# Enhancing breast cancer screening: Unveiling explainable cross-view contributions in dual-view mammography with Sparse Bipartite Graphs Attention Networks

Guillaume Pelluet, Mira Rizkallah, Mickael Tardy, Diana Mateus

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Guillaume Pelluet, Mira Rizkallah, Mickael Tardy, Diana Mateus. Enhancing breast cancer screening: Unveiling explainable cross-view contributions in dual-view mammography with Sparse Bipartite Graphs Attention Networks. Computerized Medical Imaging and Graphics, 2025, 125, pp.102620. 10.1016/j.compmedimag.2025.102620. hal-05421096

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# Enhancing breast cancer screening: Unveiling explainable cross-view contributions in dual-view mammography with Sparse Bipartite Graphs Attention Networks

Guillaume Pelluet a, b ID, Mira Rizkallah a ID, *, Mickael Tardy b ID, Diana Mateus a ID

## ARTICLE INFO

**Keywords:**

Breast cancer screening

Dual-view mammography

Bipartite Graphs

Graph Attention Networks

Sparse attentive explanations

## ABSTRACT

Medical imaging techniques like mammography enable early breast cancer detection and are part of regular screening programs. Typically, a mammogram exam involves two views of each breast, providing complementary information, but physicians rate the breast as a whole. Computer-Aided Diagnostic tools focus on detecting lesions in a single view, which is challenging due to high image resolution and varying scales of abnormalities. The projective nature of the two views and different acquisition protocols add complexity to dual-view analysis. To address these challenges, we propose a Graph Neural Network approach that models image information at multiple scales and the complementarity of the two views. To this end, we rely on a superpixel decomposition, assigning hierarchical features to superpixels, designing a dual-view graph to share information, and introducing a modified Sparse Graph Attention Layer to keep relevant dual-view relations. This improves interpretability of decisions and avoids the need to register pairs of views under strong deformations. Our model is trained with a fully supervised approach and evaluated on public and private datasets. Experiments demonstrate state-of-the-art classification and detection performance on Full Field Digital Mammographies, achieving a breast-wise AUC of 0.96 for the INbreast dataset, a sensitivity of 0.97 with few false positives per image (0.33), and a case-wise AUC of 0.92 for the VinDr dataset. This study presents a Sparse Graph Attention method for dual-view mammography analysis, generating meaningful explanations that radiologists can interpret. Extensive evaluation shows the relevance of our approach in breast cancer detection and classification.

## 1. Introduction

Breast cancer is one of the most prevalent types of cancer (Siegel et al., 2022). However, the early detection of breast cancer through screening significantly improves the chances of successful recovery (Warner, 2011). Typically, the screening process begins with a clinical examination, followed by imaging tests, with mammography being the most common (Shapiro et al., 1998). Unfortunately, mammographies are 2D X-ray images. The projection of superimposing tissues can create occlusions, e.g., a lesion might be occluded by dense tissues (illustrated in Fig. 1). During a standard mammogram, two low-dose X-ray images are taken of each breast to reduce the superimposition effect - one from top to bottom (craniocaudal view, denoted as CC) and one from the side (mediolateral oblique view, denoted as MLO), as shown in Fig. 1. The CC and MLO views follow different acquisition protocols, including distinct angles and palette compression levels. Radiologists use both

images to detect signs of breast cancer and guide patient care. This is known as ipsilateral analysis. Consequently, a radiologist interprets, on average, four mammographies per patient, which, multiplied by the increasing number of patients, results in a profusion of images to analyze.

In this context, there is a call for Computer-Aided Diagnosis (CAD) methods that reduce interpretation time and provide guidance in evaluating cancer likelihood. There has been a significant interest in developing such CAD methods, especially since the advent of deep-learning (Loizidou et al., 2023). Despite their promising classification and detection results, even in a clinical context (Ribli et al., 2018), most existing approaches focus on a mono-view analysis, e.g., Pelluet et al. (2022), Shen et al. (2021), Henriksen et al. (2019), Shen et al. (2019a) and Ribli et al. (2018).

