

Online Market | # of listings | Language | # of labeled products
---|---|---|---
Dream Market |  39,473 |  English |  1,821
AlphaBay |  25,118
Hansa |  14,149
Silk Road 3 |  1,683
Minerva |  683
Apple Market |  877
Valhalla |  12,192
Russian Silk Road |  4,600 |  Russian |  552
French Deep Web |  1,512 |  French |  211
Total: |  100,287 |  - |  2,584

00footnotetext: SMS: Support and Model Shift, JDA: Joint Distribution
Adaptation, TCA: Transfer Component Analysis; SymNets: Symmetric Networks;
SBADA-GAN: Symmetric Bi-directional ADAptive GAN; AC-GAN: Auxiliary Classifier
GAN; DAN: Domain Adaptation Networks; CyCADA: Cycle Consistent Adversarial
Domain Adaptation.

The current body of HDA research widely uses average accuracy and standard
deviation for performance evaluation [5, 29, 9]. The average accuracy
$Acc_{avg}$ is defined as follows:

$\displaystyle Acc_{avg}=\frac{1}{n}\sum_{i=1}^{n}\frac{|x^{t}:x^{t}\in
X^{t},{\hat{y}}^{t}=y^{t}|}{|x^{t}:x^{t}\in X^{t}|}$ (21)

where $x$ is a target instance, ${\hat{y}}^{t}$ is the predicted class,
$y^{t}$ is the true class label, $|.|$ denotes the cardinality of the
corresponding set, and $n$ is the number of runs. Standard deviation is also
averaged over multiple runs of each model (often 10 times). Consistent with
past HDA research, we use average accuracy and average standard deviation as
evaluation metrics for comparing HANDA with the benchmark methods. Higher
average accuracy and lower standard deviation suggest higher predictive
performance. Note that since both benchmark datasets are not class imbalanced,
accuracy is a sufficient measure for benchmark evaluations. However, for class
imbalanced cybersecurity datasets, the Area Under receiver operating
characteristic Curve (AUC) is the recommended performance measure since it
emphasizes both threat and non-threat classes [56] by establishing a trade-off
between Type I and Type II errors [57]. Given the class imbalance in our case
study, we use AUC as the performance metric. Higher AUC suggests higher
predictive performance.
We evaluate HANDA through three sets of experiments and one case study.
Experiment #1 is aimed at evaluating HANDA against alternative state-of-the-
art HDA methods (the top right and bottom right quadrants, shown in Table II).
This experiment compares HANDA’s performance to seven HDA methods, including
HDA Network based on Autoencoder (HDANA) [29], Cross-Domain Mapping (CDM) [8],
Generalized Joint Distribution Adaptation (G-JDA) [21], Transfer Neural Trees
(TNT) [28], Cross-Domain Landmark Selection (CDLS) [23], Semi-supervised
Heterogeneous Feature Augmentation (SHFA) [26], and Max-Margin Domain
Transforms (MMDT) [27]. This experiment involves two reputable e-commerce
datasets: Office31 – Caltech256 and Reuters Multilingual Collection.
Experiment #2 focuses on the qualitative evaluation of DA [28] to verify its
effectiveness by comparing the linear separability of target samples before
and after DA through visualizing the intermediate representations on both
Office31 – Caltech256 and Reuters Multilingual Collection. Experiment #3
targets convergence analysis [58] to investigate the convergence property of
the objective functions corresponding to each HANDA component by assessing the
stabilization of loss values during model training on the Office31 –
Caltech256 benchmark dataset. Finally, a case study is conducted to verify
practical utility on real-world products advertised in dark web online markets
as an emerging cybersecurity application.

Table IV: Comparison of State-of-the-Art HDA Methods with HANDA on
Multilingual Text Classification (Accuracy and Standard Deviation); P-values
significant at 0.05:*

HDA Method | 10 Labeled Samples per Target Class | 20 Labeled Samples per Target Class
---|---|---
|  $EN\rightarrow SP$ |  $FR\rightarrow SP$ |  $GR\rightarrow SP$ |  $IT\rightarrow SP$ |  $EN\rightarrow SP$ |  $FR\rightarrow SP$ |  $GR\rightarrow SP$ |  $IT\rightarrow SP$
MMDT |  $68.9\pm 0.6$ |  $69.1\pm 0.7$ |  $68.3\pm 0.6$ |  $67.5\pm 0.5$ |  $74.5\pm 0.7$ |  $74.9\pm 0.7$ |  $75.1\pm 0.8$ |  $74.9\pm 0.8$
CDM |  - |  - |  - |  - |  $75.1\pm 2.8$ |  $75.2\pm 2.8$ |  $75.3\pm 2.7$ |  $75.2\pm 2.7$
SHFA |  $67.8\pm 0.7$ |  $68.1\pm 0.6$ |  $68.4\pm 0.7$ |  $68.0\pm 0.7$ |  $74.1\pm 0.4$ |  $74.5\pm 0.6$ |  $74.7\pm 0.5$ |  $74.5\pm 0.5$
G-JDA |  $69.4\pm 0.8$ |  $70.5\pm 0.7$ |  $69.6\pm 1.0$ |  $70.1\pm 1.0$ |  $76.0\pm 0.7$ |  $76.8\pm 0.8$ |  $76.8\pm 0.7$ |  $76.6\pm 0.7$
TNT |  $70.0\pm 1.0$ |  $70.9\pm 0.8$ |  $69.9\pm 0.9$ |  $71.0\pm 0.9$ |  $76.1\pm 0.7$ |  $77.5\pm 0.8$ |  $77.1\pm 1.1$ |  $76.8\pm 0.9$
CDLS |  $70.8\pm 0.7$ |  $71.2\pm 0.8$ |  $71.0\pm 0.8$ |  $71.7\pm 0.8$ |  $77.4\pm 0.7$ |  $77.6\pm 0.7$ |  $78\pm 0.6$ |  $77.5\pm 0.7$
HDANA |  $72.1\pm 0.3$ |  $72.7\pm 0.4$ |  $71.8\pm 0.4$ |  $72.3\pm 0.3$ |  $78.3\pm 0.5$ |  $79.2\pm 0.5$ |  $80.1\pm 0.6$ |  $78.5\pm 0.3$
HANDA (No SDL) |  $23.4\pm 8.2$ |  $16.8\pm 9.0$ |  $21.3\pm 9.8$ |  $18.0\pm 6.7$ |  $29.1\pm 12.4$ |  $34.0\pm 8.9$ |  $39.5\pm 8.8$ |  $32.0\pm 10.9$
HANDA (No Adv) |  $68.0\pm 0.6$ |  $69.1\pm 0.6$ |  $67.9\pm 0.8$ |  $69.8\pm 0.7$ |  $75.7\pm 0.5$ |  $75.4\pm 0.5$ |  $75.0\pm 0.6$ |  $76.7\pm 0.6$
HANDA (Entropy) |  $73.7\pm 0.3$ |  $72.6\pm 0.5$ |  $73.4\pm 0.2$ |  $72.4\pm 0.5$ |  $79.0\pm 0.4$ |  $79.1\pm 0.3$ |  $79.5\pm 0.4$ |  $78.1\pm 0.2$
HANDA (ours) |  $74.5$±0.4^∗ |  $74.2$±0.4^∗ |  $73.8$±0.5^∗ |  $74.0$±0.6^∗ |  $79.8$±0.3^∗ |  $80.0$±0.4^∗ |  $80.5$±0.2^∗ |  $79.2$±0.5^∗

