11institutetext: School of Software, Shandong University, China
22institutetext: Joint SDU-NTU Centre for Artificial Intelligence Research
(C-FAIR),
Shandong University, China 33institutetext: Joint NTU-Webank Research
Institute on Fintech,
Nanyang Technological University, Singapore 44institutetext: Joint NTU-UBC
Research Centre of Excellence in Active Living for the Elderly,
Nanyang Technological University, Singapore 55institutetext: College of
Computing and Data Science, Nanyang Technological University, Singapore
55email<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
# Multi-modal Food Recommendation using Clustering and Self-supervised
Learning

Yixin Zhang 1122 Xin Zhou 33 Qianwen Meng 1122 Fanglin Zhu 1122
Yonghui Xu 22 Zhiqi Shen 4455 Lizhen Cui 1122

###### Abstract

Food recommendation systems serve as pivotal components in the realm of
digital lifestyle services, designed to assist users in discovering recipes
and food items that resonate with their unique dietary predilections.
Typically, multi-modal descriptions offer an exhaustive profile for each
recipe, thereby ensuring recommendations that are both personalized and
accurate. Our preliminary investigation of two datasets indicates that pre-
trained multi-modal dense representations might precipitate a deterioration in
performance compared to ID features when encapsulating interactive
relationships. This observation implies that ID features possess a relative
superiority in modeling interactive collaborative signals. Consequently,
contemporary cutting-edge methodologies augment ID features with multi-modal
information as supplementary features, overlooking the latent semantic
relations between recipes. To rectify this, we present CLUSSL, a novel food
recommendation framework that employs CLUstering and Self-Supervised Learning.
Specifically, CLUSSL formulates a modality-specific graph tailored to each
modality with discrete/continuous features, thereby transforming semantic
features into structural representation. Furthermore, CLUSSL procures recipe
representations pertinent to different modalities via graph convolutional
operations. A self-supervised learning objective is proposed to foster
independence between recipe representations derived from different unimodal
graphs. Comprehensive experiments on real-world datasets substantiate that
CLUSSL consistently surpasses state-of-the-art recommendation benchmarks in
performance.

###### Keywords:

Food Recommendation Multi-modal Clustering Self-supervised Learning.

##  1 INTRODUCTION

Dietary intake is a critical determinant of human health and well-being,
impacting both physiological and psychological states. Food recommendation
systems (FRSs) aim to leverage user interaction data, multi-modal content, and
ingredient information to personalize recipe suggestions that align with
individual dietary needs. FRSs have seen notable advancements in recent years,
driven by increased research interest and a wider range of lifestyle
applications [12, 9].

With the pervasive presence of multi-modal data linked to recipes,
contemporary advancements have witnessed the assimilation of abundant
metadata, encompassing elements such as ingredients and visual attributes, to
enhance the precision of recommendations. For example, HAFR [1] jointly models
interaction data, ingredients, and visual features. Similarly, SCHGN [13]
further considers higher-order relationships and calorie intake preferences.
However, these methods predominantly leverage user, recipe, and ingredient IDs
to capture collaborative signals, relegating multi-modal information to
secondary feature roles. Meanwhile, our preliminary investigation (Table 1)
demonstrates that directly utilizing continuous representations (embeddings)
derived from multi-modal features (e.g., image and text embeddings) for
collaborative filtering (CF) tasks may degrade recommendation performance. In
contrast, using discrete features such as IDs yields superior results.
Interestingly, employing ingredient information, also a discrete feature, as
recipe embeddings leads to competitive performance. These findings suggest
that discrete features are more effective in capturing the underlying
structure of the data. Consequently, multi-modal models like FREEDOM [30]
propose an item-item graph construction based on similarities between
transformed multi-modal features, where item IDs encapsulate the structural
relationships derived from these features. While it can represent some level
of similarity through item-item graphs, it fails to explicitly model the
underlying categorical taxonomy (e.g., desserts, casseroles) that defines a
crucial aspect of recipe semantics. This deficiency hinders its capacity to
effectively integrate and discriminate between latent thematic categories
within the culinary domain.

Table 1: Performance of different modalities as item embedding w.r.t. LightGCN
[6].

LightGCN | Allrecipes | Food.com
---|---|---
Recall@20 | NDCG@20 | Recall@20 | NDCG@20
—ID | 0.1147 | 0.0572 | 0.1365 | 0.0960
—Ingredient | 0.1140 | 0.0578 | 0.1466 | 0.1034
—Image | 0.1111 | 0.0557 | 0.1377 | 0.0932
—Text | 0.1136 | 0.0562 | 0.1365 | 0.0932

ID means default setting of [6]. For ingredient, we lookup ingredient
embedding table and aggregate the corresponding representations as item
embeddings. For image and text, we use the pre-trained features as item
embeddings via an additional projector.

To this end, this work proposes CLUSSL, a novel multi-modal food
recommendation model that employs clustering and self-supervised learning.
Specifically, CLUSSL utilizes a novel two-stage approach to exploit multi-
modal recipe information for recommendation. In the first stage, unsupervised
clustering is applied to unimodal data (e.g., image features, text embeddings)
with pre-trained continuous representations. These clusters act as “prototype
nodes”, summarizing the key semantic features within each modality.
Subsequently, for each modality, a modality-specific graph is constructed to
capture the relationships between these prototype nodes. This graph
construction leverages ID features to encode the inherent structure of the
data. Graph convolutional networks are then employed to effectively propagate
and aggregate these semantic relationships across the graphs, allowing CLUSSL
to exploit the rich relational information embedded within each modality.
Furthermore, CLUSSL incorporates a distance correlation constraint within a
self-supervised learning framework. This constraint ensures that the learned
recipe representations from different modalities (e.g., image-based and text-
based) maintain a degree of independence. By combining these techniques,
CLUSSL leverages the strengths of both unimodal data and multi-modal
relationships, leading to demonstrably improved recommendation accuracy
compared to existing baselines, as confirmed by extensive evaluations on real-
world datasets.

##  2 RELATED WORK

In this section, we review the most relevant existing methods in food
recommendation and multi-modal recommendation.

###  2.1 Food Recommendation

In response to the diversified needs for food, FRSs are committed to providing
accurate and personalized recommendation services for users. Recently,
leveraging recipe metadata, such as ingredients and images, within the general
CF framework has proven effective in mitigating data sparsity challenges and
refining user preference modeling. HAFR [1] develops a hierarchical attention
mechanism to incorporate the feature interaction between metadata for
recommendation. Moving beyond traditional methods, FGCN [2] explores
leveraging graph neural networks to capture high-order relationships through
graph propagation and aggregation. Furthermore, SCHGN [13] captures the user’s
preference on food calories with self-supervised heterogeneous graph network.
In addition, RecipeRec [15] constructs heterogeneous recipe graphs to model
the structure. GreenRec [18] accommodates health criteria into recommender to
promote sustainable lifestyles.

###  2.2 Multi-modal Recommendation

Multi-modal recommendation systems (MMRSs) strive to enhance items’
representation for better recommendation performance by incorporating features
from different modalities, including textual content and visual content [25,
19, 20, 21, 22]. Early studies, such as VBPR [5], incorporate multi-modal
contents with items’ ID embeddings to extend the general CF framework.
Inspired by the great success of graph-based recommendation methods [6, 31,
28, 17, 24], MMGCN [16] attempts to inject high-order semantics into user/item
representations via message passing on modality-specific graphs. From another
perspective, FREEDOM [30] constructs item-item semantic graph from pre-trained
multi-modal features to supplement the user-item interactions. An emerging
trend is the integration of self-supervised learning methods into MMRSs,
showcasing a notable boost. BM3 [32] and LGMRec [3] improve user and item
representation learning by adopting contrastive learning objective. DRAGON
[26] utilizes homogeneous graphs based on item multi-modal information and a
heterogeneous bipartite user-item graph for effective recommendation. DGVAE
[29] disentangles the user-item interactions and multi-modal information with
graph learning.

##  3 PRELIMINARIES

In this section, we formulate the problem of food recommendation with multi-
modal information and introduce the construction of the modality-specific
graph.

###  3.1 Problem Formulation

We formally define the problem as follows. Let $\mathcal{U}$ denote the set of
users and $\mathcal{I}$ denote the set of food recipes. The user-recipe binary
interaction matrix is denoted by
$\mathcal{Y}\in\\{0,1\\}^{|\mathcal{U}|\times|\mathcal{I}|}$, where
$|\mathcal{U}|$ and $|\mathcal{I}|$ represent the cardinalities of users and
recipes, respectively. Each entry $\mathcal{Y}_{u,i}=1$ indicates that user
$u$ has interacted with recipe $i$. Associated with each recipe $i$ is the
following modality information: i) modality information with discrete
features. We only consider recipe-ingredient relationships, denoted as
$\mathcal{M}_{\mathcal{A}_{i}}\in\\{0,1\\}^{|\mathcal{A}|}$. The collection of
ingredients across all recipes forms the complete ingredient set
$\mathcal{A}$, with cardinality $|\mathcal{A}|$. ii) modality information with
continuous features. In this work, we focus on visual features
$\mathcal{M}_{v_{i}}\in\mathbb{R}^{d_{v}}$ and textual features
$\mathcal{M}_{t_{i}}\in\mathbb{R}^{d_{t}}$. Specifically,
$\mathcal{M}_{v_{i}}$ are obtained from image of recipe $i$ through ResNet
[4], while $\mathcal{M}_{t_{i}}$ are extracted from textual description of
recipe $i$ using a pre-trained T-5 model [10].