<footnote>ª Nantes Université, École Centrale Nantes, CNRS, LS2N, UMR 6004, 1 Rue de la Noë, Nantes, 44000, France</footnote>

<footnote>ᵇHera-MI, SAS, 8 rue Duyau Trouin, Nantes, 44800, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: guillaume.pelluet@hera-mi.com (G. Pelluet), mira.rizkallah@ec-nantes.fr (M. Rizkallah), mickael.tardy@hera-mi.com (M. Tardy), diana.mateus@ec-nantes.fr (D. Mateus).</footnote>
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Dual-view mammogram acquisition of the CC and MLO views. An abnormality (red region) can be occluded by high-density tissue (white region) in one of the views (here in the CC) while being visible in the other due to the angle acquisition (here in the MLO). Color is recommended for a better visualization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

However, when analyzing an exam, radiologists first look for suspicious regions in one of the images. Then, they search in the ipsilateral view for malignant regions with compatible localizations, appearances, and sizes. If these criteria match, regions in both views are more likely to be malignant. Therefore, a dual-view analysis complements the mono-view inspection, reducing potential diagnosis errors. Likewise, building CAD algorithms relying on multiple views has improved global performance in classification and detection (Chen et al., 2024; Ribli et al., 2018).

Unfortunately, computer-aided breast cancer diagnosis based on dual-view mammography is challenging due to the significant breast deformations caused by compression during image acquisition (Fig. 1). To cope with deformations, several previous dual-view approaches rely on additional prior image alignment strategies (Yang et al., 2021; Liu et al., 2021b, 2020). Alternatively, some approaches (Chen et al., 2024; Yang et al., 2023; Wu et al., 2020) have suggested fusing the latent representations of the two views without initial detection or alignment steps. However, such methods have the disadvantage of being less interpretable.

As an intermediate solution between explicit alignment and implicit feature fusion, and similarly to the radiologist's reasoning, we propose a dual-view CAD approach based on a graph modeling the regions in the two views. It involves decomposing single views into regions at multiple scales, rating the suspiciousness of each region on each main view, and then relating lesion-like regions to potential abnormalities in the second view. We choose to represent these multi-scale and dual-view regions through a large graph that models connections within and across views, as malignant areas can have different scales and be found anywhere in the breast. Our approach removes the need for a prior alignment or detection as we exhaustively explore all possible pair-wise region matchings to extract relevant complementary information from the two views.

In practice, in this paper, we build upon our preliminary Multi-Scale Graph Convolutional Network (MSGCN) focused on mono-view classification and lesion detection. Two MSGCNs will be used here to represent each mammography's local and topological information independently. Moreover, different to the original MSGCN, we incorporate a more powerful multi-scale fully supervised feature extractor (Huang et al., 2020) to describe regions. We further introduce a novel dual-view bipartite graph to model ipsilateral relations. Bipartite graphs are characterized by having two disjoint and independent sets of nodes. In our case, each disjoint set corresponds to regions of a single mammogram, and bipartite edges connect all pairs of regions across views. Additionally, we frame the joint view classification problem as an

attention-learning task, allowing the classifier to make decisions by attending to meaningful edges only.

Unfortunately, given the mammograms' high resolution and our multi-scale processing, learning through a bipartite graph modeling all potential complementarities between ipsilateral regions becomes intractable. Consequently, we impose sparsity on the edge attention weights, encouraging them to focus exclusively on relevant complementary information. To achieve this, we adopt the Sparse Graph Attention (SGAT) approach proposed by Ye and Ji (2021). However, the original SGAT is unsuited for highly imbalanced graphs like ours. In our scenario, there are only a few expected malignant regions per view, yet these areas connect through numerous bipartite connections from the main view to the auxiliary view. To effectively handle such class imbalance, we propose a novel Class-Dependent Batch Normalization (denoted as CDBN), applied during the sparse attention update. Finally, unlike methods that fuse the dual views in the latent space, we argue that choosing a graph-based representation favors our approach's explainability (Ibrahim and Shafiq, 2023). Indeed, our method provides predictions at the ipsilateral, view-wise, and region levels. In addition, we generate heatmaps from the sparse attention on the bipartite graph to visualize and explain the interaction between the views.

In a nutshell, in this paper, we tackle different limits and challenges of CAD from mammography:

* Most existing CAD approaches do not leverage the complementarity between two views and instead focus on mono-view analysis.

* Malignant regions can have different scales calling for an explicit multi-scale analysis. Graph-based methods enabling such analysis, have only scarcely been studied in the context of mammography.

* Most dual-view CAD models, i.e., including the two views MLO and CC, require prior image alignment and/or lesion detection mechanisms due to the different acquisition angle, and the compression-induced deformations. Alignment and detection steps are however time-consuming and error prone under large deformations.