###  5.1 Experiment #1: Performance Evaluation

Experiment #1 aims to evaluate HANDA’s performance against the state-of-the-
art HDA methods in two relevant applications in international e-commerce
platforms: multilingual text classification and cross-domain product image
recognition. For multilingual text classification, following the settings in
[29], we summarize the results of domain adaptation when Spanish is the target
and English, French, German, and Italian are the source languages, with 10 and
20 labeled target samples per class (Table 5). The average accuracy is
obtained by running each experiment 10 times and precedes the average standard
deviation in Table 5 (separated by $\pm$). To see the effect of shared
dictionary learning and adversarial kernel matching in isolation, we also
conducted two baseline experiments with eliminating the shared dictionary
learning component (No SDL) and eliminating the adversarial kernel matching
component (No Adv). We further compared the performance of the proposed
adversarial kernel matching alignment loss in HANDA with the entropy-based
alignment loss proposed in [59], denoted by HANDA (Entropy) in Table 5.
$\beta$ and $\gamma$ were obtained via a small gird search as described in
Experiment #1.1. The higher performance of the proposed method is
statistically significant when compared to the second-best method, as
suggested by the paired $t$-test [60]. HANDA improves the classification
performance by approximately 2% across different source-target language pairs
with statistically significant margins. Additionally, the baseline experiments
show that both shared dictionary learning and adversarial kernel matching
contribute to achieving the state-of-the-art performance. For cross-domain
product image recognition, consistent with [29], due to the lack of labeled
data in the DSLR domain, we choose the Amazon (A), Webcam(W), and Caltech(C)
domains as the source, and DSLR (D) as the target domain. HANDA improves the
average accuracy in all domains by 1.1% on average (Table 5.1).

Table V: Cross-Features and Cross-Domain Comparison of State-of-the-Art HDA
Methods with HANDA on Product Image Recognition; P-values significant at
0.05:*

HDA | SURF to DeCAF
---|---
Method |  $A\rightarrow D$ |  $C\rightarrow D$ |  $W\rightarrow D$ |  $Average$
MMDT |  $90.5\pm 0.6$ |  $91.2\pm 0.6$ |  $90.8\pm 0.6$ |  $90.8\pm 0.6$
TNT |  $90.6\pm 0.9$ |  $92.7\pm 1.1$ |  $95.5\pm 1.0$ |  $92.9\pm 1.0$
SHFA |  $93.4\pm 1.1$ |  $93.8\pm 1.0$ |  $92.4\pm 0.9$ |  $93.2\pm 1.0$
G-JDA |  $94.3\pm 0.7$ |  $92.8\pm 0.8$ |  $95.0\pm 0.4$ |  $94.0\pm 0.6$
CDLS |  $96.1\pm 0.7$ |  $94.9\pm 1.5$ |  $95.1\pm 0.8$ |  $95.4\pm 1.5$
HDANA |  $96.1\pm 0.5$ |  $95.3\pm 0.6$ |  $96.9\pm 0.3$ |  $96.1\pm 0.5$
HANDA (No SDL) |  $20.6\pm 4.5$ |  $24.2\pm 3.8$ |  $26.1\pm 5.1$ |  $23.6\pm 4.5$
HANDA (No Adv) |  $92.8\pm 0.5$ |  $93.2\pm 0.6$ |  $93.3\pm 0.5$ |  $93.1\pm 0.5$
HANDA (Entropy) |  $96.5\pm 0.6$ |  $95.8\pm 0.4$ |  $96.6\pm 0.5$ |  $96.3\pm 0.5$
HANDA (ours) |  $97.1$±0.4^∗ |  $96.9$±0.5 ^∗ |  $97.6$±0.5^∗ |  97.2$\pm$0.4∗

Overall, HANDA outperforms mathematical optimization-based HDA methods in text
classification and product image recognition (the top right quadrant in Table
II). Moreover, HANDA outperforms the neural representation-based HDA
alternatives (the bottom right quadrant in II) in both text classification and
product image recognition tasks. Outperforming HDANA suggests that domain
invariance through adversarial learning can lead to better HDA. Outperforming
TNT, in the image classification task by a significant margin suggests that
simultaneous distribution and feature alignment are necessary for successful
HDA.

