# Unsupversied feature correlation model to predict breast abnormal variation
maps in longitudinal mammograms

Jun Bai  Annie Jin  Madison Adams  Clifford Yang  Sheida Nabavi  Department of
Computer Science and Engineering, University of Connecticut, 371 Fairfield
Way, Storrs, CT 06269, USA  University of Connecticut School of Medicine, 263
Farmington Ave. Farmington, CT 06030, USA  Department of Radiology, UConn
Health, 263 Farmington Ave. Farmington, CT 06030, USA

###### Abstract

Breast cancer continues to be a significant cause of mortality among women
globally. Timely identification and precise diagnosis of breast abnormalities
are critical for enhancing patient prognosis. In this study, we focus on
improving the early detection and accurate diagnosis of breast abnormalities,
which is crucial for improving patient outcomes and reducing the mortality
rate of breast cancer. To address the limitations of traditional screening
methods, a novel unsupervised feature correlation network was developed to
predict maps indicating breast abnormal variations using longitudinal 2D
mammograms.

The proposed model utilizes the reconstruction process of current year and
prior year mammograms to extract tissue from different areas and analyze the
differences between them to identify abnormal variations that may indicate the
presence of cancer. The model is equipped with a feature correlation module,
an attention suppression gate, and a breast abnormality detection module that
work together to improve the accuracy of the prediction. The proposed model
not only provides breast abnormal variation maps, but also distinguishes
between normal and cancer mammograms, making it more advanced compared to the
state-of-the-art baseline models. The results of the study show that the
proposed model outperforms the baseline models in terms of Accuracy,
Sensitivity, Specificity, Dice score, and cancer detection rate.

###### keywords:

longitudinal Mammogram , Deep learning , unsupervised learning , cancer
localization

##  1 Introduction

Breast cancer is one of the top health concerns for women in the world [43].
The high chance of developing breast cancer has also led to considerable
anxiety among the general public. Research has demonstrated that early
detection is crucial for reducing the burden of breast cancer. Healthcare
professionals have emphasized the importance of early detection to improve the
survival rate [11]. In particular, mammography is widely recognized as the
gold standard for breast cancer screening for asymptomatic women to identify
breast cancer before any symptom appears [46, 13]. American Cancer Society
(ACS) recommending annual mammography screening for women ages 40 and older
since 2004 [44]. Although annual screening of mammograms increases breast
cancer survival rate, the large volume of screening mammograms and the use of
double readings put a strain on the healthcare system and can compromise its
efficiency. Furthermore, the complexity of mammograms can pose challenges for
radiologists, potentially resulting in false and missed diagnoses [19, 32].
Besides, small tumors surrounded by dense fibroglandular breast tissue may go
undetected, which can delay diagnosis and prevent early detection [19].
Moreover, false positive results are possible, which can lead to unnecessary
procedures such as benign biopsies, additional expenses, and psychological
distress for patients. [36, 34].

In clinical practice, the traditional computer-aided detection (CAD) system —
relies on image processing and pattern recognition techniques — provides a
second opinion on breast cancer detection and image interpretation to
radiologists. The CAD system involves handcrafted features —using conventional
image processing methods— from mammograms and then classifies them using
statistical methods. In contrast, deep learning, a subset of machine learning,
has been increasingly used over the past decade to develop CAD systems that
can automatically extract features from raw inputs using multiple layers of
neural networks. In recent years, many studies have utilized deep learning,
especially convolutional neural networks (CNNs), for mammogram
classification[47, 16, 30, 40, 41, 28, 25, 24, 1, 18, 49]. In many deep
learning mammogram studies, Full-Field Digital Mammography (FFDM) has been
utilized to learn the data distribution, although some studies have used
reduced-size images [47, 16, 30, 40, 49], patches, or regions of interest
(ROI) to minimize computational complexity [41, 28, 25, 24, 1, 18]. Although,
deep learning based models have shown a remarkable ability to carry out a wide
range of medical imaging tasks including breast cancer screening [47, 16, 30,
40, 41, 28, 25, 24, 1, 18, 49] and have made automated breast cancer
mammography screening feasible, developing such a model still remains
challenging [7], especially for localizing abnormalities in mammograms due to
the unique characteristics of mammogram images.

Breast abnormalities are small and share features with the background tissue,
making it difficult to accurately detect tumors with ambiguous boundaries or
different shapes. Radiologists commonly use previous mammogram scans as a
reference point to make an inference when examining current mammogram scans in
order to spot suspicious tissue. Not only in clinical practice but also in
studies it has been shown that comparing current mammogram scans with prior
ones improves the outcomes of mammography classification. In the study by Kooi
and Karssemeijer twin CNNs are used to classify mammogram ROIs by comparing
primary mammograms with their corresponding history mammograms or opposite
breast mammograms. However, the model requires some level of radiologist
knowledge to identify the mass ROIs and to map them from current mammograms to
their prior ones [26]. In another study by Perek et al., CNN models were used
to extract features from current and previous year images, and long short-term
memory (LSTM) layers were employed to learn the differences and classify
mammograms. However, this method requires image registration during data pre-
processing, and training LSTM with a small dataset to learn tissue changes can
cause overfitting [38]. In our previous work, we developed a feature fusion
siamese network to predict cancer incorporate with patients’ prior and current
image[6]. While some studies have suggested using prior mammograms to classify
breast cancer, no studies have been proposed to utilize prior knowledge to
locate breast cancer.