* Dual-view CAD methods that fuse information in the latent space lack explainability, rendering clinical deployment difficult.

In summary, our contributions are as follows:

1. We introduce an enriched multi-scale mono-view graph representation of each mammogram. More precisely, for each mammography view (MLO and CC), a multi-scale graph is constructed where nodes correspond to regions in different scales,
and connections are drawn within and across scales. Features of each node are assigned using a backbone feature extractor. This constitutes a semantically enriched representation of a mammogram.

2. We propose a novel local complementarity modelization of a dual-view exam through a fully connected bipartite graph, avoiding the need for image registration or lesion detection and matching stages.

3. We extract the relevant complementary information between the views by enforcing the graph attention between views to be sparse. We propose an adaptation of Ye and Ji (2021) to bipartite graphs and a new normalization to handle imbalanced classification cases.

4. We show how our method improves the explainability of the decision, highlighting relevant regions on each view and across views to assist better radiologists during diagnosis.

The results of our experiments on both public and private datasets, demonstrate that our method surpasses the state-of-the-art breast-wise classification and lesion detection. These experiments include validation on digital and digitized mammograms from various populations and unseen manufacturers and countries, coming from INBreast (Moureira et al., 2012), CMMD (Chunyan et al., 2021), VinDr (Nguyen et al., 2023), DDSM (Heath et al., 1998), and CBIS-DDSM (Lee et al., 2017).

## 2. Related work

Significant research has contributed to developing and improving computer-aided mammography analysis (Loizidou et al., 2023; Stadnick et al., 2021; Wang et al., 2025; Zhou et al., 2020; Du et al., 2019; George et al., 2019), and more recently to dual-view breast cancer analysis (Chen et al., 2024, 2022; Liu et al., 2021b, 2020; Ma et al., 2021; Wu et al., 2020). For both cases, an increased research emphasis has been placed on multi-scale approaches (Wang et al., 2025; Li et al., 2025) and graph-based representations (Zhou et al., 2020; Du et al., 2019; George et al., 2019; Liu et al., 2021b, 2020). In the dual context, studies have focused on developing strategies for ipsilateral information fusion or for finding explicit spatial relations between two views. In this section, we first provide a review of graph-based representations, tailored for both mono- and dual-view mammography analysis then present the related work on fusion strategies for dual-view mammography analysis and decision explainability.

### 2.1. Graph-based methods

Our framework is based on a multi-scale graph decomposition of each view inspired by the work of Min et al. (2019). We model a mammography as a multi-scale attributed graph, where regions are nodes spatially connected across and within scales. We then perform a mono-view analysis based on a Graph Neural Network (GNN) that acts as a soft detector. Finally, we propose a second bipartite graph with an SGAT with a sparse attention mechanism for dual-analysis. As described next, several advantages motivate our choice of a multi-scale decomposition and a graph-based modeling both in the mono and dual-view analysis steps.

**Mono-View Analysis.** Firstly, as shown by Zhou et al. (2020), graphs are powerful tools in capturing the structural and spatial relationships in medical imaging data. Graphs allow for easy decomposition of images into multi-scale representations. In the context of mammography analysis, leveraging multi-scale graph methods has further improved performance by capturing both global and local structures. Du et al. (2019) introduced a fully supervised Graph Attention Network (GAT) for mono-view classification, where each node in the multi-scale graph represents a squared patch at a particular scale and inter-scale connections mimic radiologists' zooming operations. In

contrast to these approaches, we based our multi-scale graph decomposition on a superpixel segmentation, where each node of our graph corresponds to a superpixel with coherent texture regions at various scales, connected to its direct neighbors within and across scales. The above studies affirm that integrating multi-scale region-level details with morphological context through message passing not only refines feature representation but also enhances the detection and classification performances of breast lesions. Such topological information has been also useful for automatically classifying calcification morphology and distribution from mono-view mammograms (George et al., 2019; Du et al., 2023). We show here that multi-scale decomposition and topological information have the potential to improve classification and detection performances in more general cases, i.e., involving several breast lesions (masses, clusters of calcifications, and distortions). However, analyzing mammography through multi-scale attributed graphs alone does not allow for the integration of complementary information between views. While mono-view approaches effectively capture intra-view topological context, they are inherently limited in leveraging cross-view relationships that can be crucial for accurate diagnosis. Therefore, to fully exploit the complementary information present in dual-view mammography, it is necessary to design models that can explicitly model and fuse information across both views.