####  5.1.1 Experiment #1.1: Sensitivity to Parameters $\beta$ and $\gamma$

As noted in Section 4, to empirically search the parameter space induced by
$\beta$ and $\gamma$ in (15), we conducted a grid search with four $\beta$
values selected from {$1e-2,1e-3,1e-4,1e-5$} and four $\gamma$ values selected
from {$1e-2,1e-1,1,10$}. Following [12], reverse cross-validation [61] is
adopted for hyperparameter tuning to ensure that validation is not conducted
on labeled target data. Table VI shows the parameter values associated with
the best performance during the empirical parameter tuning for $\beta$ and
$\gamma$ in (15) on multilingual text dataset (with 10 and 20 labeled data in
the source domain) and product image dataset (with three labeled data in the
source domain).

Table VI: Results of Empirical Parameter Tuning for $\beta$ and $\gamma$ in (15) on Multilingual Text Dataset and Image Product Recognition Dataset HDA Task | 10 Labels / 3 Labels | 20 Labels
---|---|---
|  $\beta(SDL)$ |  $\gamma(Adv)$ |  $\beta(SDL)$ |  $\gamma(Adv)$
$EN\rightarrow SP$ |  $1e-5$ |  $1$ |  $1e-2$ |  $1e-4$
$FR\rightarrow SP$ |  $1e-4$ |  $1$ |  $1e-5$ |  $1$
$GR\rightarrow SP$ |  $1e-4$ |  $1$ |  $1e-1$ |  $1e-4$
$IT\rightarrow SP$ |  $1e-4$ |  $1$ |  $1e-4$ |  $1$
$A\rightarrow D$ |  $1e-1$ |  $1e-4$ |  $-$ |  $-$
$C\rightarrow D$ |  $1e-4$ |  $1$ |  $-$ |  $-$
$W\rightarrow D$ |  $1e-4$ |  $1$ |  $-$ |  $-$

As seen, a sparse search in the parameter space induced by $\beta$ and
$\gamma$ yields the state-of-the-art performance reported in Table 5.
Additionally, the fact that $\beta=1e-4$ and $\gamma=1$ yields the best
performance in the majority of domain adaptation experiments for both
benchmark datasets signifies that (15) is not unreasonably sensitive to
parameter setting.

####  5.1.2 Experiment #1.2: Ablation analysis

To further analyze the effect of the internal components of HANDA
architecture, we conducted two sets of ablation experiments. The first set
examines the effect of the depth of the feature extractor. Best performances
are shown in bold face. As seen in Table VII, the results show performance
improvement with multiple hidden layers for both datasets.

Table VII: Ablation Analysis of the Depth of Feature Extractor in Multilingual Text Classification Dataset and Product Image Recognition Dataset Model | 10 Labeled Samples per Target Class | 20 Labeled Samples per Target Class
---|---|---
|  $EN\rightarrow SP$ |  $FR\rightarrow SP$ |  $GR\rightarrow SP$ |  $IT\rightarrow SP$ |  $EN\rightarrow SP$ |  $FR\rightarrow SP$ |  $GR\rightarrow SP$ |  $IT\rightarrow SP$
1-layer |  $73.0\pm 0.4$ |  $72.7\pm 0.5$ |  $71.6\pm 0.6$ |  $72.2\pm 0.5$ |  $77.5\pm 0.2$ |  $77.9\pm 0.5$ |  $79.6\pm 0.3$ |  $78.4\pm 0.4$
2-layer |  $\bm{74.5}\pm\bm{0.4}$ |  $74.2\pm 0.4$ |  $\bm{73.8}\pm\bm{0.5}$ |  $74.0\pm 0.6$ |  $79.8\pm 0.3$ |  $\bm{80.0}\pm\bm{0.4}$ |  $\bm{80.5}\pm\bm{0.2}$ |  $\bm{79.2}\pm\bm{0.5}$
3-layer |  $74.4\pm 0.3$ |  $\bm{74.7}\pm\bm{0.6}$ |  $72.2\pm 0.7$ |  $\bm{74.3}\pm\bm{0.7}$ |  $80.0\pm 0.4$ |  $79.3\pm 0.3$ |  $80.1\pm 0.4$ |  $79.1\pm 0.5$
4-layer |  $74.2\pm 0.5$ |  $74.0\pm 0.5$ |  $72.5\pm 0.5$ |  $73.5\pm 0.6$ |  $\bm{80.2}\pm\bm{0.4}$ |  $79.3\pm 0.4$ |  $79.5\pm 0.3$ |  $78.3\pm 0.6$
5-layer |  $72.3\pm 0.7$ |  $72.5\pm 0.7$ |  $72.0\pm 0.8$ |  $72.1\pm 0.9$ |  $79.5\pm 0.5$ |  $78.6\pm 0.5$ |  $78.2\pm 0.5$ |  $77.9\pm 0.6$
SDL+Adv (Sequential) |  $71.1\pm 0.4$ |  $71.2\pm 0.5$ |  $70.4\pm 0.5$ |  $69.9\pm 0.6$ |  $76.6\pm 0.4$ |  $76.2\pm 0.5$ |  $75.8\pm 0.5$ |  $75.2\pm 0.5$

It is observed that having three (and rarely four) hidden layers adds marginal
improvements compared to two hidden layers. That is, the majority of best
performances are attained with two hidden layers. As such, to promote a
parsimonious architecture that yields the best performance in most
heterogeneous domain adaptation tasks, we used a neural net with two hidden
layers as the feature extractor of HANDA. The second set of experiments
examines the contribution of simultaneous learning of the shared dictionary
and adversarial kernel matching in the HANDA’s unified framework versus the
sequential learning of these two components. In the sequential case, denoted
by (SDL+Adv) in Table VII, we conducted a two-step learning process, in which
we first optimized HANDA’s shared dictionary learning loss (without involving
adversarial kernel matching loss). Subsequently, we applied the adversarial
kernel learning on the projected space obtained from the shared dictionary
learning. The results suggest that simultaneous learning of the shared
dictionary and adversarial kernel matching in HANDA’s unified architecture
outperforms sequential learning on multilingual text classification dataset.