In addition to the challenge of extracting effective features from complex
breast tissue, the analysis of mammograms is constrained by a small sample
size, particularly with accurately annotated, datasets [51, 7]. Mammogram data
labeling presents a number of formidable challenges, chief among which is the
requirement for specialized domain knowledge to ensure accurate and reliable
labeling. Compounding this challenge is the considerable variability in
mammogram quality, resolution, and orientation, rendering the accurate pixel-
level identification and labeling of regions of interest a complex and arduous
task. This directly leads to heavy human labor for data annotation and non-
generalized annotation. One solution to the challenge of the non-annotated
data and the difficulty of extracting useful features from complex breast
tissue is to use an unsupervised learning approach. The breast cancer
screening technique, which involves comparing current mammogram images with
prior ones, naturally lends itself to building an unsupervised learning model
that can learn the differences between images through the image reconstruction
process. In this study, in light of U-Net’s [29, 42] empirical effectiveness
and the reality of mammogram data scarcity, we propose UFCN, an unsupervised
feature correlation network, to predict a map showing abnormal variations by
comparing the history of mammograms, which we call it abnormal variation map
(AVM). Specifically, inspired by the radiologist’s reading procedure, we
propose a parallel feature correlation encoder to compares high resolution
prior and current mammograms to predict and visualize tumor location without
using annotated training data. The contributions of this paper are summarized
as follows:

  * •

We introduce a novel model that can detect breast cancer without requiring
pixel level labeled data and that covers the entire process from start to
finish.

  * •

We present a novel feature correlation module that can accurately pinpoint
feature discrepancies between the current and previous image.

  * •

We propose a novel attention suppression gate to enhance the model’s capacity
in differentiating between normal and cancer cases.

  * •

We propose a novel module to predict abnormal maps of the breast, which can
help localizing tumors.

  * •

To the best of our knowledge, this is the first time an unsupervised model has
been used to predict a breast abnormality variation map by utilizing patients’
current and prior mammograms.

##  2 Related Study

Breast cancer localization using FFDM has been extensively studied using deep
learning algorithms. Researchers have explored various advanced models to
achieve accurate localization of breast cancer, including convolutional neural
networks (CNNs), recurrent neural networks (RNNs), and hybrid models. Despite
the success of supervised deep learning approaches, unsupervised deep learning
algorithms have limited implementation in breast cancer localization. This
section will review studies that employed deep learning to localize breast
cancer and unsupervised segmentation studies.

###  2.1 Breast Cancer localization studies

In the case of breast cancer localization, the goal is to determine the
precise location of the abnormal object within the cancerous patient’s image.
The main model — end-to-end model — used to detect cancer is CNN [39, 45, 3,
4]. Several researchers have introduced different approaches to detect and
locate different types of abnormalities in mammography images such as region-
based network (R-CNN) for ADs [15], dual CNN-based visual search system for
mass [23], multi-scale deep belief network [9], self-transfer learning model
[20], U-Net for all types of cancer[2] and adversarial model for mass [53].
These methods involve pre-processing, image enhancement, and normalization
techniques to improve detection and localization accuracy.

In many mammogram localization studies, patches are often used to overcome
computation challenges [45, 12, 10]. In the study by Choukroun et al., the
authors proposed detecting microcalcifications (Cals) using discriminative
local information contained in patches. The patch-based approach has some
limitations, as the input patches are obtained from non-overlapping regions,
leading to potential difficulties in precisely localizing masses. Furthermore,
the small size of the input patches can create challenges in distinguishing
between normal and abnormal tissue, which can negatively impact the accuracy
of the detection and diagnosis of medical conditions. These issues highlight
the need for continuing research and the development of more effective
approaches for breast cancer detection.

Besides the aforementioned data-driven models, there are a few general models
to localize breast cancer such as the YOLO-based models [39, 4], UNet-based
models [5], and attention UNet-based models [27]. The remarkable success
achieved by these cutting-edge models in localizing cancer cannot be
overstated. However, even the most advanced models have a few limitations that
must be addressed. One particularly significant limitation is the difficulty
in accurately predicting results for normal patients. This is because these
models are designed to operate under the assumption that patients have already
been diagnosed with cancer or are suspected of having cancer. As a result, the
models are trained using only cancer and benign data, making their prediction
ability for normal patients uncertain. In addition, the supervised training
process for these models presents a challenge. Annotating breast tumors is a
costly and unclear process due to the varying and non-standardized tumor
location annotation process Different levels of experience and practice in
breast cancer diagnostics could cause different annotation styles. For
example, unlike other object annotations, Cals — a type of breast cancer
screened as clusters of tiny bright dots —poses a challenge in determining
whether to annotate the entire area or each individual dot.

###  2.2 Unsupervised segmentation studies

Unsupervised segmentation is a rapidly emerging field that has attracted the
attention of researchers across various disciplines, including medical image
analysis. Through meticulous investigation, researchers have developed
cutting-edge techniques to cluster similar pixels and segment objects in
natural images by assigning pixel-level labels to images [21, 22]. Despite
this, the application of these methods in medical image analysis poses
significant challenges as the pixel intensity fails to exhibit significant
differences, rendering this approach ineffective. Unlike objects in nature
images, cancer and disease present a multitude of distinct characteristics
during their development stages, presenting an opportunity to apply innovative
unsupervised segmentation techniques that could revolutionize the field of
medical image analysis.