**Dual-View Analysis.** A second advantage of graph-based image representation comes from the suitability of bipartite graphs to explicitly model the relationships between views. Liu et al. (2020) also use a bipartite graph to model the relations of ipsilateral views in breast mass detection. However, while Liu et al. use the cross-view graph information to update the spatial feature map used later by a mask R-CNN detector (He et al., 2017), we update the node features and maintain the more interpretable graph structure capable of providing predictions at the node, graph, and bipartite-graph levels. Additionally, Liu et al. rely on identifying pseudo-anatomical landmarks (nipples, breast border, pectoral muscle) for placing a node grid on top of the image. In contrast, we avoid alignment and automate the process using superpixel segmentation. Moreover, we create nodes at various scales to account for varying-sized lesions (instead of only masses as in Liu et al. (2020)). Also, unlike Liu et al. who base bipartite graph edges on spatial priors and node features similarity scores, we retain all bipartite connections to accommodate large deformations and arbitrary lesion locations and consider all similar and complementary information across views potentially relevant. To cope with the resultant large edge set, we propose to train a sparse GAT layer to find the most pertinent connections before the final classification layer. Apart from Liu et al. (2020), we are unaware of other methods using bipartite graphs to model ipsilateral breast views. To fully leverage the complementary information available in the bipartite graphs, it is essential to consider how information from both views can be effectively combined.

### 2.2. Information fusion methods

Information fusion methods have been categorized as early, intermediate, or late according to the layers where feature fusion occurs (Truong et al., 2023). In the context of CAD models for dual-mammography analysis, an early fusion approach grants the network access to both views at the input stage thereby exploiting their complementary information. Often based on the simple concatenation of the views as channels of a single image, early fusion methods may rely on additional registration steps (Yang et al., 2021; Liu et al., 2021b, 2020), e.g., considering pseudo-landmarks as the nipple to guide an affine warping alignment. However, such alignment strategies can be susceptible to errors and, thus, introduce inaccuracies into the global analysis.

Late fusion approaches combine decisions from several sub-models (Pathak et al., 2024; Lopez et al., 2022; Wu et al., 2020). However, as the two views are first analyzed independently, this type of fusion
<figure><img src="image_5.png" /><figcaption>Fig. 2. The two columns correspond to two ipsilateral views of one INbreast (Moreira et al., 2012) case (i.e., MLO and CC of the same breast). For a specific query of a suspicious region found by the radiologist or detected by the model (i.e., the cluster of calcifications inside the green circle in one view), our proposed approach finds the contribution of the different regions in the other view to the malignancy probability prediction. The contribution value ranges from blue (not related) to red (closely related). Color is recommended for a better visualization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

does not leverage the potential complementarities between ipsilateral abnormalities.

Finally, the intermediate fusion strategy learns common low-
dimensional representations through specifically designed fusion blocks
(Truong et al., 2023; Chen et al., 2024; Yang et al., 2023; Vu et al.,
2023), connecting one or several intermediate layers across views. Such
local co-occurence (Chen et al., 2024), cross-view (Yang et al., 2023), or
cross-attention (Vu et al., 2023) modules explicitly exploit relationships
between features in the two views. However, the learned relations
remain difficult to interpret. Approaches such as Vu et al. (2023), Zhao
et al. (2022) and Yan et al. (2020) also perform intermediate fusion
by leveraging a detector to find abnormalities in each view, followed
by a joint matching or classification module. Relying on a detector
avoids the need for prior image alignment and reduces the number of
candidate complementary regions to model between views.

Sparser detections have been shown to generalize better to clinically representative data (Vu et al., 2023), where most of the data contains no findings. Conversely, such methods may struggle to recover from detection errors, especially false negatives. This work proposes an alternative intermediate fusion approach that avoids registration, alignment, or detection steps while remaining interpretable. Our method models individual mammography as attributed graphs and learns a node-wise GNN classifier on each view. Such mono-view models act as soft detectors, integrating topological information within the updated node features while keeping all the information available to the dual-view fusion. Toward the fusion, we design a bipartite graph that explicitly models the relationships between regions from both views. Finally, a GAT merges the learned mono-view latent node representations. In the latter step, we adapt the sparse attention mechanism from Ye and Ji (2021) to focus on critical bipartite connections for the final dual-view classification. Moreover, keeping only the important connections in the graph structure allows us to generate visual attribution explanations, highlighting decision areas that most contribute to the disease classification.