###  5.2 Experiment #2: Qualitative Analysis

In domain adaptation research, the quality of generated representations can be
assessed via visualizing the obtained representations before and after DA
[28]. The target representation from HANDA is visualized in 2-D space by
$t$-distributed Stochastic Neighbor Embedding ($t$-SNE) [62] (Figure 4). The
decision boundaries are obtained by linear SVM.

(a)

(b)

(c)

(d)

Figure 4: Qualitative Comparison of HANDA Before and After Domain Adaptationin
in Multilingual Text Classification. Target samples have been visualized in
2-D before and after domain adaptation from Italian (b), French (c), and
English (d) to Spanish.

As seen in Figure 3a, target documents are not linearly separable before DA.
The new representations obtained from HANDA lead to more linearly separable
samples after domain adaptation from Italian (Figure 3b), French (Figure 3b),
and English (Figure 3d). The majority of documents in the ‘Economics,’
‘Social,’ and ‘Performance’ classes are distinguished via light blue, light
green, and dark red hyperplanes, respectively. The same effect is observed in
the cross-domain product image recognition task as a result of DA (Figure 5).

(a)

(b)

(c)

Figure 5: Qualitative Comparison of HANDA Before and After Domain Adaptation
in Cross-Domain Product Image Recognition. Target samples are visualized in
2-D before (a) and after (b) domain adaptationfrom Caltech to DSLR domain.

Similarly, target images are not linearly separable before DA (Figure 4a). A
considerable number of product images in ‘mouse’ (light red), ‘headphone’
(orange), ‘backpack’ (dark purple), ‘mug’ (light purple), and ‘keyboard’
(light green) cannot be distinguished (shown with a red circle). HANDA
representations lead to more linearly separable samples after adaptation from
Caltech to DSLR (Figure 4b) compared to before adaptation (Figure 4a). Almost
all product images are classified correctly except the ‘laptop’ (light blue)
and ‘calculator’ (dark green) that have excessive visual similarity (both have
a display and keypad).

###  5.3 Experiment #3: Convergence Analysis

The quality of adversarial training is often empirically verified by
investigating the convergence property of the losses [58]. We monitor
adversarial kernel learning, shared dictionary learning, and classification
loss on Office31 – Caltech256. All three losses stabilize after 1,000 training
batches (red markers in Figure 6). Although both dictionary learning and
adversarial kernel learning have non-convex objective functions, they both
converge in all three domains (Amazon (Figure 5a), Caltech (Figure 5b), and
Webcam (Figure 5c)).

(a)

(b)

(c)

Figure 6: Convergence Analysis of HANDA on Amazon (a), Caltech (b), and Webcam
(c) Domains for Image Recognition Task on Office31-Caltech256 Dataset. Loss
variations stabilize after a certain number of iterations in all domains.

In sum, with our feature and distribution alignment approaches, HANDA is able
to outperform extant HDA methods in image recognition and text classification
tasks. Specifically, outperforming HANDA alternatives, HDANA and TNT, shows
that simultaneous feature and distribution alignment with a focus on domain
invariance can lead to better HDA. HANDA can alleviate the lack of training
data in e-commerce applications and improve product search and indexing in
online markets. Furthermore, HANDA shows loss convergence property during the
adversarial training process. This suggests that HANDA can be robust and
generalizable to unknown domains. Finally, the domain-invariant
representations obtained from HANDA are of high quality and can increase the
performance of downstream text and image classification tasks.

###  5.4 Cybersecurity Case Study

It is useful to assess the utility of HDA models in real-world applications,
in addition to common benchmark evaluations. Monitoring products sold on dark
web markets is an emerging area in cybersecurity that can highly benefit from
HDA in providing actionable cyber threat intelligence. We demonstrate the
practical utility of the HANDA framework on a real-world cybersecurity dataset
obtained from English, Russian, and French dark web markets. This case study
has two main purposes. First, it aims to assess if a model that is trained by
Algorithm 1 on English markets can aid the detection of cyber threats in
Russian and French markets in practice. Second, it is meant to show examples
of cyber threats that are recognized by HANDA but would be missed in the
absence of DA. To gauge the performance improvement offered by HANDA, we
compare the AUC to a neural network without DA (Figure 7).

Figure 7: HANDA’s AUC on Russian and French Dark Web Online Markets. Note:
Softmax function was applied to all network outputs to obtain the
probabilities for AUC calculation.

To this end, a feedforward neural network (NN) trained on Russian and French
markets serves as a baseline. HANDA was trained on English markets as the
source, while Russian and French were the targets. HANDA increases the AUC in
Russian markets by 3% (from 0.96 to 0.98). Similarly, HANDA results in a 4%
AUC increase in French markets (from 0.85 to 0.89). Table VIII shows the
examples of products that HANDA identifies in Russian and French as cyber
threats, but are missed by the baseline NN without DA. By juxtaposing the
training samples, testing samples, and model’s output, we discovered that
there were no instances of “Trojan” in the French training set. Nevertheless,
HANDA was able to identify the Trojan as a cyber threat in the French testing
set, showing that our model is able to learn from Trojan instances in the
source (English) dataset. This implies that the domain adaptation from English
to French allows HANDA to distinguish the ‘unseen’ examples in the target
language that are not present in the training set. As a result, HANDA can
significantly increase the cyber threat intelligence performance in dark web
markets with limited training data.