Based on the given notation, our objective is to predict the probability that
user $u$ will consume recipe $i$, taking into account user-recipe interactions
and the recipe’s multi-modal information.

###  3.2 Construction of Modality-Specific Graphs

Although heterogeneous graphs can include multiple types of vertices and
edges, which helps to alleviate data sparsity and improve recommendation
effectiveness [13, 15], their complex structure poses significant challenges
for model training. In this work, we propose constructing modality-specific
bipartite graphs based on the discrete or continuous features for each
modality.

####  3.2.1 Construct Bipartite Graph via Discrete Features.

Given the ingredient set $\mathcal{A}=\\{a\\}$ and the recipe set
$\mathcal{I}=\\{i\\}$, the observed relationships between these sets are
captured by the matrix
$\mathcal{R}^{\mathcal{A}}\in\\{0,1\\}^{|\mathcal{A}|\times|\mathcal{I}|}$,
where each entry $\mathcal{R}_{a,i}^{\mathcal{A}}=1$ if ingredient $a$ belongs
to item $i$, otherwise $\mathcal{R}_{a,i}^{\mathcal{A}}=0$. The $i$-th column
denotes the discrete features $\mathcal{M}_{\mathcal{A}_{i}}$ of recipe $i$
regarding the ingredient modality. Based on the relationship matrix
$\mathcal{R}^{\mathcal{A}}$, we construct a bipartite graph
$\mathcal{G}_{\mathcal{A}}=\\{(a,\mathcal{R}_{a,i}^{\mathcal{A}},i)|a\in\mathcal{A},i\in\mathcal{I},\mathcal{R}_{a,i}^{\mathcal{A}}=1)\\}$.

Figure 1: (a) exemplifies a recipe with its associated modalities, (b)
showcases the construction of the modality-specific graph via continuous
multi-modal features, and (c) illustrates the overall framework of the
proposed CLUSSL.

####  3.2.2 Construct Bipartite Graph via Continuous Features.

According to [8], closely binding item representations with raw modality
features learned by pre-trained model can be detrimental. Thus, instead of
using raw feature as an individual node representations, we introduce
modality-specific cluster centres as “prototype nodes”. Specifically, taking
visual features as an example, we utilize K-means to cluster the modality
feature vectors into $|\mathcal{N}_{v}|$ cluster centers, i.e.,
$\mathcal{N}_{v}$ denotes visual prototype nodes. Then we select the top $k$
nearest prototypes to define the visual-specific relationships for each recipe
and form the matrix
$\mathcal{R}^{v}\in\\{0,1\\}^{|\mathcal{N}_{v}|\times|\mathcal{I}|}$, where
each entry $\mathcal{R}_{n,i}^{v}=1$ if prototype node $n$ belongs to top $k$
set of recipe $i$, otherwise $\mathcal{R}_{n,i}^{v}=0$. Based on the
relationship matrix $\mathcal{R}^{v}$, we construct a bipartite graph
$\mathcal{G}_{v}=\\{(n,\mathcal{R}_{n,i}^{v},i)|n\in\mathcal{N}_{v},i\in\mathcal{I},\mathcal{R}_{n,i}^{v}=1)\\}$.
Similarly, we construct the textual-specific bipartite graph
$\mathcal{G}_{t}=\\{(n,\mathcal{R}_{n,i}^{t},i)|n\in\mathcal{N}_{t},i\in\mathcal{I},\mathcal{R}_{n,i}^{t}=1)\\}$.

##  4 METHODOLOGY

This section delves into the individual components of CLUSSL. The overall
architecture of the proposed method is illustrated in Fig. 1.

###  4.1 Graph Collaborative Filtering Backbone

In general, GNN-based CF methods [6] produce informative representations for
users and items based on the message propagation and aggregation scheme, which
exploit higher-order connectivity in the user-item graph and achieve state-of-
the-art performance for recommendation. Following [32, 30, 3] , we employ an
efficient and effective LightGCN [6] as backbone to encode the structure of
the user-recipe bipartite graph. Formally, we denote this user-recipe graph as
$\mathcal{G}=\\{(u,\mathcal{Y}_{u,i},i)|n\in\mathcal{U},i\in\mathcal{I},\mathcal{Y}_{n,i}=1)\\}$
based on user-recipe interaction matrix
$\mathcal{Y}\in\mathbb{R}^{|\mathcal{U}|\times|\mathcal{I}|}$. We obtain the
adjacency matrix of the user-item graph as follows:

$\displaystyle\mathbf{A}=\begin{pmatrix}0\;&\;\mathcal{Y}\\\
\mathcal{Y}^{T}\;&\;0\end{pmatrix}.$ (1)

Given $l$-th layer embedding matrix $\mathbf{H}^{l}$, the simplifed message
passing process in LightGCN is defined as:

$\displaystyle\mathbf{H}^{l+1}=(\mathbf{D}^{-1/2}\mathbf{A}\mathbf{D}^{-1/2})\mathbf{H}^{l},$
(2)

where $\mathbf{H}^{0}\in\mathbb{R}^{(|\mathcal{U}|+|\mathcal{I}|)\times d}$ is
the $0$-th layer embedding matrix. User embeddings are randomly initialized
and recipes embeddings are learned through different modality-specific graphs
(introduced in section 4.2). $\mathbf{D}$ is a
$(|\mathcal{U}|+|\mathcal{I}|)\times(|\mathcal{U}|+|\mathcal{I}|)$ diagonal
matrix, also called as degree matrix, and the node embeddings of the
$(l+1)$-th layer are only linearly aggregated from the $l$-th layer with a
symmetrically normalized matrix
$\mathbf{D}^{-1/2}\mathbf{A}\mathbf{D}^{-1/2}$. Lastly, representations from
all hidden layers are aggregated through a readout function to obtain the
final embedding matrix used for recommendation:

$\displaystyle\mathbf{H}_{u}$
$\displaystyle=\text{READOUT}(\mathbf{H}_{u}^{0},\mathbf{H}_{u}^{1},\dots,\mathbf{H}_{u}^{L}),$
$\displaystyle\mathbf{H}_{i}$
$\displaystyle=\text{READOUT}(\mathbf{H}_{i}^{0},\mathbf{H}_{i}^{1},\dots,\mathbf{H}_{i}^{L}),$
(3)

where $\mathbf{H}_{u}$ and $\mathbf{H}_{i}$ denote the final representations
of user $u$ and recipe $i$, respectively, the READOUT function can be any
differentiable function. Common designs include weighted sum, last-layer only,
and others. We use the default mean function [30, 32] in practice.

To generate recipe recommendations for user $u$, we first predict the
interaction scores between the user and candidate recipes. Then, we rank
candidate recipes based on the predicted scores in descending order and select
the top-k recipes as recommendations for the user. The interaction score is
calculated as:

$\displaystyle\hat{y}_{u,i}={\mathbf{H}_{u}}^{T}\mathbf{H}_{i},$ (4)

where $\hat{y}_{u,i}$ is the prediction score of user $u$ towards recipe $i$.
A high score suggests that the user prefers the recipe.

To capture the collaborative information from implicit feedback, we adopt
Bayesian Personalized Ranking (BPR) loss [11] in model training. Specifically,
BPR loss ensures that the prediction score of the observed interactions higher
than sampled unobserved ones. Formally:

$\displaystyle\mathcal{L}_{Rec}=\sum_{(u,i^{+},i^{-})\in\mathcal{O}}-\textit{log}\sigma(\hat{y}_{u,i^{+}}-\hat{y}_{u,i^{-}}),$
(5)

where $\sigma$ is the sigmoid function,
$\mathcal{O}=\\{(u,i^{+},i^{-})|\mathcal{Y}_{u,i^{+}}=1,\mathcal{Y}_{u,i^{-}}=0\\}$
denotes the pairwise training data, and $i^{-}$ denotes a sampled recipe that
user $u$ has not interacted with.

###  4.2 Unimodal Graph Representation Learning

Given the modality-specific bipartite graphs $\mathcal{G}_{\mathcal{A}}$,
$\mathcal{G}_{v}$, and $\mathcal{G}_{t}$ towards different modalities, we
employ graph convolutional networks to perform information propagation and
aggregation. Without losing generality, we use LightGCN as the graph encoder,
which similar to Eq. 2 and Eq. 4.1 derived from the corresponding adjacency
matrix Eq. 1. We transform these discrete features into dense-valued vectors
through embedding lookup tables: recipes
($\mathbf{E}_{\mathcal{I}}\in\mathbb{R}^{|\mathcal{I}|\times d}$), ingredients
($\mathbf{E}_{\mathcal{A}}\in\mathbb{R}^{|\mathcal{A}|\times d}$), image
prototypes ($\mathbf{E}_{v}\in\mathbb{R}^{|\mathcal{N}_{v}|\times d}$), and
text prototypes ($\mathbf{E}_{t}\in\mathbb{R}^{|\mathcal{N}_{t}|\times d}$),
where $d$ is the embedding space dimensionality. Utilizing these embeddings as
the initial representations ($0$-th layer), we perform graph propagation and
aggregation on each modality-specific graph to obtain the final
representations of recipe $i$, denoted as $\mathbf{E}^{\mathcal{A}}_{i}$,
$\mathbf{E}^{v}_{i}$, and $\mathbf{E}^{t}_{i}$, respectively.