In the world of clinical diagnostics, it is essential to assess a patient’s
disease development to predict any possible occurrence of a particular
ailment. In other words, by screening patients’ current condition, a synthetic
history screen can be generated to predict any abnormal variation areas. In a
pioneering study by Van Voorst et al., the authors employed a deep generative
model to generate prior images using patients’ lesion-contained current-year
images [48]. This approach involved using the difference map as segmentation
for abnormal lesions. Furthermore, this technique has also been applied in
breast cancer localization, as outlined in the research by Park et al.. In
their work, the authors proposed using StyleGAN2 to generate patients’
synthesized normal images based on their current images, which aids in
localizing abnormal tissue. The researchers trained StyleGAN2 on normal
mammograms to predict abnormal tissue on the difference between generated
synthetic normal images and their corresponding suspicious current images[37].
Pioneering models have demonstrated the feasibility of unsupervised learning
in disease localization. However, there are certain limitations when it comes
to generating prior images to learn the difference map as a disease
segmentation technique. One such limitation is that normal prediction remains
unknown, which poses a significant challenge to researchers.

##  3 Methods

The proposed model in this study, which we call it Unsupervised Feature
Correlation Network (UFCN), takes advantage of the deep U-shaped residual
connected autoencoder reconstruction process to learn the abnormal variation
maps. In the following section, we present our model method in detail.

###  3.1 Definition

In this study, we define inputs as
$I_{i}=\\{(C_{i}\in\mathbb{R}^{2},P_{i}\in\mathbb{R}^{2}\\}$, where $C_{i}$ is
a current year image that can be biopsy-confirmed cancer or normal and $P_{i}$
is a prior image that is normal. Let
$f:\mathbb{R}^{2}\rightarrow\mathbb{R}^{p}$ be a feature extraction function
and $g:\mathbb{R}^{p}\rightarrow\mathbb{R}^{2}$ be a feature transpose
function. For an $f$ and $g$, the estimate of ${C}_{i}$, $\hat{C}_{i}$, can be
obtained using these functions. On the other hand, if $f$ and $g$ can be
learned through training for a given $\hat{C}_{i}$ then learning $f$ and $g$
can be considered as a typical image reconstruction problem. If functions $f$
and $g$ have the property of being differentiable, then their parameters can
be optimized using gradient descent. However, our study aims to predict the
abnormal variation map (AVM) by training $f$ and $g$ in an unsupervised
manner. Particularly, the proposed model will be trained to learn $f$ and $g$
under the task of reconstruction and prediction of the AVM using the learned
feature difference between $C_{i}$ and $P_{i}$. To put this into practice, we
solved two sub-problems: training parameters of $f$ and $g$ with given
$\hat{C}_{i}$ and prediction of the optimal AVM with learned $f$ and $g$.
Because we also want to predict no abnormal changes for normal patients
($C_{i}$s) where AVM should detect nothing, we introduced a mapping function
$h:\mathbb{R}^{p}\rightarrow\mathbb{R}$ in $g$ to map the probability of
binary labels of $C_{i}$s, $y_{i}$s. In our case, the $y_{i}$ represents
binary label of either normal or cancer of current mammograms.

###  3.2 Unsupervised feature correlation network (UFCN)

Figure 1: Overview of the proposed model’s structure. The model consists of
two encoders with inputs $C_{i}$ (current mammogram) and $P_{i}$ (previous
mammogram), and one decoder output $\hat{C}_{i}$. The green panel is the
feature correlation map module (FCM), which computes the signal difference
between features extracted using function $f$ from current and previous
mammograms at each layer. The yellow panel is attention suppress gate (ASG).
The red panel is the breast abnormality detection map module (BAM), which
predicts the abnormal variation maps (AVM) as output. $\oplus$ is
concatenation, and $\ominus$ is matrix subtraction.

Our proposed model, UFCN, is an unsupervised CNN-based model. UFCN consists of
an identical parallel twin encoder and a reconstruction decoder (Figure 1).
UFCN embeds feature correlation modules (FCMs) into encoder layers and
attention suppress gate modules (ASGs) into decoder layers. The breast
abnormality map detection module (BAM) is embedded at the decoder’s layer
$L-1$, where $L$ is the total number of layers, to generate AVMs. A pair of
current and prior images are input into the two identical parallel CNN blocks
to learn the features. In each corresponding CNN block, the learned features
of pairs of images using function $f$ are fed into FCMs to learn differences
between current and prior images and their features. The output of FCM,
$D_{l}$, represents the breast tissue changes from prior mammograms ($P_{i}$)
to current mammograms ($C_{i}$). $D_{l}$s residual connect to ASG at the
decoder stage. The output of the decoder is the reconstruction of current
mammograms, $\hat{C}_{i}$.

Selecting an activation function to trigger the model neurons in an
unsupervised learning model is critical. Hence, we employed three activation
functions in this study: 1) ReLU activation function ($\sigma_{1}$) shown in
equation 1, sigmoid activation function ($\sigma_{2}$) shown in equation 2,
and SiLU activation function ($\sigma_{3}$) shown in equation 3 [14].