2.3. Explainability

In the context of breast cancer classification, saliency heatmaps,
and attribution maps have been used to qualitatively highlight or

detect suspicious areas (Chen et al., 2024; Ribli et al., 2018) or as
local pseudo-labels fed back to the model to improve their perfor-
mance (Chen et al., 2024; Lei Lei et al., 2020; Shen et al., 2019b).
However, the above works rely on additional external post-hoc explain-
ability algorithms to generate the saliency maps, which can also be
computationally expensive. Our approach provides an in-built strategy
to generate attribution maps by looking at the node-wise predictions, as
shown in Fig. 2. To demonstrate such advantages, we provide a quan-
titative evaluation of attribution map explanations in the context of
breast cancer classification for the first time. To this end, we challenge
our models against state-of-the-art methods using a top-k% incremental
deletion approach (Nauta et al., 2023) to measure the quality of the
explanations.

3. Methods

**Problem Definition.** In the context of a breast screening exam, our method aims to assist the diagnosis by providing a cancer probability score and highlighting the regions involved in the decision. An exam being composed of at least two views, the input to our model are the two most common views, CC and MLO, denoted hereafter $I_{CC}$ and $I_{MLO}$. Our model focuses on detecting different types of lesions (e.g., masses, calcifications, and distortions) at different scales and exploiting the complementary information from both mammography views. To this end, we propose a fully supervised dual-view framework shown in Fig. 3 that consists of the following steps:

(A) Generating a multi-scale graph representation for each view (see Section 3.1.1);

(B) Extracting a feature representation for each node in the multi-scale graph with a multi-scale backbone network $\mathcal{B}$ (see Section 3.1.2);

(C) Updating the local feature representation of each node with in-
formation from its neighbors, and making node-wise predictions
with the MSGCN (Section 3.1.3);

(D) Constructing two directed bipartite graphs (Section 3.2.1) to explicitly model the complementary information between two mammography views (Section 3.2.1);

(E) Feeding the bipartite graphs to an adapted SGAT network to ob-
tain final local and global malignancy probabilities while high-
lighting regions contributing to the decision from both views
(Section 3.2.2).

3.1. Mono-view modeling

3.1.1. Multi-scale graph generation

The first building block of our framework constructs a multi-scale graph for each mammography view $I \in \{I_{CC}, I_{MLO}\}$. We start with a superpixel over-segmentation of the image. To allow for better detection of malignant regions with variable sizes (i.e., all abnormalities and not only masses), we adapt the method proposed by Min et al. (2017) to cluster $I$ into superpixels at $M$ different scales. The size of the superpixels within a given scale is determined with a heuristic taking into account the lesion size statistics in our dataset with pixel-wise annotations of abnormalities.<fnref n="1" /> The number of scales $M$ is defined to cover the range size of abnormalities while maintaining a reasonable computational complexity. For each scale $m \in \{1, 2, \dots, M\}$, we generate region candidates taking into account texture information, by

<footnote n="1">¹ Given the expected size range of abnormalities [$A_{min}$, $A_{max}$], the pixel spacing $P$, the resize ratio $R$ and the number of scales $M$, we can roughly estimate the global range of the superpixels' sizes to be [$L_{min}$, $L_{max}$] = $\frac{1}{P \cdot R} [2\sqrt{A_{min}}/\pi, 2\sqrt{A_{max}}/\pi]$. We then split the global range following an exponential scale with $M$ intervals of length $\Delta = (\frac{L_{max}}{L_{min}})^{1/M}$. Thus, for scale $m$, the superpixel size is: $L_{min} \cdot \Delta^{m-1}$ for $m = 1, 2, \dots, M$.</footnote>
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Overview of the proposed learning framework consisting of five steps: (A) mono-view multi-scale graph generation; (B) feature extraction to assigning attributes to each graph node; (C) mono-view feature update and node-wise predictions with the MSGCN; (D) bipartite graphs generation (bipartite arrows are represented with two different colors for illustration purpose, i.e., black and orange for $G_{MLO-CC}$ and $G_{CC-MLO}$, respectively); (E) a dual-view prediction with the SBIP. The framework requires as input a mammogram from each view (i.e., $I_{CC}$ and $I_{MLO}$), the lesion size range $[A_{min}, A_{max}]$, and the number of scales $M$. As output, the model provides a probability of malignancy $\hat{Y}_d$ for the whole breast and a pair of heatmaps highlighting relevant dual-view bipartite connections. Nodes's color denote different scales. Color is recommended for a better visualization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

relying on the modified version (Pelluet et al., 2021) of the Scalable Simple Linear Iterative Clustering (SSLIC) (Lowekamp et al., 2018). As a result of this step, we obtain a multi-scale clustering $S$ of the mammogram $I$, such that $S = \{S_m\}_{m=1}^M$, with $S_m$ the superpixel segmentation at scale $m$. Equivalently, $S$ can be seen as a collection of superpixels $S = \{s_i\}_{i=1}^N$ with $N$ the total number of superpixels over scales.