Based on the embeddings mentioned above, we aggregate these embeddings to
define the $0$-th embedding of recipe $i$ in Eq. 2:

$\displaystyle\mathbf{H}_{i}^{0}=\text{Aggregate}(\mathbf{E}^{\mathcal{A}}_{i},\mathbf{E}^{v}_{i},\mathbf{E}^{t}_{i}).$
(6)

In this work, we simply define $\text{Aggregate}(\cdot)$ as vector summation.
The embedding $\mathbf{H}_{i}^{0}$ encompasses holistic perspective of the
recipe’s multi-modal profile, which is further used to capture collaborative
information from user-recipe interactions.

###  4.3 Cross-modal Self-supervised Learning

To ensure the stability of learning recipe representations across different
modality-specific graphs, we propose a self-supervised regularization to
encourage the recipe representations (i.e., $\mathbf{E}^{\mathcal{A}}_{i}$,
$\mathbf{E}^{v}_{i}$, and $\mathbf{E}^{t}_{i}$) to preserve sufficient
independent information and avoid information redundancy. Although we learn
the representations from different modality-specific graphs, there might still
be redundancy due to high-order aggregation. To further promote independence
among these representations, we adopt the distance correlation [14, 23] as a
regularization technique. Distance correlation can capture the relationship
between representations learned from different modalities while encouraging
them to retain informative independence. Formally, we define it as follows:

$\displaystyle\mathcal{L}_{Cor}=\sum_{m,n\in\\{\mathcal{A},v,t\\},m\neq
n}\frac{dCov(\mathbf{E}^{m}_{i},\mathbf{E}^{n}_{i})}{\sqrt{dVar(\mathbf{E}^{m}_{i})\cdot
dVar(\mathbf{E}^{n}_{i})}},$ (7)

where $dCov(\cdot)$ is the distance covariance between two matrices, and
$dVar(\cdot)$ represents its own distance covariance.

###  4.4 Multi-task Learning

The proposed CLUSSL can be optimized in an end-to-end manner through a unified
objective function, defined as follows:

$\displaystyle\mathcal{L}=\mathcal{L}_{Rec}+\lambda\sum_{i\in(i^{+},i^{-})}\mathcal{L}_{Cor}+\eta\|\Theta\|_{2}^{2},$
(8)

where $\lambda$ is trade-off coefficient that balance the contributions of the
self-supervised loss. $\eta$ and $\Theta$ represent the $L_{2}$ regularization
coefficient and model parameters, respectively.

##  5 EXPERIMENTS

###  5.1 Experimental Settings

####  5.1.1 Dataset.

We conduct experiments on two datasets collected from real-world platforms
www.allrecipes.com and www.food.com. Each recipe in the datasets includes its
ingredients, texts, images and the corresponding ratings from users, as shown
in Fig. 1(a). Among them, the ratings in the range of [1,5], we treat each
rating as an implicit feedback record. Following [1, 13], we holdout the
latest $30\%$ of interaction history to construct the test set, and split the
remaining data into training $(60\%)$ and validation $(10\%)$ sets. The
statistics of two datasets after preprocessing are summarized in Table 2.

Table 2: Statistics of the experimental dataset. Characteristics | Allrecipes | Food.com
---|---|---
#Users | 68,768 | 7,596
#Items | 45,630 | 29,943
#Interactions | 1,093,845 | 323,199
#Ingredients | 19,987 | 5,098
Sparsity (%) | 99.96 | 99.85

####  5.1.2 Metrics and Evaluation.

During training, we sample one negative recipe for each user-recipe pair in
the training set. The performance of different methods is assessed by two
widely used evaluation metrics: Recall@$K$ and Normalized Discounted
Cumulative Gain@$K$ (denoted by NDCG@$K$), where K is empirically set to 10
and 20. For each metric, we first compute the accuracy for each user on the
testing data, and then report the averaged accuracy for all testing users.
Following [1, 13], there are 500 sampled negative recipe with popularity bias
for one user and her interacted recipes in the test set.

####  5.1.3 Baseline Methods.

We compare the proposed CLUSSL with the following baseline methods. General
Collaborative Filtering: BPR [11], NeuMF [7], LightGCN [6]. Multi-Modal
Recommendation: VBPR [5], MMGCN [16], BM3 [32]. FREEDOM [30], LGMRec [3]. Food
Recommendation: HAFR111https://github.com/elisagao122/HAFR [1], FGCN [2],
SCHGN222https://github.com/TAEYOUNG-SYG/SCHGN [13].

####  5.1.4 Implementation Details.

All the baseline methods are implemented by PyTorch 333https://pytorch.org/
and evaluated on a NVIDIA TITAN RTX GPU card. For fair comparison, the hyper-
parameters of baseline methods are selected following the original paper, and
the optimal settings are determined based on the grid-search and validation
set. Multi-modal baselines are implemented based on the unified MMRec
framework [27]. For the proposed CLUSSL, we empirically set batch size to 512,
embedding size to 64, learning rates to 0.002 and 0.001 for Allrecipes and
Food.com, respectively. Step decay of the learning rate is also adopted. The
regularization coefficient $\eta$ is set to 0.01. The trade-off coefficient
$\lambda$ tuned in {0, 0.001, 0.005, 0.01, 0.05, 0.1, 0.5, 1}. The number of
GCN layers, prototype nodes are also searched in grad. The number of top-$k$
nearest prototypes are set to 6 and 10 for Allrecipes and Food.com,
respectively. We repeat the experiments five times and report the average
results.

###  5.2 Performance Comparison

The performance achieved by different recommendation methods on two real-world
datasets are summarized in Table 3. From the table, we have the following
observations.

Table 3: The recommendation performance achieved by different methods. The
best results are in boldface, and the second best results are underlined.

Method | Allrecipes | Food.com
---|---|---
Recall@10 | Recall@20 | NDCG@10 | NDCG@20 | Recall@10 | Recall@20 | NDCG@10 | NDCG@20
BPR | 0.0637 | 0.1101 | 0.0418 | 0.0555 | 0.0750 | 0.1255 | 0.0726 | 0.0877
NeuMF | 0.0636 | 0.1106 | 0.0411 | 0.0550 | 0.0741 | 0.1253 | 0.0725 | 0.0879
LightGCN | 0.0668 | 0.1147 | 0.0430 | 0.0572 | 0.0829 | 0.1365 | 0.0802 | 0.0960
VBPR | 0.0667 | 0.1115 | 0.0453 | 0.0575 | 0.0757 | 0.1315 | 0.0757 | 0.0923
MMGCN | 0.0669 | 0.1143 | 0.0440 | 0.0580 | 0.0767 | 0.1293 | 0.0744 | 0.0901
BM3 | 0.0676 | 0.1152 | 0.0442 | 0.0583 | 0.0810 | 0.1313 | 0.0793 | 0.0938
FREEDOM | 0.0710 | 0.1191 | 0.0441 | 0.0585 | 0.0843 | 0.1405 | 0.0827 | 0.0996
LGMRec | 0.0661 | 0.1119 | 0.0452 | 0.0586 | 0.0849 | 0.1409 | 0.0847 | 0.1008
HAFR | 0.0703 | 0.1142 | 0.0480 | 0.0608 | 0.0712 | 0.1248 | 0.0685 | 0.0855
FGCN | 0.0666 | 0.1138 | 0.0426 | 0.0567 | 0.0756 | 0.1284 | 0.0725 | 0.0886
SCHGN | 0.0720 | 0.1186 | 0.0480 | 0.0617 | 0.0818 | 0.1338 | 0.0744 | 0.0906
CLUSSL | 0.0880 | 0.1372 | 0.0690 | 0.0822 | 0.0943 | 0.1516 | 0.1144 | 0.1262

Firstly, the superiority of CLUSSL. The proposed CLUSSL demonstrates
significant superiority over general CF models, multi-modal recommendation
models and the state-of-the-art food recommendation models across all dataset.
This indicates that the proposed CLUSSL is exceptionally well-designed for
food recommendation, effectively leveraging both multi-modal information with
discrete and continuous features.

Secondly, the effectiveness of multi-modal features. By incorporating multi-
modal features reasonably, almost all models have achieved better performance.
For instance, VBPR outperforms the backbone BPR. Multi-modal recommenders
based on LightGCN (i.e., BM3, FREEDOM, and LGMRec) basically achieve better
results than LightGCN alone. Additionally, HAFR and SCHGN take into account
not only visual features but also and ingredients information, demonstrating
superior performance over other multi-modal models on Allrecipes.

Thirdly, the variability of modal semantics on performance. Almost all multi-
modal models showcase improved recommendation results. However, we observe
that the performance of BM3 is inferior to LightGCN on Food.com. Moreover,
HAFR and SCHGN are designed to deeply integrate multi-modal features with the
recipe embeddings for prediction, yet their performance on Food.com is less
than satisfactory. One potential reason might be that interactive
collaborative signals are more easily captured by deep networks in relatively
dense datasets, leading complex multi-modal semantics to contribute adverse
effects without well-designed modules. The proposed CLUSSL mitigates this
issue by transforming semantic features into structural representation.

Finally, the effectiveness of self-supervised learning. SCHGN achieves better
performance than HAFR by employing a self-supervised ingredient prediction
objective. BM3 and LGMRec leverage contrastive learning as an auxiliary
optimization function, achieving notable success. We also partially attribute
significant improvements of CLUSSL to self-supervised learning. More in-depth
discussions can be found in ablation study and sensitivity analysis.