$\sigma_{1}(x)=max(0,x),$ (1) $\sigma_{2}(x)=\frac{1}{1+e^{-x}},$ (2)
$\sigma_{3}(x)=x\cdot\sigma_{2}(\beta x),$ (3)

where $\beta$ is a trainable parameter and $x$ is input feature. The SiLU
activation function has a desirable characteristic known as self-
stabilization. This means that the point at which the derivative of the
function is zero acts as a “soft floor” for the weights, which helps to
regulate the learning process by discouraging the development of excessively
large weights. We implemented the SiLU activation in the FCM modules and CNN
blocks in the encoder and decoder; the ReLU activation in the ASG modules for
faster gradient descent; and the sigmoid activation in the ASG and BAM
modules.

###  3.3 Feature correlation module (FCM).

To take advantage of the paired images through the reconstruction process, we
embedded FCM modules into each layer of the encoder stage. FCM (Figure 2.a.)
learns multi-scaled feature correlation between current and prior mammograms
to learn newly grown tumors. The FCM module output, $D_{l}\in\mathbb{R}^{p}$,
can be expressed as $D_{l}=\sigma_{3}(F_{C}^{l})\ominus\sigma_{3}(F_{P}^{l})$,
where $F_{C}^{l}=f(C_{i})\in\mathbb{R}^{p}$ and
$F_{P}^{l}=f(P_{i})\in\mathbb{R}^{p}$ are the feature maps of the current and
prior mammograms at layer $l$, $\ominus$ is matrix subtraction, and
$\sigma_{3}$ is the SiLU activation function [14].

###  3.4 Attention suppress gate module (ASG).

The ASG module is embedded into each layer of the decoder stage at the image
$C_{i}$ reconstruction process with function $g$. The ASG (Figure 2.b.) aims
to selectively highlight specific areas of an image through attention
weightings. In our specific problem, we also utilize ASGs to completely remove
any activation from the normal patients’ images. As the model is trained, the
soft attention aspect will prioritize regions with greater weights while the
hard suppresser — mapping function $h$ — eliminates any activity from the
normal images.

ASG adds weight to breast tissue areas and reduces the impact of changes in
breast borders. ASG at layer $l$ outputs attention coefficients
$A_{l}\in\mathbb{R}^{p}$ whiles takes $D_{l}$ and $E_{l-1}\in\mathbb{R}^{p}$
as input, where $E_{l-1}$ is decoder output at layer $l-1$. $A_{l}$ is
computed as $A_{l}=\sigma_{2}(\sigma_{1}(W_{E}^{T}E_{l-1}\otimes
W_{D}^{T}D_{l})W_{A}^{T})W_{E}^{T}E_{l-1}$, where $\sigma_{2}$ is the sigmoid
activation function, and $\otimes$ is Hadamard product. To have more
aggressive soft attention, we introduced a threshold $\lambda$ to suppress the
attention coefficients lower than the threshold and to remain the attention
region for the attention coefficients higher than the threshold. To prevent
neurons from dying, we suppress the lease-activated region (the feature map
region below the threshold) to a small constant value instead of zero.

The hard suppressor acts as a regularizer that maps region-activated feature
map to probability of $\hat{y}$ as
$\hat{y}=h(A_{l})=\sigma_{2}(W_{f}^{T}A_{l})\in\mathbb{R}$ where
$W_{f}\in\mathbb{R}^{p}$ is a vector of trainable parameters in our study. The
mapped probability of normal and cancer,$\hat{y}$, are participated in loss
term to compute the gradient. ASG progressively suppresses features responding
in irrelevant background regions and normal patient’s image. The output of ASG
at each layer $l$ is concatenated with its corresponding encoder features at
each layer $l$, and then the features are fed forward to the next layer until
reaching the last layer that reconstructs $C_{i}$ and outputs $\hat{C_{i}}$.

Figure 2: a. Block diagram of the feature correlation module (FCM).
$F_{C}^{l}$ and $F_{P}^{l}$ are current year and previous year feature maps,
respectively, generated in the layer $l$ of the decoder (function $f$).
$D_{l}$ is output from FCM in layer $l$. The $\ominus$ is matrix subtraction.
b. Block diagram of the attention suppresses gate module (ASG). $E_{l}$ is
feature generated in encoder (function $g$) layer $l$, $D_{l}$ is output of
FCM, and $A_{l}$ is attention coefficients. The $\otimes$ is Hadamard product.
c. Block diagram of the breast abnormality detection module (BAM). $F_{A}^{l}$
is the feature map from layer $L-1$.

###  3.5 Breast abnormality detection module (BAM).

As we defined in the previous section, the optimal AVM is predicted with
learned $f$ and $g$. To achieve an accurate binary mask AVM indicating the
abnormal regions, we embedded BAM in the decoder stage. The BAM module (Figure
2.c.) is applied to layer $L-1$ which outputs and generates AVMs as
$AVM=\sigma_{2}(W_{V}^{T}F_{A}^{L-1})$, where $F_{A}^{L-1}$ is the extracted
feature vector at layer $L-1$. The module applies a convolution layer to blend
the $F_{A}$ features, then employs the sigmoid activation function. Finally,
using a threshold $\tau$ (we used $0.5$ in our study), BAM selects the most
activated regions as AVMs, indicating cancer regions.