Table VIII: Russian and French Product Descriptions Correctly Identified as Cyber Threats by HANDA while Missed by the Baseline Method. |  Language |  Product Description Excerpt |  Translation by Native Speaker |  Cyber Threat Category |  HANDA Confidence Score
---|---|---|---|---|---
|  Russian |  “ банковской карты без физического носителя.После покупки вы получите данные в следующем формате:[…]. ” |  Bank card data without physical media. After the purchase, you will receive data in the following format: […]. |  Stolen financial credentials |  0.9
|  Russian |  “Взлом GMAIL.COM-Клиент сообщает предмет взлома—ID жертвы и.т.п[…] После взлома, клиент получает доказательства проделанной работы.-Оплата заказа […].” |  Hacking GMAIL.COM-The client reports the subject of hacking — victim ID, etc.[…]-After hacking, the client receives evidence of the work done […]. |  E-mail hacking service |  0.9
|  French |  “ Ce logiciel vous permet de checker vos logs pour trouver ceux qui ont un accés à la boite email. Une fois un email:pass valide trouver une option vous permet de télécharger tous les documents de cette boite email […].” |  This software allows you to check your logs to find those who have access to the mailbox. Once you have found a valid email: pass, there will be an option that will let you download all the documents from that mailbox […]. |  E-mail hacking tool |  0.7
|  French |  “Un pack de 3 différents botnet rare avec 5 RAT et trojan, pour vos intrusions les plus importantes. Des centaines de pc victimes obéïssant à tous vos ordres […] .” |  A pack of 3 different rare botnets with 5 RAT and Trojan, for your most important intrusions. Hundreds of pc victims obeying all your orders […]. |  Trojan |  0.6

##  6 Conclusion and Future Directions

Given the growing adoption of machine learning models to analyze novel online
markets, adapting previously learned models to unseen domains is a promising
strategy. The adaptation process is challenging when dealing with
heterogeneous domains where the source and target domains differ in both
feature space and data distribution. This poses a significant problem in
e-commerce and emerging fields such as cybersecurity. HDA is a crucial
approach to address this emerging challenge. However, most extant HDA methods
focus on minimizing the distance via non-neural representations, which may
suffer from a lack of transferability. Adversarially learned representations
have been shown to yield more transferrable representations. Nonetheless, they
are not designed for HDA problems. To address this gap, we developed a novel
framework for Heterogeneous Adversarial Neural Domain Adaptation (HANDA), a
neural network architecture that employs dictionary learning and nonparametric
adversarial kernel matching to jointly minimize the feature space discrepancy
and distribution divergence in a unified architecture. HANDA extends
adversarial domain adaptation for heterogeneous domains and incorporates
shared dictionary learning in a neural network architecture to benefit from
labeled data. We conducted in-depth evaluations to evaluate HANDA’s
performance against state-of-the-art HDA methods in two benchmark learning
tasks in common e-commerce applications (i.e., product image recognition and
multilingual text classification). HANDA improves the classification
performance on the benchmark datasets with statistically significant results.
HANDA can be employed to improve product search and indexing in online
markets. We also showed the advantage of utilizing HANDA in emerging dark web
online markets. HANDA is able to better identify cyber threats among the
products sold on dark web online markets. Two promising future directions are
envisioned. First, improving the interpretability of the model by
incorporating components such as attention mechanism can shed light on the DA
process in HANDA. Second, given the prevalence of sequence data in e-commerce
applications, extending HANDA to account for the temporal factor in sequential
inputs is another promising area in HDA research.

## Acknowledgments

This material is based upon work supported by the National Science Foundation
(NSF) under grants CNS-1936370 (SaTC CORE) and OAC-1917117 (CICI). Yidong Chai
was supported in part by the NSFC (91846201, 72101079), Shanghai Data Exchange
Cooperative Program (W2021JSZX0052), and is the corresponding author.