###  5.3 Ablation Study

To study the importance of each component of CLUSSL, we consider the following
CLUSSL variants for evaluation: i) w/o $\mathcal{M}_{v_{i}}$, ii) w/o
$\mathcal{M}_{t_{i}}$, iii) w/o $\mathcal{M}_{\mathcal{A}_{i}}$. These
variants involve removing specific modal features related to recipes, thereby
excluding their respective modality-specific graphs. iv) w/o
$\mathcal{L}_{Cor}$: we set $\lambda$ to 0 in Eq. 8 to eliminate the self-
supervised learning component.

Table 4: The recommendation performance of CLUSSL and its variants. Method | Allrecipes | Food.com
---|---|---
Recall@20 | NDCG@20 | Recall@20 | NDCG@20
w/o $\mathcal{M}_{v_{i}}$ | 0.1214 | 0.0655 | 0.1477 | 0.1176
w/o $\mathcal{M}_{t_{i}}$ | 0.1240 | 0.0677 | 0.1479 | 0.1236
w/o $\mathcal{M}_{\mathcal{A}_{i}}$ | 0.1268 | 0.0694 | 0.1477 | 0.1196
w/o $\mathcal{L}_{Cor}$ | 0.1246 | 0.0621 | 0.1487 | 0.1110
CLUSSL | 0.1372 | 0.0822 | 0.1516 | 0.1262

Table 4 summarizes the performance of CLUSSL variants on Allrecipes and
Food.com datasets. Several observations are noteworthy: CLUSSL consistently
outperforms w/o $\mathcal{M}_{v_{i}}$, w/o $\mathcal{M}_{t_{i}}$, and w/o
$\mathcal{M}_{\mathcal{A}_{i}}$ across both datasets, indicating that removing
any multi-modal information leads to decreased performance. This underscores
the utility of all modalities in enhancing recommendation accuracy.
Additionally, the effectiveness of these modalities varies. Generally, visual
features prove more crucial than textual or ingredient features. Textual
information often contains redundant data, while ingredient features are
confined by predefined sets. In contrast, visual features vividly depict food
appearance, color, shape, and composition, crucial for stimulating user
interest and appetite, thereby offering significant advantages. Furthermore,
experiments w/o $\mathcal{L}_{Cor}$ highlight the role of the self-supervised
learning in improving recipe representations for food recommendation. By
promoting distinctiveness across modalities, CLUSSL ensures independence among
multi-modal information, thereby enhancing recommendation effectiveness.

###  5.4 Parameter Sensitivity Study

We also perform experiments to study the impacts of three hyper-parameters:
the trade-off coefficient $\lambda$, the number of prototypes in graph
$\mathcal{G}_{v}$ and $\mathcal{G}_{t}$, and the top-$k$ nearest prototypes.
Fig. 2 shows the performance of CLUSSL with respect to different settings of
these three hyper-parameters on both datasets.

Figure 2: The performance trends of CLUSSL with respect to different settings
of coefficient $\lambda$, prototypes number, and top-$k$ nearest on Allrecipes
and Food.com datasets.

As depicted in Fig. 2, the results of the coefficient $\lambda$ on the two
datasets showcase a consistent trend: the performance first improves to reach
optimal and then declines as $\lambda$ increases. These results suggest that
reasonable self-supervised constraints enable recipe representations to retain
more comprehensive information, thereby enhancing recommendation performance.
Regarding the number of prototypes, the performance trend appears relatively
stable. Additionally, the best performance is achieved by setting top-$k$ to 6
and 10 on Allrecipes and Food.com datasets, respectively.

##  6 CONCLUSION

In this paper, we propose a novel food recommendation model, namely CLUSSL,
which employs clustering to transform modal semantics into modality-specific
graph across each modality. Moreover, CLUSSL leverages cross-modal self-
supervised learning to encourage that recipe representations induced by
different modality-specific graphs preserve sufficiently independent
information. The backbone network can further benefit from independent
representations with the self-supervised constraints, which providing superior
performance. Experimental results on two real-world datasets verify that
CLUSSL consistently outperforms state-of-the-art baseline recommendation
models.

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# Space-resolved Chemical Information from Infrared Extinction Spectra

Kalpa de Silva1, Proity Akbar2, and Reinhold Blümel1 1Department of Physics,
Wesleyan University, Middletown, Connecticut 06459-0155  2Department of
Chemistry, Wesleyan University, Middletown, Connecticut 06459-0155

###### Abstract

Based on the classical Lorentz model of the index of refraction, a new method
is presented for the extraction of the complex index of refraction from the
extinction efficiency of homogeneous and layered dielectric spheres that
simultaneously removes scattering effects and corrects measured extinction
spectra for baseline shifts, tilts, curvature, and scaling. No reference
spectrum is required and the method automatically satisfies the Kramers-Kronig
relations. Thus, the method yields pure absorbance spectra for unambiguous
interpretation of the chemical information of the sample. In the case of
homogeneous spheres, the method also determines the radius of the sphere. In
the case of layered spheres, the method determines the radii of the layers and
the substances within each layer. Only a single-element detector is required.
Using simulated $Q_{ext}$ data of polymethyl-methacrylate (PMMA) and
polystyrene homogeneous and layered spheres we show that our reconstruction
algorithm is reliable and accurately extracts pure absorbance spectra from
$Q_{ext}$ data. Reconstructing the pure absorbance spectrum from a published,
experimentally measured raw absorbance spectrum shows that our method also
works for uncorrected spectra, reliably removes scattering effects and, given
shape information, simultaneously corrects for spectral distortions.

##  I Introduction

With roots going back several decades in time, infrared (IR) spectroscopy has
evolved into one of the most powerful and successful tools for the analysis of
biological cells and tissues for applications in biophysics, chemistry, and
medical pathology Bha (12); MRDW (05); LBZ+ (15); JDM+ (98). Far from being a
successful, but stagnant field of study, with the recent advent of tunable IR
laser sources HM (16), IR spectroscopy is currently experiencing growing
interest and expansion into new fields of application. No matter whether the
spectra are taken with thermal, laser, or synchrotron IR sources, two tasks
always have to be performed: (1) Cleaning up of the raw spectra and (2)
reconstructing the refractive index (revealing the chemistry) of the
(biological) sample under investigation. Powerful tools exist for cleaning up
the spectra, i.e., removing artefacts introduced by the spectrographs and IR
sources that result, e.g., in baseline shifts, tilts, curvature, and
multiplicative distortions of the spectra SGP+ (19); VDMCB (13).

This paper focuses on single-cell IR spectroscopy where the cell sizes are
approximately of the same order of magnitude as the wavelength of the incident
IR radiation. Thus, the corresponding IR spectra exhibit pronounced scattering
effects, such as Mie scattering Hul (81), that modify absorbance spectra
considerably and need to be removed before interpreting the spectra.

In this paper we present a new technique that is based on the classical
Lorentz model of the index of refraction Gri (99) and is capable of
accomplishing the tasks (1) and (2) above without the need of a reference
spectrum SGP+ (19) or the Kramers-Kronig relations SGP+ (19); VDMCB (13) as
required by leading spectral correction methods. For our examples, we use two
substances, polymethyl-methacrylate (PMMA) and polystyrene (PS).

##  II Methods

In subsection II.1 we start by describing the general method used in IR
spectroscopy. Then, in subsection II.2, we describe our method of
reconstructing the space- and wavenumber-dependent complex index of refraction
$\eta(\vec{r},\tilde{\nu})$, i.e., the hyperspectral complex refractive index,
that is based on the classical Lorentz model Gri (99) of the index of
refraction. Concluding this section, based on the methods described in
subsections II.1 and II.2, we describe in subsection II.3 our numerical
procedures for reconstructing the complex refractive index
$\eta(\vec{r},\tilde{\nu})$, and with it pure absorbance spectra (i.e.,
$\Im[\eta(\vec{r},\tilde{\nu})]$).

###  II.1 General

Typically in single-detector IR spectroscopy, a beam of IR radiation of
wavelength $\lambda$ (wavenumber $\tilde{\nu}=1/\lambda$) and intensity
$I_{0}(\tilde{\nu})$ is directed toward a target that may be a biological
cell, a sample of biological tissue, or a grain of biological or inanimate
matter, and the transmitted intensity $I(\tilde{\nu})$ is measured in forward
direction. Because of absorption of IR radiation by the target, and because of
scattering of IR radiation out of the forward direction, we have
$I(\tilde{\nu})<I_{0}(\tilde{\nu})$. Once $I(\tilde{\nu})$ is measured, the
result of the measurements is typically reported as the apparent absorbance

${\cal
A}(\nu)=-\log_{10}\left[\frac{I(\tilde{\nu})}{I_{0}(\tilde{\nu})}\right].$ (1)

While the apparent absorbance ${\cal A}$ is convenient for recording and
reporting experimental results, cross sections are more convenient for
analysis of experiments, numerical simulations, and the extraction of
refractive indexes. We denote by $\sigma_{\rm scat}$ and $\sigma_{\rm abs}$
the scattering and absorption cross sections, respectively. Then, the
extinction cross section is defined as Hul (81)

$\sigma_{\rm ext}=\sigma_{\rm scat}+\sigma_{\rm abs}.$ (2)

We also define scattering, absorption, and extinction efficiencies according
to Hul (81)

$Q_{\rm scat}=\sigma_{\rm scat}/g,\ \ \ Q_{\rm abs}=\sigma_{\rm abs}/g,\ \ \
Q_{\rm ext}=\sigma_{\rm ext}/g,$ (3)

respectively, where $g$ is the geometric cross section of the sample under
investigation. Denoting by $G\gg g$ the reception area of the detector, the
radiative power received by the detector without the sample present is

$P_{0}=GI_{0}$ (4)

and the radiative power received by the detector with the sample present is

$P_{I}=GI=GI_{0}-I_{0}\sigma_{ext}.$ (5)

From this, we obtain

$Q_{\rm ext}=\frac{\sigma_{\rm
ext}}{g}=\frac{GI_{0}-GI}{gI_{0}}=\left(\frac{G}{g}\right)\left[1-\left(\frac{I}{I_{0}}\right)\right].$
(6)

Via (1), this can immediately be related to the apparent absorbance ${\cal A}$
according to

$Q_{\rm ext}=\left(\frac{G}{g}\right)\left[1-10^{-{\cal A}}\right].$ (7)

Since, via (7), $Q_{\rm ext}$ and ${\cal A}$ contain the same information, we
will, in the following, present our theoretical analysis and reconstructions
of refractive indexes on the basis of $Q_{\rm ext}$ or ${\cal A}$ depending on
convenience.