###  3.6 Loss function

The proposed loss function $LOSS$ consists of a constraint on current year
image reconstruction — the similarity index measure(SSIM) reconstruction loss
[50], a layer wise constraint on the probability of binary labels (normal and
cancer) of images $y$ — the binary cross function (BE), and a constraint on
weights — the $L2$ norm function, denoted as follows:

$LOSS=\underbrace{\frac{1}{N}\sum_{p\in
P}1-SSIM(p)}_{\text{Recons}}+\underbrace{\lambda_{1}\sum_{l\in
L}BE(y,\hat{y})}_{\text{Prob}}+\underbrace{\lambda_{2}\sum_{w_{i}\in\mathbf{w}}w_{i}^{2}}_{\text{$L_{2}$
Regularizer}}.$ (4)

where

$SSIM(p)=\frac{2\mu_{i}\mu_{j}+C_{1}}{\mu_{i}^{2}+\mu_{j}^{2}+C_{1}}\cdot\frac{2\sigma_{ij}+C_{2}}{\sigma_{i}^{2}+\sigma_{j}^{2}+C_{2}},$
(5)

where $\mu$ represents the mean of pixel intensities, $\sigma$ in this
equation denotes the standard deviation of pixel intensities, $C_{1}$ and
$C_{2}$ are constant for stability. $C_{1}$ is given by $C_{1}=(K_{1}T)^{2}$
and $C_{2}=(K_{2}T)$ where $K_{1}$ and $K_{2}$ are constant values, and $T$ is
the dynamic range of pixel intensities.

The probability distribution constraint is defined as:

$BE(y,\hat{y})=-(y\log(\hat{y})+(1-y)\log(1-\hat{y})),$ (6)

where $y$ is the binary label for the $h(x)$ at ASG, $\hat{y}$ is prediction
of the $h(x)$, and $x$ is input feature map.

##  4 Baseline and Variant models

In the course of the experiments, we used the following models as baseline
models and variants of the proposed model. All baseline models are supervised
autoencoder-shaped models. We trained the baseline models, proposed model, and
variation models with the same training dataset and input dimension. However,
the baseline models were only trained using cancer images due to their design.
To have a fair comparison, all baseline models and variation models employed
the same numbers of building blocks.

###  4.1 U-Net

We compared the performance of the proposed method with that of the U-Net
[29]. We kept the structure of U-Net as standard U-Net and optimized the
feature depth at each building block. The U-Net model has contained five
building blocks. The feature depth of each building block is indicated as
$64,128,256,512,1024$. We used dice loss (Equation 7) to optimize the U-Net
gradient as follow:

$L_{Dice}=1-\frac{\sum_{n=1}^{N}s_{n}r_{n}+\epsilon}{\sum_{n=1}^{N}s_{n}+r_{n}+\epsilon}-\frac{\sum_{n=1}^{N}(1-s_{n})(1-r_{n})+\epsilon}{\sum_{n=1}^{N}2-s_{n}-r_{n}+\epsilon},$
(7)

where $N$ is the number of images in this equation, $s$ is predicted
probability, $r$ is ground truth, and $\epsilon$ is a hyperparameter to ensure
the stability of the loss function.

###  4.2 Attention U-Net

We also compared the performance of the proposed model with that of U-Net
attention[35]. The structure of attention U-Net reminded the same as its
original and we optimized the feature depth at each building block. The
feature depths of building blocks are $64,128,256,512,1024$. We used dice loss
(Equation 7) to optimize the attention U-Net gradient.

###  4.3 U-Net++

Another baseline model we used in this study is U-Net++ [52]. The structure of
the U-Net++ reminded the same. We used feature depth of $32,64,128,256,512,64$
for building blocks. U-Net++ is an extension of the U-Net architecture for
semantic image segmentation. The model structure is similar to U-Net, but with
additional nested and dense skip connections. We used dice loss (Equation 7)
to optimize the attention U-Net++ gradient.

###  4.4 SegResNet

We used SegResNet [33] for performance comparison too. SegResNet is a deep
neural network architecture designed for semantic image segmentation tasks.
The model is based on the ResNet [17] architecture. The SegResNet enhance the
performance of ResNet for image segmentation tasks by adding a decoder network
to the architecture. This decoder network is composed of several
deconvolutional (or transposed convolutional) layers, which upsample the
features extracted by the ResNet encoder and generate a pixel-wise
segmentation mask. We used dice loss (Equation 7) to optimize the SegResNet
gradient.

###  4.5 V-Net

We also compared the proposed model with V-Net [31]. The V-Net architecture
bears some resemblance to the U-Net architecture, but with some differences.
Firstly, V-Net does not employ Batch Normalization, unlike U-Net. In addition,
while U-Net uses element-wise summation after each successive convolutional
layer, V-Net does not. In the experiment, we kept the same structure as the
original V-Net. We used dice loss (Equation 7) to optimize the V-Net gradient.