## References

  * [1] Z. Cao, L. Ma, M. Long, and J. Wang, “Partial adversarial domain adaptation,” in _European Conference on Computer Vision (ECCV)_ , 2018, pp. 135–150.
  * [2] M. Ghifary, D. Balduzzi, W. B. Kleijn, and M. Zhang, “Scatter component analysis: A unified framework for domain adaptation and domain generalization,” _IEEE Transactions on Pattern Analysis and Machine Intelligence_ , vol. 39, no. 7, pp. 1414–1430, 2017.
  * [3] Z. Zhong, L. Zheng, Z. Luo, S. Li, and Y. Yang, “Learning to adapt invariance in memory for person re-identification,” _IEEE Transactions on Pattern Analysis and Machine Intelligence_ , pp. 1–1, 2020.
  * [4] W. Li, J. Yin, and H. Chen, “Supervised topic modeling using hierarchical dirichlet process-based inverse regression: experiments on e-commerce applications,” _IEEE Transactions on Knowledge and Data Engineering_ , vol. 30, no. 6, pp. 1192–1205, Jun. 2018.
  * [5] J. Li, K. Lu, Z. Huang, L. Zhu, and H. T. Shen, “Heterogeneous domain adaptation through progressive alignment,” _IEEE Transactions on Neural Networks and Learning Systems_ , vol. 30, no. 5, pp. 1381–1391, 2018.
  * [6] J. Hoffman, E. Tzeng, T. Park, J.-Y. Zhu, P. Isola, K. Saenko, A. Efros, and T. Darrell, “CyCADA: Cycle-consistent adversarial domain adaptation,” in _International Conference on Machine Learning (ICML)_ , J. Dy and A. Krause, Eds., vol. 80. Stockholm, Sweden: PMLR, Jul. 2018, pp. 1989–1998.
  * [7] Y. Li, X. Tian, M. Gong, Y. Liu, T. Liu, K. Zhang, and D. Tao, “Deep domain generalization via conditional invariant adversarial networks,” in _European Conference on Computer Vision (ECCV)_ , 2018, pp. 624–639.
  * [8] W.-C. Fang and Y.-T. Chiang, “A discriminative feature mapping approach to heterogeneous domain adaptation,” _Pattern Recognition Letters_ , vol. 106, pp. 13–19, 2018.
  * [9] Y. Yao, X. Li, Y. Ye, F. Liu, M. K. Ng, Z. Huang, and Y. Zhang, “Low-resolution image categorization via heterogeneous domain adaptation,” _Knowledge-Based Systems_ , vol. 163, pp. 656–665, 2019.
  * [10] J. Ren, J. Yang, N. Xu, and D. J. Foran, “Factorized adversarial networks for unsupervised domain adaptation,” _arXiv preprint arXiv:1806.01376_ , 2018\.
  * [11] M. Long, Y. Cao, Z. Cao, J. Wang, and M. I. Jordan, “Transferable representation learning with deep adaptation networks,” _IEEE Transactions on Pattern Analysis and Machine Intelligence_ , 2018.
  * [12] Y. Ganin, E. Ustinova, H. Ajakan, P. Germain, H. Larochelle, F. Laviolette, M. Marchand, and V. Lempitsky, “Domain-adversarial training of neural networks,” _The Journal of Machine Learning Research_ , vol. 17, no. 1, pp. 2096–2030, 2016.
  * [13] E. Tzeng, J. Hoffman, K. Saenko, and T. Darrell, “Adversarial discriminative domain adaptation,” in _IEEE Conference on Computer Vision and Pattern Recognition (CVPR)_ , 2017, pp. 7167–7176.
  * [14] I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, “Generative Adversarial Nets,” in _Advances in Neural Information Processing Systems (NeurIPS)_ , Z. Ghahramani, M. Welling, C. Cortes, N. D. Lawrence, and K. Q. Weinberger, Eds. Curran Associates, Inc., 2014, pp. 2672–2680. [Online]. Available: http://papers.nips.cc/paper/5423-generative-adversarial-nets.pdf
  * [15] K. Weiss, T. M. Khoshgoftaar, and D. Wang, “A survey of transfer learning,” _Journal of Big Data_ , vol. 3, no. 1, p. 9, 2016.
  * [16] S. J. Pan and Q. Yang, “A Survey on Transfer Learning,” _IEEE Transactions on Knowledge and Data Engineering_ , vol. 22, no. 10, pp. 1345–1359, Oct. 2010.
  * [17] Y. Bengio, A. Courville, and P. Vincent, “Representation learning: A review and new perspectives,” _IEEE Transactions on Pattern Analysis and Machine Intelligence_ , vol. 35, no. 8, pp. 1798–1828, 2013.
  * [18] M. Long, J. Wang, G. Ding, J. Sun, and P. S. Yu, “Transfer feature learning with joint distribution adaptation,” in _IEEE international conference on computer vision_ , 2013, pp. 2200–2207.
  * [19] S. J. Pan, I. W. Tsang, J. T. Kwok, and Q. Yang, “Domain adaptation via transfer component analysis,” _IEEE Transactions on Neural Networks_ , vol. 22, no. 2, pp. 199–210, 2011.
  * [20] X. Wang and J. Schneider, “Flexible transfer learning under support and model shift,” in _Advances in Neural Information Processing Systems (NeurIPS)_ , 2014, pp. 1898–1906.
  * [21] Y.-T. Hsieh, S.-Y. Tao, Y.-H. H. Tsai, Y.-R. Yeh, and Y.-C. F. Wang, “Recognizing heterogeneous cross-domain data via generalized joint distribution adaptation,” in _International Conference on Multimedia and Expo (ICME)_. IEEE, 2016, pp. 1–6.
  * [22] S. Herath, M. Harandi, and F. Porikli, “Learning an invariant hilbert space for domain adaptation,” in _IEEE Conference on Computer Vision and Pattern Recognition (CVPR)_ , 2017, pp. 3845–3854.
  * [23] Y. H. H. Tsai, Y. R. Yeh, and Y. C. Frank Wang, “Learning cross-domain landmarks for heterogeneous domain adaptation,” in _IEEE Conference on Computer Vision and Pattern Recognition (CVPR)_ , 2016, pp. 5081–5090.
  * [24] M. Xiao and Y. Guo, “Feature space independent semi-supervised domain adaptation via kernel matching,” _IEEE Transactions on Pattern Analysis and Machine Intelligence_ , vol. 37, no. 1, pp. 54–66, 2015.
  * [25] J. T. Zhou, I. W. Tsang, S. J. Pan, and M. Tan, “Heterogeneous domain adaptation for multiple classes,” in _Artificial Intelligence and Statistics_ , 2014, pp. 1095–1103.
  * [26] W. Li, L. Duan, D. Xu, and I. W. Tsang, “Learning with augmented features for supervised and semi-supervised heterogeneous domain adaptation,” _IEEE Transactions on Pattern Analysis and Machine Intelligence_ , vol. 36, no. 6, pp. 1134–1148, 2014.
  * [27] J. Hoffman, E. Rodner, J. Donahue, T. Darrell, and K. Saenko, “Efficient learning of domain-invariant image representations,” in _International Conference on Learning Representations (ICLR)_ , Scottsdale, AZ, 2013.
  * [28] W. Y. Chen, T. M. H. Hsu, Y. H. H. Tsai, Y. C. F. Wang, and M. S. Chen, “Transfer neural trees for heterogeneous domain adaptation,” in _European Conference on Computer Vision (ECCV)_. Springer, 2016, pp. 399–414.
  * [29] X. Wang, Y. Ma, Y. Cheng, L. Zou, and J. J. Rodrigues, “Heterogeneous domain adaptation network based on autoencoder,” _Journal of Parallel and Distributed Computing_ , vol. 117, pp. 281–291, 2018.
  * [30] M. Chen, Z. Xu, K. Q. Weinberger, and F. Sha, “Marginalized denoising autoencoders for domain adaptation,” in _International Conference on Machine Learning (ICML)_ , USA, 2012, pp. 1627–1634, event-place: Edinburgh, Scotland.
  * [31] M. Long, J. Wang, Y. Cao, J. Sun, and S. Y. Philip, “Deep learning of transferable representation for scalable domain adaptation,” _IEEE Transactions on Knowledge and Data Engineering_ , vol. 28, no. 8, pp. 2027–2040, 2016.