###  II.2 Reconstruction via Classical Lorentz Model

The main point of our method is to extract the space- and wavenumber-dependent
complex index of refraction $\eta(\vec{r},\tilde{\nu})$ from $Q_{\rm
ext}(\tilde{\nu})$. This may sound ambitious, since $Q_{\rm ext}(\tilde{\nu})$
has no space dependence. Nevertheless, it is possible, at least for a sphere
with two layers, as demonstrated in Section III. To implement the method, we
discretize space into voxels, which can be any shape or size. The smaller, the
more resolution. The more regular (such as cubes or shells), the easier the
computations. Labeling the voxels with the discrete index $j=1,\ldots,J$, and
denoting by $\vec{r}_{j}$ a representative point of voxel number $j$ (for
instance its center in the case of cubes or a point on the center shell in the
case of shells), we represent the refractive index inside of a voxel by its
(spatially) constant value
$\eta(\vec{r}_{j},\tilde{\nu})\equiv\eta_{j}(\tilde{\nu})$, which varies in
wavenumber as a sum of Lorentzians of the form

$\eta_{j}(\tilde{\nu})=\sum_{m=1}^{M}\frac{h_{m}^{(j)}}{1+[(\tilde{\nu}-\tilde{\nu}_{m}^{(j)}/\Gamma_{m}^{(j)}]^{2}},\
\ \ j=1,\ldots,J,$ (8)

where, inside voxel number $j$, $\tilde{\nu}_{m}^{(j)}$ is the wavenumber
location of an IR absorption band, $h_{m}^{(j)}$ is the corresponding peak
height, $\Gamma_{m}^{(j)}$ is the width of the absorption band, $m=1,\ldots,M$
numbers the absorption bands, and $M$, a parameter, decides how many bands we
include in our reconstructions. $\tilde{\nu}_{m}^{(j)}$, $h_{m}^{(j)}$, and
$\Gamma_{m}^{(j)}$ are adjustable parameters to be determined via a 3D
scattering code such that the $Q_{\rm ext}(\tilde{\nu})$ predicted on the
basis of (8) optimally reproduces $Q_{\rm ext}^{({\rm given})}(\tilde{\nu})$,
where $Q_{\rm ext}^{({\rm given})}(\tilde{\nu})$ is the given $Q_{\rm
ext}(\tilde{\nu})$, either obtained experimentally, or from a numerical
simulation (see Section III).

In the simplest case, the entire scatterer may be represented as a single
voxel, in which case $M=1$. This is appropriate for homogeneous scatterers,
i.e., scatterers with a spatially constant index of refraction, such as a
homogeneous sphere. Another example is a sphere with two layers, i.e., a core
and a shell, each homogeneously filled with a medium of spatially constant
index of refraction as discussed in Section III. In this case two voxels,
i.e., the core and the shell, suffice, each endowed with its own series (8) of
Lorentzians. The method now determines the unknown parameters
$\tilde{\nu}_{m}^{(j)}$, $h_{m}^{(j)}$, and $\Gamma_{m}^{(j)}$ as the optimum
values that best reproduce $Q_{\rm ext}^{({\rm given})}(\tilde{\nu})$. This
can be done with any standard nonlinear fit algorithm that minimizes a target
function $S$, for instance,

$S[\tilde{\nu}_{m}^{(j)},h_{m}^{(j)},\Gamma_{m}^{(j)}]=\sum_{l}\left\\{Q_{\rm
ext}^{({\rm
model})}[\tilde{\nu}_{m}^{(j)},h_{m}^{(j)},\Gamma_{m}^{(j)};\tilde{\nu}_{l}]-Q_{\rm
ext}^{({\rm given})}(\tilde{\nu}_{l})\right\\}^{2},$ (9)

where $Q_{\rm ext}^{({\rm
model})}[\tilde{\nu}_{m}^{(j)},h_{m}^{(j)},\Gamma_{m}^{(j)};\tilde{\nu}_{l}]$
is the extinction efficiency evaluated at $\tilde{\nu}_{l}$ with fit
parameters $\tilde{\nu}_{m}^{(j)}$, $h_{m}^{(j)}$, and $\Gamma_{m}^{(j)}$,
computed via a suitable 3D scattering code and $\tilde{\nu}_{l}$ are the
wavenumbers at which $Q_{\rm ext}^{({\rm given})}(\tilde{\nu})$ has been
measured or pre-determined numerically.

The main characteristic of the Lorentzian method is that, in contrast to other
spectral-correction methods (e.g., SGP+ (19)), no reference spectrum is needed
to scatter-correct $Q_{\rm ext}$ spectra, whether simulated via a forward
model or obtained experimentally, and that no Kramers-Kronig transformation is
needed. This is so, since the complex Lorentzian functions in (8)
automatically satisfy the Kramers-Kronig relations, and thus
$\eta_{j}(\tilde{\nu})$, as a finite sum of such functions, automatically
satisfies the Kramers-Kronig relations as well.

###  II.3 Numerical Simulations

To demonstrate the power of the Lorentzian method, we performed four types of
numerical simulations, labeled I, II, III, and IV. Types I, II, and III are
for homogeneous spheres and type IV is for a layered sphere.

In our type-I simulations, we fit accurate experimental data for
$\eta(\tilde{\nu})$ of PMMA TYKY (18) and PS MTD+ (18) with $M=18$ (PMMA) and
$M=22$ (PS) Lorentzians, respectively, and compute $Q_{\rm ext}^{({\rm
given})}(\tilde{\nu})$ with $\eta$ in (8) using a standard Mie scattering
code. The results of these type-I simulations are presented and discussed in
Section III.1.1.

In our type-II simulations, we compute $Q_{\rm ext}^{({\rm
given})}(\tilde{\nu})$ directly on the basis of the experimental data for
$\eta$. The results of our type-II simulations are presented and discussed in
Section III.1.2.

Our type-III simulations take $Q_{\rm ext}^{({\rm given})}(\tilde{\nu})$
directly from an experimental absorbance spectrum published in BBLK (16). In
this case we also perform baseline, tilt, scaling, and curvature corrections
of the experimental raw spectrum, by adding the baseline-, tilt-, scaling-,
and curvature parameters as additional fit parameters to our Lorentzian
method. As shown in Section III.1.3 this works very well, and thus our
Lorentzian method performs both the correction of raw spectra and scattering
corrections in a single step, without the need of a reference spectrum or the
Kramers-Kronig transform.

In our type-IV simulations, we use our Lorentzian method to reconstruct the
complex space-dependent index of refraction for a sphere with two layers,
i.e., PMMA in the core and PS in the shell. This is a case with two voxels,
i.e., $j=1$ representing the complex refractive index in the core and $j=2$
representing the complex refractive index in the shell. In this case, we
construct $Q_{\rm ext}^{({\rm given})}(\tilde{\nu})$ using a standard Mie code
for stratified spheres with $\eta^{({\rm PMMA})}(\tilde{\nu})$ in the core and
$\eta^{({\rm PS})}(\tilde{\nu})$ in the shell, both taken directly from the
corresponding experimental complex refractive indexes. The results of these
simulations, reported in Section III.2, prove that the Lorentzian method with
only a single-element detector, and a single $Q_{\rm ext}(\tilde{\nu})$ as
input, can reveal space-dependent chemistry, at least for this two-layer
model.

One characteristic feature of our Lorentzian method is that, initially, as
starting conditions, we place $M$ Lorentzians, equi-spaced (unbiased) into the
wavenumber interval under consideration. This way, in addition to using random
initial values for Lorentzian peak heights and peak widths, we obtain an
initial condition that is not only unbiased, but an initial Lorentzian peak is
always near to an actual absorption peak in the pure absorbance spectrum,
which then needs only a relatively small adjustment in position, height, and
widths, to morph into the actual absorption peak. This feature is crucial. It
avoids, to a large extent, getting trapped in secondary optimization minima,
i.e., a stationary but not global minimum of the target function $S$ [see
(9)]. We can still get trapped in secondary minima, but because of our choice
of equi-spaced initial Lorentzian positions, the chance of getting trapped in
a secondary minimum that results in a particularly bad fit is vastly reduced.

##  III Results

In this section we apply our Lorentzian reconstruction method to two important
cases: (a) Homogeneous spheres (see Section III.1) and (b) layered spheres
(see Section III.2). While these examples are important for testing validity
and robustness of our method, IR spectroscopy on homogeneous and layered
spheres may also have practical importance, for instance in mineralogy, or for
characterizing micro- and nano-spheres, such as PMMA or PS spheres. PMMA
spheres, in particular, are frequently used as model systems for biological
cells VDMCB (13); BBLK (16); LBZ+ (15); BBB+ (09).