###  4.6 UFCN-variants

As mentioned in the Method section (section 3), the activation function is
important to obtain accurate abnormal variation maps. Therefore, to explore
how the activation function impacts the proposed model, we studied two
variations of the proposed model: 1) UFCN-T, and 2) UFCN-R. In the UFCN-T
model, We define a new activation function, which we called it Tilu, to
enhance the activated region by dropping the low-signaled neurons. The Tilu
activation function can be expressed as $tiLU(x)=max(\lambda,x)$, where
$\lambda$ is a small constant value as hard floor. The UFCN-R used regular
ReLU activation function in the entire model. The loss function remains the
same as that of the proposed method expressed in Equation 4.

##  5 Data & Experimental Setup

Figure 3:  Examples of current and prior mammograms of a. an abnormal patient
and b. a normal patient from our dataset. The yellow circle indicate the
abnormal location.

###  5.1 Experiment setup

We used PyTorch to implement the proposed method, its variants and the
baseline models. Data pre-processing was performed with High-Performance
Computing (HPC) with 36 cores Xeon CPU. The proposed method was trained on
Xsede with multiple 32 GB V100 GPU nodes [8]. We explored the starting
learning rate in a range from $1\mathrm{e}{-2}$ to $1\mathrm{e}{-5}$. We used
a learning rate scheduler to optimize the model’s learning rate. The proposed
model code is available at https://github.com/NabaviLab/ufcn.

###  5.2 Data

The proposed and baseline models were trained, tested, and validated on the
UConn Health Center (UCHC) dataset, which includes both current and historical
mammograms. This dataset was compiled by collecting FFDMs from patients who
underwent mammogram exams at UCHC between October 31, 2006, and August 23,
2021, using a Hologic machine. The UCHC Institutional Review Board approved
the data collection, and the Diagnostic Imaging Informatics Department at UCHC
provided support in exporting the DICOMs from the Picture Archiving and
Communication Systems (PACS) at UCHC. To ensure patient privacy, identifiers
were removed and replaced with a standard naming convention. The mammograms in
the dataset were annotated by radiologists.

In this collection, 493 mammogram pairs (current and their corresponding prior
normal mammograms) are labeled cancer, and 581 mammogram pairs are labeled
normal. Data pre-processing includes normalization, re-scale, and augmentation
are applied. No alignment is performed in this study. The ground truth used
for evaluation is annotated by radiologists.

To ensure the diversity and generalizability of the dataset, various types of
tumors and breast densities were included. The mass type in the dataset
includes round, oval, architectural distortion, irregular, and lobulated,
while the microcalcification type includes amorphous, coarse, fine linear
branching, pleomorphic, punctate, and round with regular shapes. All types of
breast densities, including fatty, fibroglandular dense, heterogeneously
dense, and extremely dense breasts, were also included. The fibroglandular
dense and heterogeneously dense breast types cover a significant portion of
the dataset.

##  6 Results and discussion

We compared the performance of the proposed model and its variant with the
baseline model explained in Section4, in terms of Dice score, cancer detection
rate (cDR), and normal detection rate(nDR) for different cancer types (Mass,
microcalcifications (Calc), Architectural Distortion (AD)). The results for
different cancer types are shown in Table 1.

We define cancer detection as binary detection when for cancer cases a cancer
region is detected and for normal cases, a minimal region that below the
threshold as shown in Equation 9 is detected . Additionally, we compared the
performance of all the models in terms of Accuracy, Sensitivity, Precision,
and F1 in detecting abnormalities. True Positive ($TP$) and True Negative
($TN$) used in computing the aforementioned metrics are defined in Equations 8
and 9, respectively.

$TP=\begin{cases}1,&\text{if $dice(I)>0.01$}\\\
0,&\text{otherwise}\end{cases},$ (8)

where $I$ is the input test mammogram image.

$TN=\begin{cases}1,&\text{if $\sum_{i,j\in w,h}I(i,j)<0.01$}\\\
0,&\text{otherwise}\end{cases},$ (9)

where $w,h$ are the width and height of the input image.

###  6.1 Overall results

Table 1 highlights the superiority of the proposed model, UFCN, in terms of
cancer detection. This model achieves the best cancer detection rate for both
masses and microcalcifications, as well as the best Dice score for masses.
Furthermore, the proposed UFCN also performs well in architectural distortion
cancer type, achieving the second-best performance in terms of the Dice score
and the third-best in terms of cancer detection rate. When compared to its
variant, UFCN-R, which uses the ReLU activation function, the proposed UFCN
outperforms in all types of cancers. The inferior performance of UFCN-R may be
caused by the dying ReLU, in which ASG suppresses the majority of nodes to
zero, resulting in a decrease in the activated regions and shrinkage of the
abnormal variation map. In contrast, the use of the "soft floor" SiLU
activation function in UFCN prevents dead neurons and provides the necessary
stability to activate the attention regions while simultaneously suppressing
the irrelevant background of cancer images and normal images. The results
demonstrate the superior performance of UFCN in cancer detection, even though
the model is trained in an unsupervised fashion.

For the architectural distortion cancer type, UFCN-T shows superior
performance in both Dice score and cancer detection rate. Although the TiLU
activation function uses a hard floor like ReLU, it employs a slightly tighter
bound as a hard floor to avoid the dying ReLU caused by the properties of
zero, unlike the ReLU activation function that uses $0$ for the hard floor. In
other words, UFCN-T maximizes the variation between the current year image and
the prior image, which is also observable by its superior performance in
detecting microcalcifications and comparable performance in detecting masses.