  * [32] I. Goodfellow, Y. Bengio, A. Courville, and Y. Bengio, _Deep learning_. MIT Press Cambridge, 2016, vol. 1.
  * [33] P. Liu, X. Qiu, and X. Huang, “Adversarial multi-task learning for text classification,” vol. 1, 2017, pp. 1–10.
  * [34] H. Zhao, S. Zhang, G. Wu, J. M. F. Moura, J. P. Costeira, and G. J. Gordon, “Adversarial multiple source domain adaptation,” in _Advances in Neural Information Processing Systems (NeurIPS)_ , S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, Eds. Curran Associates, Inc., 2018, pp. 8559–8570.
  * [35] Z. Luo, Y. Zou, J. Hoffman, and L. F. Fei-Fei, “Label efficient learning of transferable representations acrosss domains and tasks,” in _Advances in Neural Information Processing Systems (NeurIPS)_ , 2017, pp. 165–177.
  * [36] P. Russo, F. M. Carlucci, T. Tommasi, and B. Caputo, “From source to target and back: symmetric bi-directional adaptive gan,” in _IEEE Conference on Computer Vision and Pattern Recognition (CVPR)_ , 2018, pp. 8099–8108.
  * [37] M.-Y. Liu and O. Tuzel, “Coupled generative adversarial networks,” in _Advances in neural information processing systems (NeurIPS)_ , 2016, pp. 469–477.
  * [38] S. Sankaranarayanan, Y. Balaji, C. D. Castillo, and R. Chellappa, “Generate to adapt: Aligning domains using generative adversarial networks,” in _IEEE Conference on Computer Vision and Pattern Recognition (CVPR)_ , 2018, pp. 8503–8512.
  * [39] Y. Zhang, H. Tang, K. Jia, and M. Tan, “Domain-symmetric networks for adversarial domain adaptation,” in _IEEE Conference on Computer Vision and Pattern Recognition (CVPR)_ , 2019, pp. 5031–5040.
  * [40] S. Ben-David, J. Blitzer, K. Crammer, A. Kulesza, F. Pereira, and J. W. Vaughan, “A theory of learning from different domains,” _Machine learning_ , vol. 79, no. 1-2, pp. 151–175, 2010.
  * [41] S. Ben-David, J. Blitzer, K. Crammer, and F. Pereira, “Analysis of representations for domain adaptation,” in _Advances in neural information processing systems (NeurIPS)_ , 2007, pp. 137–144.
  * [42] A. Smola, A. Gretton, L. Song, and B. Schölkopf, “A Hilbert space embedding for distributions,” in _International Conference on Algorithmic Learning Theory_. Springer, 2007, pp. 13–31.
  * [43] C. Garcia-Cardona and B. Wohlberg, “Convolutional dictionary learning: A comparative review and new algorithms,” _IEEE Transactions on Computational Imaging_ , vol. 4, no. 3, pp. 366–381, Sep. 2018.
  * [44] C.-L. Li, W.-C. Chang, Y. Cheng, Y. Yang, and B. Póczos, “Mmd gan: Towards deeper understanding of moment matching network,” in _Advances in Neural Information Processing Systems (NeurIPS)_ , 2017, pp. 2203–2213.
  * [45] X. Glorot, A. Bordes, and Y. Bengio, “Domain adaptation for large-scale sentiment classification: A deep learning approach,” in _International Conference on Machine Learning (ICML)_ , 2011, pp. 513–520.
  * [46] I. Titov, “Domain adaptation by constraining inter-domain variability of latent feature representation,” in _49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies-Volume 1_. Association for Computational Linguistics, 2011, pp. 62–71.
  * [47] Y. Chen, S. Song, S. Li, L. Yang, and C. Wu, “Domain space transfer extreme learning machine for domain adaptation,” _IEEE Transactions on Cybernetics_ , vol. 49, no. 5, pp. 1909–1922, 2018.
  * [48] A. Gretton, K. M. Borgwardt, M. J. Rasch, B. Schölkopf, and A. Smola, “A kernel two-sample test,” _Journal of Machine Learning Research_ , vol. 13, no. Mar, pp. 723–773, 2012.
  * [49] B. K. Sriperumbudur, K. Fukumizu, A. Gretton, G. R. Lanckriet, and B. Schölkopf, “Kernel choice and classifiability for RKHS embeddings of probability distributions,” in _Advances in neural information processing systems (NeurIPS)_ , 2009, pp. 1750–1758.
  * [50] S. Shekhar, V. M. Patel, H. V. Nguyen, and R. Chellappa, “Generalized domain-adaptive dictionaries,” in _IEEE Conference on Computer Vision and Pattern Recognition (CVPR)_ , 2013, pp. 361–368.
  * [51] X. Cai, F. Nie, H. Huang, and C. Ding, “Multi-class L2,1-norm support vector machine,” in _IEEE International Conference on Data Mining_ , Dec. 2011, pp. 91–100.
  * [52] M. Amini, N. Usunier, and C. Goutte, “Learning from multiple partially observed views-an application to multilingual text categorization,” in _Advances in neural information processing systems (NeurIPS)_ , 2009, pp. 28–36.
  * [53] B. Gong, K. Grauman, and F. Sha, “Connecting the dots with landmarks: Discriminatively learning domain-invariant features for unsupervised domain adaptation,” in _International Conference on Machine Learning (ICML)_ , 2013, pp. 222–230.
  * [54] J. Donahue, Y. Jia, O. Vinyals, J. Hoffman, N. Zhang, E. Tzeng, and T. Darrell, “Decaf: A deep convolutional activation feature for generic visual recognition,” in _International conference on machine learning (ICML)_ , 2014, pp. 647–655.
  * [55] M. Ebrahimi, M. Surdeanu, S. Samtani, and H. Chen, “Detecting Cyber Threats in Non-English Dark Net Markets: A Cross-Lingual Transfer Learning Approach,” in _IEEE International Conference on Intelligence and Security Informatics (ISI)_. IEEE, 2018, pp. 85–90.
  * [56] C. Wheelus, E. Bou-Harb, and X. Zhu, “Tackling Class Imbalance in Cyber Security Datasets,” in _IEEE International Conference on Information Reuse and Integration (IRI)_ , Jul. 2018, pp. 229–232.
  * [57] T. Hastie, R. Tibshirani, and J. Friedman, _The elements of statistical learning_. Springer series in statistics New York, 2017, no. 12.
  * [58] M. Arjovsky, S. Chintala, and L. Bottou, “Wasserstein generative adversarial networks,” in _International Conference on Machine Learning (ICML)_ , ser. Proceedings of Machine Learning Research, D. Precup and Y. W. Teh, Eds., vol. 70. International Convention Centre, Sydney, Australia: PMLR, Aug. 2017, pp. 214–223.
  * [59] P. Morerio, J. Cavazza, and V. Murino, “Minimal-entropy correlation alignment for unsupervised deep domain adaptation,” in _International Conference on Learning Representations_ , 2018.
  * [60] J. Demšar, “Statistical comparisons of classifiers over multiple data sets,” _Journal of Machine learning research_ , vol. 7, no. Jan, pp. 1–30, 2006\.
  * [61] E. Zhong, W. Fan, Q. Yang, O. Verscheure, and J. Ren, “Cross validation framework to choose amongst models and datasets for transfer learning,” in _Joint European Conference on Machine Learning and Knowledge Discovery in Databases_. Springer, 2010, pp. 547–562.
  * [62] L. v. d. Maaten and G. Hinton, “Visualizing data using t-SNE,” _Journal of machine learning research_ , vol. 9, no. Nov, pp. 2579–2605, 2008\.