###  III.1 Homogeneous Spheres (types I, II, and III)

In this section we demonstrate the validity of our reconstruction method for
homogeneous spheres, all of radius $10\mu$m, in three steps, working with two
different substances: PMMA and PS. We start by simulating PMMA and PS $Q_{\rm
ext}^{({\rm given})}(\tilde{\nu})$ spectra based on a Lorentzian approximation
of the complex refractive index and show that for all three substances our
method exactly reconstructs the complex index of refraction (see Section
III.1.1). Then, we simulate PMMA and PS $Q_{\rm ext}^{({\rm
given})}(\tilde{\nu})$ spectra based directly on experimental data of the
complex index of refraction and demonstrate that in this case, as well, near-
perfect reconstructions are obtained (see Section III.1.2). Finally, we
reconstruct the complex index of refraction from an experimentally measured
PMMA spectrum BBLK (16), which also includes baseline, tilt, scale, and
curvature corrections (see Section III.1.3). We show that a satisfactory
result is achieved in this case as well.

####  III.1.1 Lorentzian Extinction (type-I)

Approximating the experimental data of $\eta$ by a set of Lorentzians, and
computing $Q_{\rm ext}^{({\rm given})}(\tilde{\nu})$, on the basis of these
Lorentzians, we obtain the reconstructions of the real and imaginary parts of
the refractive index as shown in Fig. 1. Although we start with initial
conditions (green lines) that are far off the final result (magenta lines), we
see that our reconstructions (magenta lines) overlap the target refractive
indexes (blue lines) nearly perfectly. This shows that our type-I
reconstructions are near perfect. Given that we start our reconstruction
algorithm (green lines) far from the target (blue lines) it also shows that
our Lorentzian reconstruction algorithm is robust. Adding to the robustness,
we also simulated reconstructions (not shown) adding 10% noise to $Q_{\rm
ext}^{({\rm given})}(\tilde{\nu})$. We obtained reconstructed spectra of
similar accuracy. This shows that our reconstruction algorithm is robust also
to perturbations in $Q_{\rm ext}^{({\rm given})}(\tilde{\nu})$. Thus, the main
result of this section is that our Lorentzian method works well and is robust
with respect to initial conditions and noise.

(a) PMMA reconstruction; real part of $\eta$.

(b) PMMA reconstruction; imaginary part of $\eta$.

(c) PS reconstruction; real part of $\eta$.

(d) PS reconstruction; imaginary part of $\eta$.

Figure 1: Reconstructions of real and imaginary parts of the complex
refractive index $\eta$ of PMMA and PS using a Lorentzian fit to experimental
data (blue lines) for obtaining $Q_{\rm ext}^{({\rm given})}(\tilde{\nu})$. 18
Lorentzians were used for the PMMA reconstructions and 22 Lorentzians were
used for the PS reconstructions. Although the initial guess of the complex
refractive indexes is random (green lines), the reconstructions (magenta
lines) are near perfect.

####  III.1.2 Extinction based on experimental refractive index (type-II)

In this section we make it slightly harder for our reconstruction algorithm by
not approximating the experimental refractive index by Lorentzians, but
compute $Q_{\rm ext}^{({\rm given})}(\tilde{\nu})$ directly on the basis of
the experimental complex $\eta$. The result is shown in Fig. 2. Again,
although starting far from the optimal values of the Lorentzian fit
parameters, we obtain near perfect reconstructions of real and imaginary
refractive indexes. In this case, too, we checked for the influence of noise,
and found our algorithm robust with respect to noise perturbations.

(a) PMMA reconstruction; real part of $\eta$.

(b) PMMA reconstruction; imaginary part of $\eta$.

(c) PS reconstruction; real part of $\eta$.

(d) PS reconstruction; imaginary part of $\eta$.

Figure 2: Reconstructions of real and imaginary parts of the complex
refractive index $\eta$ of PMMA and PS using experimental data (blue lines)
for obtaining $Q_{\rm ext}^{({\rm given})}(\tilde{\nu})$. 18 Lorentzians were
used for the PMMA reconstructions and 22 Lorentzians were used for the PS
reconstructions. Although the initial guess of the complex refractive indexes
is random (green lines), the reconstructions (magenta lines) are near perfect.

####  III.1.3 Experimental Extinction (type-III)

In our third numerical experiment concerned with homogeneous spheres, we
reconstructed the complex PMMA refractive index from an experimental apparent
absorbance spectrum BBLK (16), simultaneously performing baseline-, tilt-,
scaling-, and curvature corrections of the the raw spectrum. The result is
shown in Fig. 3. Starting our Lorentzian reconstruction algorithm once more
with random initial conditions, we obtained reconstructions (magenta lines) of
the real and imaginary parts of the complex PMMA index of refraction in
satisfactory agreement with the experimental data (blue lines). This shows
that our algorithm also works for experimental raw spectra that are neither
scatter corrected, nor corrected for experimental systematic errors. Our
algorithm can handle both simultaneously without the need of a reference
spectrum or the Kramers-Kronig transformation.

(a) PMMA reconstruction from experimental data; real part of $\eta$.

(b) PMMA reconstruction from experimental data; imaginary part of $\eta$.

Figure 3: Reconstructions of real and imaginary parts of the complex
refractive index $\eta$ of PMMA (blue lines) for an experimental PMMA
extinction spectrum of a PMMA sphere BBLK (16). 18 Lorentzians were used for
the reconstructions. Although the initial guess of the complex refractive
index is random (green lines), the reconstructions (magenta lines) of real and
imaginary parts are close to their experimental values.

###  III.2 Layered Sphere (type-IV)

In Section III.1 we concentrated on exploring the power of our Lorentzian
method in the well-defined case of homogeneous spheres. We now ask the
question whether our Lorentzian algorithm is powerful enough to obtain the
space-resolved complex refractive index, i.e., via the imaginary part of the
complex refractive index (absorption), space-resolved chemistry. To answer
this question, we focus on a stratified sphere with two layers. We fill the
core of the layered sphere with PMMA, the shell with PS, and compute $Q_{\rm
ext}^{({\rm given})}(\tilde{\nu})$ on the basis of (8) with $M=2$. The outer
radius of the sphere is $10\mu$m; the inner radius, i.e., the core radius, is
$8\mu$m. For the PMMA refractive index in the core we used experimental PMMA
data. For the PS refractive index in the shell, we used the known imaginary
part of the refractive index and computed the real part using the Kramers-
Kronig transformation. We emphasize that the use of the Kramers-Kronig
transformation in this case has nothing to do with our reconstruction
algorithm (which never uses the Kramers-Kronig transformation), and is used
only to generate the real part of the PS refractive index. We could have, as
well, used a complete set of PS experimental data for real and imaginary parts
of the refractive index, avoiding the Kramers-Kronig transformation
altogether, but we were unable to locate a suitable, published set. In any
case, constructing $Q_{\rm ext}^{({\rm given})}(\tilde{\nu})$ on the basis of
this input, we obtained the reconstructions of the complex indexes of
refraction in the core and in the shell as shown in Fig. 4.

The result of our Lorentzian reconstruction of the space-dependent complex
refractive index is shown in Fig. 4. We see that, not only does our Lorentzian
algorithm, based only on the extinction efficiency, correctly identify the two
substances and their spatial locations (PMMA in the core and PS in the shell),
the reconstructions themselves (magenta lines) are close to their actual
values (blue lines). This is encouraging, the more that, again, we started
from completely unbiased, random initial conditions (green lines). This
demonstrates that our Lorentzian algorithm is capable of revealing space-
resolved chemistry based only on a single-element detector. We mention that we
also used our Lorentzian method to discover the core and sphere radii, assumed
unknown. In this case we add the core and sphere radii as additional
parameters to our Lorentzian method. We found that in this case our Lorentzian
method is not only able to reconstruct the complex indexes of refraction, but
simultaneously also determines the core and sphere radii. As a result of this
type-IV simulation, we find that in this case, too, we can reconstruct the
complex refractive indexes, space- and wavenumber-dependent, simultaneously
with determining sphere size and information on internal structure (in this
case the core radius, which may stand for the nucleus of a biological cell).

(a) Reconstruction of the real part of $\eta$ of the core material; it is
correctly identified as the real part of $\eta$ of PMMA.

(b) Reconstruction of the imaginary part of $\eta$ of the core material; it is
correctly identified as the imaginary part of $\eta$ of PMMA.

(c) Reconstruction of the real part of $\eta$ of the shell material; it is
correctly identified as the real part of $\eta$ of PS.

(d) Reconstruction of the imaginary part of $\eta$ of the shell material; it
is correctly identified as the imaginary part of $\eta$ of PS.

Figure 4: Reconstructions of real and imaginary parts of the complex
refractive index $\eta$ (blue lines) for a layered sphere consisting of PMMA
in the core and PS in the shell. $Q_{\rm ext}^{({\rm given})}(\tilde{\nu})$
was produced via a standard Mie scattering code for stratified spheres. 18
Lorentzians were used for the PMMA reconstructions and 22 Lorentzians were
used for the PS reconstructions. The Lorentz reconstruction algorithm,
although only looking at the total $Q_{\rm ext}^{({\rm given})}(\tilde{\nu})$
of the layered sphere (single-element detector), correctly identifies PMMA in
the core and PS in the shell. In addition, although the initial guesses of the
complex refractive indexes are random (green lines), the reconstructions
(magenta lines) of real and imaginary parts are close to their experimental
values (blue lines). This shows that space-resolved chemistry (in this case
for a sphere with two layers) is possible with a single-element detector
recording only radiation emitted in forward direction.