The proposed model, UFCN, outperforms all baseline models including U-Net,
U-Net attention, U-Net++, SegResNet, and V-Net in almost all the metrics.
Among all baseline models, U-Net++ showed the best performance in terms of
cancer detection rate and Dice score in architectural distortion and mass
cancer types, while U-Net showed a decent Dice score and cancer detection rate
in Cals among all baseline models. However, both models showed relatively low
performance in normal tissue classification, as indicated by their low nDR. In
contrast, UFCN achieved the best performance in terms of cancer detection rate
and Dice score for mass and the second-best for calcifications, as well as the
highest nDR among all the models. These findings demonstrate the superior
performance of our proposed UFCN, which is trained in an unsupervised fashion.
Specifically, UFCN-T showed the best performance overall, with a Dice score of
0.66 and a cDR of $0.86$, followed by UFCN with a Dice score of $0.69$ and a
cDR of $0.91$. These findings demonstrate the superior performance of our
proposed UFCN, which is trained in an unsupervised fashion.

Table 1: Models’ performance on localizing abnormalities and detection rate normal and cancer | AD | Mass | Cals | Normal
---|---|---|---|---
Model |  Dice |  cDR |  Dice |  cDR |  Dice |  cDR |  nDR
U-Net |  0.47 |  0.71 |  0.64 |  0.87 |  0.44 |  0.71 |  0.09
U-Net attention |  0.48 |  0.79 |  0.66 |  0.87 |  0.40 |  0.68 |  0.09
U-Net++ |  0.60 |  0.86 |  0.68 |  0.89 |  0.38 |  0.58 |  0.08
SegResNet |  0.58 |  0.86 |  0.63 |  0.85 |  0.39 |  0.61 |  0.21
V-Net |  0.46 |  0.64 |  0.58 |  0.75 |  0.29 |  0.45 |  0.08
UFCN-T |  0.66 |  0.86 |  0.61 |  0.76 |  0.59 |  0.61 |  0.17
UFCN-R |  0.35 |  0.64 |  0.58 |  0.73 |  0.36 |  0.55 |  0.58
UFCN |  0.60 |  0.79 |  0.69 |  0.91 |  0.57 |  0.74 |  0.73

In addition to evaluating cancer detection rates and Dice scores, we also
assessed the model’s performance in detecting normal and cancer cases in terms
of Accuracy, Sensitivity, Precision, and F1 scores (see Table 2). Notably, all
the baseline models do not perform well when applied to normal cases. The
baseline models originally proposed to identify abnormal tissue areas in
cancer images, and it often relies on pre-classified cancer data. This
limitation causes the baseline models to fail to distinguish between cancer
and normal cases. As a result, the U-Net model shows poor performance in terms
of Accuracy ($0.41$), Sensitivity ($0.43$), and F1 score ($0.56$) but a better
Precision score ($0.80$). The SegResNet showed slightly better performance in
Accuracy ($0.47$) and Sensitivity ($0.46$) compare with U-Net. The V-Net shows
least performance in terms of all evaluation metrices.

Table 2: Models’ cancer and normal detection performance Model |  Accuracy |  Sensitivity |  Precision |  F1
---|---|---|---|---
U-Net |  0.41 |  0.43 |  0.80 |  0.56
U-Net attention |  0.42 |  0.43 |  0.80 |  0.56
U-Net++ |  0.40 |  0.42 |  0.79 |  0.55
SegResNet |  0.47 |  0.46 |  0.78 |  0.58
V-Net |  0.34 |  0.37 |  0.64 |  0.47
UFCN-T |  0.43 |  0.43 |  0.73 |  0.54
UFCN-R |  0.62 |  0.57 |  0.67 |  0.62
UFCN |  0.78 |  0.72 |  0.84 |  0.78

Although UFCN-T shows a higher detection rate for architectural distortion and
microcalcification, its normal detection rate is lower, and its accuracy
($0.43$), sensitivity ($0.43$), and F1 score ($0.54$) are comparable with
those of U-Net. Similar to U-Net, the precision score of UFCN-T yields the
third-best result. UFCN-R shows a better normal detection rate compared to
U-Net and UFCN-T. However, the trade-off to increasing the normal detection
rate in UFCN-R is a lower detection rate for cancer cases. Hence, its accuracy
($0.62$), sensitivity ($0.57$), and F1 score ($0.62$) are the second-best
results. However, its precision is the lowest compared to those of the other
models. The proposed UFCN shows the best performance in terms of all the
evaluation metrics compared to the other models. The UFCN achieves the best
normal detection rate ($0.73$) while still maintaining a better performance
for cancer detection. As Table 2 demonstrates, UFCN shows the best accuracy
($0.78$), sensitivity ($0.72$), precision ($0.84$), and F1 score ($78$).

###  6.2 Cancerous case results

Figure 4: Outputs of the baseline and proposed models. The first row shows
current year, second row shows prior year, and third row shows ground truth
(GT) images. The yellow circle is enlarged area for better visualization. F
indicate failed to localize abnormal tissue.