|  Mohammadreza (Reza) Ebrahimi received his master’s degree in Computer
Science from Concordia University, Canada in 2016, and his Ph.D. in
Information Systems from Artificial Intelligence (AI) Lab at the University of
Arizona in 2021. He is an assistant professor at the University of South
Florida (USF). His research interests include statistical machine learning,
adversarial machine learning, and security of AI. His work has appeared in
journals, conferences, and workshops, including IEEE S&P, AAAI, IEEE ISI,
Digital Forensics, and Applied Artificial Intelligence. He has served as a
Program Chair and Program Committee member in IEEE ICDM Workshop on Machine
Learning for Cybersecurity (MLC) and IEEE S&P Workshop on Deep Learning and
Security (DLS). He has contributed to several projects supported by the
National Science Foundation (NSF). He is a member of the IEEE, ACM, AAAI, and
AIS.
---|---
|  Yidong Chai received his bachelor’s degree in information system from
Beijing Institute of Technology, and his Ph.D. degree in Management
Information Systems from Tsinghua University. He is currently a professor at
the Hefei University of Technology. His research fields include machine
learning, signal processing, and natural language processing. His work has
appeared in journals including Knowledge-Based Systems and Applied Soft
Computing, as well as conferences and workshops including IEEE S&P, INFORMS
Workshop on Data Science, Workshop on Information Technology Systems,
International Conference on Smart Health, and International Conference on
Information Systems.
---|---
|  Hao Helen Zhang is a professor at the University of Arizona, in the
Department of Mathematics, Statistics Interdisciplinary Program, and Applied
Mathematics Interdisciplinary Program there. With Bertrand Clarke and Ernest
Fokoué, she is the author of the book Principles and Theory for Data Mining
and Machine Learning. She earned a bachelor’s degree in mathematics in 1996
from Peking University. She completed her Ph.D. in statistics in 2002 from the
University of Wisconsin–Madison. Her dissertation, supervised by Grace Wahba,
was Nonparametric Variable Selection and Model Building Via Likelihood Basis
Pursuit. She was elected to the International Statistical Institute and as a
fellow of the American Statistical Association in 2015. She became a fellow in
the Institute of Mathematical Statistics in 2016, and has been selected as the
2019 Medallion Lecturer of the Institute of Mathematical Statistics.
---|---
|  Hsinchun Chen received the BS degree from the National Chiao-Tung
University in Taiwan, the MBA degree from the State University of New York at
Buffalo, and the Ph.D. degree in information systems from New York University.
He is a regents professor at the University of Arizona. He has served as a
scientific counselor/advisor of the US National Library of Medicine, the
Academia Sinica, Taiwan, and the National Library of China, China. He was
ranked #8 in publication productivity in information systems (CAIS 2005) and
#1 in Digital Library research (IP&M 2005) in two bibliometric studies. His
COPLINK system, which has been quoted as a national model for public safety
information sharing and analysis, has been adopted in more than 550 law
enforcement and intelligence agencies in 20 states. He received the IEEE
Computer Society 2006 Technical Achievement Award. He is a fellow of the IEEE
and the AAAS.
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