##  IV Discussion

In contrast to other spectroscopic methods, such as, e.g., Raman spectroscopy,
the IR power in IR spectroscopy is low and thus does not harm the cells. In
addition, since IR spectroscopy does not require staining, IR spectroscopy
does not alter the cells or the cell chemistry. Thus, IR spectroscopy enables
in-vivo investigations of cells and tissues. In their natural state,
biological cells have a 3D structure, which, combined with the fact that cells
and tissues have sizes that are of the order of the IR wavelength, leads to
large scattering contributions that need to be removed to obtain pure
absorbance spectra that only then can be interpreted as to their chemical
information content. Our new Lorentzian method, compact and powerful,
accomplishes just that, and, as demonstrated in Section III, can even be
combined with baseline, tilt, curvature, and scaling corrections of raw
spectra. The method is also suitable for extracting space-resolved chemistry
as demonstrated in Section III.2 with the help of a layered sphere.

Our results also show that focal plane arrays (FPAs) may not be necessary to
obtain space-resolved chemistry. For instance, as shown for the layered
sphere, a single-element detector suffices. FPAs may still be needed if the
scatterer has a more detailed shape or internal structure. However, rotating
the sample, or using different illumination directions, akin to X-ray
tomography, we may still get away with only a single-element detector.

Concerning stability and reliability of our Lorentzian method, we performed
several checks. (a) We perturbed the simulated $Q_{\rm ext}$ spectrum with up
to 10% of noise and found that reconstruction was still possible. (b) We
always start our reconstructions with random inputs for peak widths, peak
heights, and peak locations. We always find convergence to the correct pure
absorbance spectrum. This demonstrates that our method is robust and does not
require fine-tuning of input parameters.

With the advent of new IR sources, such as tunable quantum cascade lasers, IR
spectroscopy has recently received a rejuvenating boost that is ideally suited
for the application of our method, which works well with coherent illumination
of samples. We mention that in the case of coherent IR sources, optical
effects, such as interference and scattering are more important and more
controlled as compared with thermal IR sources (e.g., GLOBAR) or (partially
coherent) synchrotron sources. Thus, our Lorentzian method is ideally suited
for obtaining pure absorbance spectra in combination with coherent laser
sources. We also mention that lasers are cheaper and more accessible than
synchrotron sources, which makes our method ideally suited for laboratory
applications.

##  V Conclusion

In this paper we have shown that it is possible to reconstruct the spatially
resolved, wavenumber-dependent complex index of refraction (the spatially
resolved chemistry) of a sample on the basis of extinction spectra which
require only a single-element detector. The method is robust and reliable. It
can be extended in several directions. (a) How many different layers of a
stratified sphere can we resolve with a single-element detector? (b) Extension
of the method to spheres with internal structure that does not have rotational
symmetry. (c) Extension to 3D shapes with 3D internal structure. The most
important question to answer is the following: Up to what point is a single-
element detector enough, and at what point is it more advantageous to work
with an FPA? These topics define exciting directions for future research. In
addition, our method may find practical applications in biophysics, including
in medical diagnostics, medical pathology, and single-cell spectroscopy.

##  VI Acknowledgments

We thank the experimental team at the Norwegian University of Life Sciences
for the raw data of the experimental PMMA $Q_{\rm ext}$ spectrum published in
BBLK (16) which was used for the reconstructions shown in Fig. 3.

##  VII Author contributions

RB suggested the method and supervised the project. KdS coded and performed
all computer simulations. All authors contributed to the writing of the paper.

## References

  * BBB+ [09] Paul Bassan, Hugh J Byrne, Franck Bonnier, Joe Lee, Paul Dumas, and Peter Gardner.  Resonant Mie scattering in infrared spectroscopy of biological materials–understanding the ‘dispersion artefact’.  Analyst, 134(8):1586–1593, 2009.
  * BBLK [16] Reinhold Blümel, M Bağcioğlu, R Lukacs, and A Kohler.  Infrared refractive index dispersion of polymethyl methacrylate spheres from Mie ripples in Fourier-transform infrared microscopy extinction spectra.  Journal of the Optical Society of America, 33(9):1687–1696, 2016.
  * Bha [12] Rohit Bhargava.  Infrared spectroscopic imaging: the next generation.  Applied spectroscopy, 66(10):1091–1120, 2012.
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  * LBZ+ [15] R. Lukacs, R. Blümel, B. Zimmerman, M. Bağcıoğlu, and A. Kohler.  Recovery of absorbance spectra of micrometer-sized biological and inanimate particles.  Analyst, 140(9):3273–3284, 2015.
  * MRDW [05] B. Mohlenhöff, M. Romeo, M. Diem, and B. R. Wood.  Mie-type scattering and non-Beer-Lambert absorption behavior of human cells in infrared microspectroscopy.  Biophys. J., 88(5):3635–3640, 2005.
  * MTD+ [18] Tanya L. Myers, Russell G. Tonkyn, Tyler O. Danby, Matthew S. Taubman, Bruce E. Bernacki, Jerome C. Birnbaum, Steven W. Sharpe, and Timothy J. Johnson.  Accurate measurement of the optical constants $n$ and $k$ for a series of 57 inorganic and organic liquids for optical modeling and detection.  Applied Spectroscopy, 72(4):535–550, 2018.
  * SGP+ [19] J. H Solheim, Evgeniy Gunko, Dennis Petersen, Frederik Großerüschkamp, Klaus Gerwert, and Achim Kohler.  An open-source code for Mie extinction extended multiplicative signal correction for infrared microscopy spectra of cells and tissues.  J. Biophotonics, 12:e201800415, 2019.
  * TYKY [18] Shinichiro Tsuda, Shuhei Yamaguchi, Yoshiaki Kanamori, and Hiroo Yugami.  Spectral and angular shaping of infrared radiation in a polymer resonator with molecular vibrational modes.  Optics Express, 26(6):article number 318844, 2018.
  * VDMCB [13] Thomas Van Dijk, David Mayerich, P Scott Carney, and Rohit Bhargava.  Recovery of absorption spectra from Fourier transform infrared (FT-IR) microspectroscopic measurements of intact spheres.  Applied Spectroscopy, 67(5):546–552, 2013.


# A life cycle assessment of the ISIS-II Neutron
and Muon Source

H. M. Wakeling1<EMAIL_ADDRESS>John Adams Institute for
Accelerator Science  University of Oxford  U.K.
1also at the ISIS Neutron and Muon Source  Rutherford Appleton Laboratory
STFC  UK

###### Abstract

The ISIS-II Neutron and Muon source is the proposed next generation of, and
successor to, the ISIS Neutron and Muon Source based at the Rutherford
Appleton Laboratory in the United Kingdom. Anticipated to start construction
in 2031, the ISIS-II project presents a unique opportunity to incorporate
environmental sustainability practices from its inception. A Life Cycle
Assessment (LCA) will examine the environmental impacts associated with each
of the ISIS-II design options across the stages of the ISIS-II lifecycle,
encompassing construction, operation, and eventual decommissioning. This
proactive approach will assess all potential areas of environmental impact and
seek to identify strategies for minimizing and mitigating negative impacts,
wherever feasible. This paper will provide insights into the process and first
results of the LCA of the entirety of the ISIS-II project.

##  1 INTRODUCTION

Today, climate scientists report that to have a 50% chance of keeping the
Earth below the $1.5^{\circ}$C temperature increase from pre-industrial
baselines, humanity can only emit six more years of cumulative carbon dioxide
equivalent (CO2e) emissions at current levels [1]. Global tipping points, if
humanity continues as usual, could occur as soon as the 2030s[2].

Scientific research itself has environmental impacts; many of which are
largely reducible. To continue research for the overall benefit of humanity,
including aiding the fight to keep the Earth habitable, the research community
is swiftly altering practises and increasing efforts to reduce the direct
environmental impact of research activities [3].

The ISIS-II Neutron and Muon Source is proposed as the UK’s next generation
source for the international neutron and muon user community. The ISIS-II
project is currently at the feasibility and optioneering phase. This is the
stage of design which has most influence on the overall environmental impact
of the facility [4].

Understanding and identifying all environmental impacts, both major and minor,
is the first step in mitigating or reducing the proposed facility’s
environmental impact. Thus, as part of its efforts in environmental
consideration, the ISIS-II project is performing a Life Cycle Assessment (LCA)
to inform its design process.

Figure 1: The BS EN17472:2022 engineering standard for building LCAs, which
has been altered to be more applicable particle accelerator facilities [12].

##  2 METHODOLOGY OF AN ISIS-II LIFE CYCLE ASSESSMENT

An LCA is an environmental impact assessment standard. It is an iterative
four-step process that examines the life cycle of an object. The four steps
are:

  1. 1.

Goal & Scope

  2. 2.

Inventory Analysis

  3. 3.

Life Cycle Impact Assessment (LCIA)

  4. 4.

Life Cycle Interpretation (LCI)

To perform an LCA, resource information is required from each area of the
accelerator facility, thus the methodology for performing the LCA is broken
down into multiple steps.