We examined the AVM outputs of the propose model and its variant and also the
segmentation outputs of the baseline models. As shown in Figure 4, UFCN’s
prediction is very close to the ground truth annotations. Especially for
architectural distortion ( 4.e.) and microcalcification ( 4.a.), the UFCN can
generates more precise abnormal tissue maps (Figure 4 a & e). As can be seen
in Figure 4.a, U-Net, attention U-Net, U-Net++ and SegResNet models fail to
detect microcalcification. UFCN-R misses the detection for architectural
distortion. As mentioned before, the hard floor of ReLU causes the active
region to shrink as shown in the Figure. UFCN-T generates larger abnormal
tissue areas compared with UFCN and UFCN-R.

Figure 5: A demo for special cases. a. The abnormal tissue area is located at
breast skin. b. There is a normal high intensity region.

What stands out in our results is the skin tumor case as shown in Figure 5.a.
This case was only in our test data set. As the figure shows, the U-Net model
misses the skin area and wrongly detects a few other regions as tumor
locations. On the other hand, the proposed UFCN model is able to precisely
generate the abnormal region, which indicates that the ASG module in the
proposed model was not activated in the breast tissue area, but instead it was
activated in the area where the abnormal changes were exist. This demonstrates
the effectiveness of the ASG mechanism in accurately localizing the abnormal
tissue region in medical images. Furthermore, this finding highlights the
importance of developing models that are specifically designed to handle
diverse abnormalities in medical images. The proposed UFCN model demonstrates
superior performance in detecting abnormal tissue areas, including those that
may not be related to the specific medical condition under consideration, such
as in the case of skin tumors.

In Figure 5.b., we visualized the output maps generated by all baseline models
and our proposed UFCN on a mass case. As can be observed in Figure 5.b., U-Net
mistakenly identified a bright round area as an abnormal tissue region,
leading to false negative detection. This limitation is a common issue with
U-Net, where non-cancerous bright round areas are frequently misidentified as
abnormal. U-Net++ and SegResNet also failed to detect cancer in this
particular case. In contrast, our proposed model, UFCN, effectively
distinguishes between normal and abnormal bright areas by comparing current
and previous images. Consequently, the abnormal variation map (AVM) generated
by UFCN shows more precise and accurate cancer detection.

###  6.3 Non-cancerous results

Figure 6: The models’ output of baseline model and proposed models. The first
column is current year image, second column is prior year. The black output
indicate no any suspicious tissue detected.

The Figure 6 illustrates the prediction of all the models when inputs are
normal cases. All baseline models showed detected tissues, and the wrongly
detected tissue locations are similar in all models. Although UFCN-R showed
minor wrongly detected tissue areas compared with U-Net and UFCN-T, it still
performed relatively well. However, the proposed model UFCN showed no
detection of abnormal tissues in these normal cases, indicating its high
accuracy in distinguishing between normal and abnormal cases.

In summary of our study, we demonstrate that by learning the differences
between the current and prior images we can achieve unsupervised cancer area
localization. Labeling in medical image studies is expensive and prone to
errors, making unsupervised learning an ideal approach. Our results show that
with prior images, the proposed model can achieve results as good as those of
a supervised model. Additionally, the proposed model outperformed the
supervised model in detecting complex tumors that the latter was unable to
detect.

Overall, our study highlights the potential of unsupervised learning for
medical image analysis, particularly for tasks such as cancer area
localization. By leveraging longitudinal data and advanced machine learning
techniques, we can reduce the need for costly and time-consuming manual
labeling while still achieving high levels of accuracy and sensitivity in
cancer detection. These findings have important implications for improving the
efficiency and effectiveness of cancer screening and diagnosis, ultimately
leading to better patient outcomes.

##  7 Conclusion

Breast cancer remains a leading cause of death for women worldwide. Early
detection and accurate diagnosis of breast abnormalities are crucial for
improving patient outcomes. However, traditional screening methods such as
mammography have limitations in terms of accuracy and sensitivity, leading to
missed or misdiagnosed cases. One of the main challenges in detecting cancer
is the lack of large annotated datasets to train advanced segmentation models.

To address this issue, we developed a novel unsupervised feature correlation
network to predict breast abnormal variation maps using 2D mammograms. Our
proposed model takes advantage of the reconstruction process of the current
year and prior year images to extract tissue from different areas without a
need for ground truth. By analyzing the differences between the two images,
our model can identify abnormal variations that may indicate the presence of
cancer.

The model is embedded with a novel feature correlation module, an attention
suppression gate, and a breast abnormality module, all of which work together
to improve the accuracy of the prediction. The feature correlation module
allows the model to identify patterns and relationships between different
features, while the attention suppression gate helps to filter out irrelevant
information. The breast abnormality module then uses this information to
classify the input as normal or cancerous.

Notably, our proposed model not only provides breast abnormal variation maps
but is also able to distinguish between normal and cancer inputs, making it
more advanced compared to the state-of-the-art segmentation models. The state-
of-the-art segmentation models need already classified cancer images, which
requires applying a classification method first, then, using the segmentation
method. The results of our study show that the proposed model outperforms or
performs as well as the supervised state-of-the-art segmentation models not
only in localizing abnormal regions but also in recognizing normal tissues.

## Acknowledgments

This work is supported by a grant from the University of Connecticut Research
Excellence Program, PIs: Nabavi and Yang. This work used the Bridges-2 system
at the Pittsburgh Supercomputing Center (PSC) as part of the Extreme Science
and Engineering Discovery Environment (XSEDE) which is supported by the
National Science Foundation, under project number CIS220028, PI: Nabavi.

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