As the ISIS-II facility is in the feasibility and design phase, performing a
simplified LCA of a still-to-be-designed facility can incur multiple sources
of uncertainty at many different levels. In particular, the current estimates
of materials and resources necessary for construction and operation of the
ISIS-II facility have large amounts of uncertainty. Thus an iterative approach
to an LCA is beneficial to the evaluation of the ISIS-II facility throughout
is evolving design process.

In addition, the complexity of a full LCA performed on a large accelerator
facility could be prohibitive in the progress towards results in a useful and
timely manner. Thus, the LCA that will be performed will be a “simplified"
LCA. In the first instance this means that the larger impacts will be
considered first, with more detail being added as it becomes available. In the
second instance, the LCA will require $>$90% of the materials and resources of
the ISIS-II facility to be defined, with the remaining undefined materials and
resources considered and accounted for. These undefined materials will not be
ignored and due diligence will be taken to ensure that their impact is not
significant with respect to the reported final results of the ISIS-II LCA.

###  2.1 Defining the Goal

The goal of the LCA is to identify the lowest lifetime environmental impact
between the proposed designs of the compression ring111Each of the ISIS-II
ring designs have a corresponding linear accelerator (LINAC) design necessary
to inject protons at the correct energy. for ISIS-II.

###  2.2 Deciding the Scope

It has been proposed for the ISIS-II facility to deliver a 2.4 MW beam of 1.2
GeV protons to the neutron and muon community. The construction of ISIS-II is
proposed to start in the 2030s. After construction, the operational lifetime
of ISIS-II (2040-2100) is defined using the expected 60 year lifetime of the
current ISIS neutron and muon source. The decommissioning due to radioactive
isotope storage restrictions is then expected to be limited to 70 years
(2100-70). Thus the functional unit of the final LCA is defined as: “One ISIS-
II facility that will deliver a beam of 1.2 GeV protons to the international
neutron and muon community over a period of 60 years, with a decommissioning
period of 70 years”.

The ISIS-II LCA will be consider the Cradle-to-Grave life cycle of ISIS-II and
its components. Fig. 1 is being used as a basis to compile the life cycle
inventory. The ReCiPe:2016[5] LCIA method has been chosen to evaluate the
Midpoint (H) impact factors222Radionuclides from operation and the
decommissioning stage may need an impact additional assessment method to be
adequately evaluated..

To exhibit the performance of a LCA for a particle accelerator facility using
open-source software and free-to-use (for academics) databases, OpenLCA
software (v2.0.3 [6]) and the Idemat [7] LCA database were used for the first
order-of-magnitude study. Idemat is a free database for academics and has a
large selection of data available to the user evaluating a particle
accelerator to the first order. In the next iteration of the LCA, this study
will move to the use of the Ecoinvent database [8]. This is due to the impact
that the temporal and geographical boundaries of that free-to-use databases
have on results that require more accuracy.

Uncertainties are provided in the estimation of the inventory data 333For a
direct measurement apply: 0%-5% uncertainty in the data; for reliable non-
measured data: 15% uncertainty; for calculated data and extrapolations: 30%
uncertainty; for approximated data: 50% uncertainty; and for order-of-
magnitude estimates: 80% uncertainty. following the example from Bilan Carbone
[9]. When performing the LCIA, a Monte Carlo simulation with a log-normal
distribution evaluates the result with the uncertainty of the inventory data
and data quality of the database (EcoInvent Data Quality System [8]).

###  2.3 Collecting An Inventory

Inventory collection comprises of an evaluation of all materials and resources
used in the construction, operation and decommissioning of ISIS-II. The design
and modelling of ISIS-II is far from complete, thus the first evaluations
performed for the LCA is of the components that are common in each of the
designs of ISIS-II. There is less uncertainty in the designs of common
components such as the Ion Source, low energy LINAC, the target and
instruments. Thus this study focuses on the ISIS-II LINAC up to a proton
energy of $180$ MeV. Where designs are not yet available, existing facilities
and components are used as models for the LCA:

  * •

Ion source and low energy LINAC: RAL Front End Test Stand (FETS)

    * –

H- Ion Source

    * –

Low Energy Beam Transfer (LEBT)

    * –

Radio-Frequency Quadrupole (RFQ)

    * –

Medium Energy Beam Transfer (MEBT)

  * •

Drift Tube LINAC (DTL): ISIS-II

  * •

Separated Drift Tube LINAC (SDTL): ISIS-II

  * •

LINAC shielding: ISIS-II

  * •

LINAC buildings and tunnelling: ISIS-II

This includes specific additional ancillaries (klystrons, moderators, vacuum
pumps), shielding, cut-and-cover tunnelling and buildings.

The operational data presented only includes UK grid electricity generation
CO2e emissions factor predicted up until the year 2050, which is then used as
a baseline value for the remaining operational years of ISIS-II [10].
Therefore, these specific operational impact results are predicted to be an
overestimate, particularly due to the current efforts to de-carbonise the UK
grid. The building data assumes a worst case scenario (WCS) build of 1,000 kg
CO2e per m2 of gross internal area [11] until further information on building
suppliers and methods are available.

##  3 INITIAL RESULTS

The LCA is an iterative assessment, allowing space for improvement of data
quality and, hence, uncertainties. Thus, first order-of-magnitude Global
Warming Impact (GWI) from the ReCiPe:2016 LCIA results are presented for the
ISIS-II facility for the low energy LINAC up to 180 MeV. Results presented
follow EN17472[12] stages A1-3 and B7. Results from the End of Life (C) study
- and therefore decommissioning of ISIS-II - are not yet available.

Figure 2: Distribution of the GWI for the construction materials (A1-A3)
between the FETS, DTL, SDTL, shielding and buildings for the 180 MeV LINAC.

It could be inferred from the order-of-magnitude result in Fig. 2 that the
construction materials of the ISIS-II 180 MeV LINAC buildings and shielding
structure of the accelerator could have a significantly higher environmental
impactful than the materials used in the fabrication of the accelerator
components in that section. In addition, the GWI of the defined ISIS-II LINAC
components shows construction (A1-5) and operation (B7) to be of the same
order of magnitude (Table 1).

Table 1: GWI of the 180 MeV LINAC for Cradle-to-Gate and Construction (A1-5) and the Lifetime Operational Energy Use (B7) Life Cycle | Global Warming
---|---
Information | [kt CO2 eq]
A. Construction | $\mathcal{O}(20)$
B. Operation | $\mathcal{O}(40)$
C. Decommissioning | TBC

This effectively provides a hotspot analysis result, indicating that our first
point of concern is focusing on reducing the environmental impact of the
buildings, structure and shielding of ISIS-II.

Ultimately, this study has been able to provide a first insight into the
environmental impact of a large accelerator facility, and has opened a
discourse on actions to be taken into consideration when designing ISIS-II.
With the expansion of the LCA to include more areas of the ISIS-II facility,
inclusion of more of its life-cycle, further reduction in uncertainty of
inventory estimations and access to more accurate models, the LCA will be able
provide a comprehensive evaluation of the full lifetime environmental impact
of the ISIS-II facility.

##  4 CONCLUSION

The first LCA results of the ISIS-II LINAC up to an energy of 180 MeV
indicates construction and operation to be of a similar order of magnitude.
With the shift of the UK grid towards net-zero, it can be expected that the
construction of the ISIS-II facility will have a higher GWI than its entire
lifetime of operations. Investigation is underway and efforts ongoing on
mitigating and reducing this environmental impact.

##  5 ACKNOWLEDGEMENTS

This work was supported by the Science and Technology Facilities Council via
ST/V001655/1 and the ISIS Neutron and Muon Source. Personal thanks to Alan
Letchford at RAL for providing first models of the DTL and SDTL for ISIS-II.

## References

  * [1] H. Ritchie, “How much CO2 can the world emit while keeping warming below 1.5°C and 2°C?”, Our World in Data, 2023
  * [2] “The Global Tipping Points Report”, 2023.
https://global-tipping-points.org

  * [3] Sustainable HECAP+ Initiative, “Environmental sustainability in basic research: a perspective from HECAP+”, submitted for publication.
  * [4] Institution of Civil Engineers, “Guidance Document for PAS 2080”, https://www.ice.org.uk/media/vm0nwehp/2023-03-29-pas_2080_guidance_document_april_2023.pdf
  * [5] M. Huijbregts, Z. Steinmann, P. Elshout, et al.. “ReCiPe2016: a harmonised life cycle impact assessment method at midpoint and endpoint level”, Int. J. Life Cycle Assess., vol. 22, p. 138–147, 2017.
https://doi.org/10.1007/s11367-016-1246-y

  * [6] GreenDelta, “openLCA V.2.0.3. Windows, macOS, and Linux”. 2024. https://openlca.org.
  * [7] Idemat, https://idematapp.com/.
  * [8] Ecoinvent, https://ecoinvent.org/.
  * [9] Association Bilan Carbone, “Methodological guidelines: Accounting principles and objectives”, https://abc-transitionbascarbone.fr/wp-content/uploads/2022/03/guide-methodologique-en-v2.pdf
  * [10] Statista, “Carbon intensity outlook of the power sector in Great Britain from 2020 to 2050”, https://www-statista-com.ezproxy-prd.bodleian.ox.ac.uk/statistics/1189677/carbon-intensity-outlook-of-great-britain/.
  * [11] Circular Ecology, “Net Zero Carbon Buildings by Circular Ecology”, https://circularecology.com/net-zero-carbon-buildings.html
  * [12] The British Standards Institution, “BS EN 17472:2022 Sustainability of construction works. Sustainability assessment of civil engineering works. Calculation methods”, 2022. doi:10.3403/30408035