To capture both intra-scale and inter-scale correlations, we build a multi-scale graph $G = \{V, E, X\}$ of the mammogram $I$ from its multi-scale superpixel clustering $S$ (as shown in Fig. 3.A). Here, $V$ represents a finite set of nodes, $E$ is a set of edges, and $X$ is the matrix with aggregated features extracted from the backbone network. Each node in $V$ corresponds to a superpixel $s_i \in S$, therefore $|V| = N$. To build $E$, we connect each node in $V$ to itself, to its direct four neighbors in the spatial (2D) domain (i.e., top, bottom, left, and right), and to its direct neighbors across scales i.e., the overlapping superpixels on the nearest smaller and larger scales. Equivalently, the edges can be represented as a binary adjacency matrix $A$. The resulting multi-scale graph is illustrated in Fig. 3.C.

### 3.1.2. Backbone features extractor

Furthermore, we assign a feature vector to each node in the graph (i.e., to each superpixel $s_i \in S$), and store it in the $i$th row $x_i$ of a feature matrix $X$. The feature extraction backbone, hereafter denoted as $B$, relies on a pre-trained multi-scale UNet 3+ (Huang et al., 2020). For each scale $m$, the backbone computes a three dimensional tensor $i.e.,$ a feature map $F_m \in \mathbb{R}^{H_m \times W_m \times C}$, where $C$ stands for the number of channels, and, $H_m$ and $W_m$ are the height and width of the rescaled feature maps$^2$ at scale $m$.

Given the scaled mammogram $I_m$, every pixel $(x, y)$ in the corresponding image domain $\Omega_m \subset \mathbb{R}^{H_m \times W_m}$ gets represented by the tensor slice $F_m(x, y) \in \mathbb{R}^C$. To assign a single feature vector $x_i$ to a superpixel $s_i$, we aggregate the feature vectors of all pixels in $s_i$, retaining the highest values for each channel. By concatenating the features of the $N$ superpixels, we obtain the matrix $X \in \mathbb{R}^{N \times C}$.

### 3.1.3. Mono-View Multi-scale Graph Convolutional Network (MSGCN)

Once the multi-scale graph $G$ is built and the associated features $X$ are extracted, we define the MSGCN. Its goal is to encode both the node's features and the topological information inherent to the graph in an updated latent representation $H \in \mathbb{R}^{N \times D}$. The architecture is presented in Fig. 4. The network is trained to output both node-wise predictions, $\hat{y} \in (\mathbb{R}^+)^N$, and graph-wise predictions $\hat{Y} \in \mathbb{R}^+$, where $\hat{Y}$ corresponds to the max-pooling of node-wise predictions. When a graph is classified as benign, all node-wise predictions $\hat{y}^{(i)}$ are forced to 0. In practice the global and local loss functions are combined as:

$$ \mathcal{L}_{ms}(\hat{y}, \hat{Y}, y, Y) = \mathcal{L}(\hat{y}, y) + \mathcal{L}(\hat{Y}, Y), \quad (1) $$

where $Y$ and $y$ are ground truth labels, and $\mathcal{L}$ a binary cross-entropy function. Moreover, an updated feature representation $H$ is recovered from the penultimate network layer and used to characterize nodes in the bipartite graph. In summary, the MSGCN can be modeled with the following function: $\{\hat{y}, \hat{Y}, H\} = \text{MSGCN}_{\theta}(A, X)$, with learnable parameters $\theta$.

## 3.2. Dual-view modeling

For each view, we compute the segmentation at different scales, build the multi-scale graph, then update node features with a forward pass via MSGCN to obtain $H_{CC}$ and $H_{MLO}$. To exploit all the complementary information provided by both views, despite appearance and location differences, we design two oriented bipartite graphs $G_{CC-MLO}$, and $G_{MLO-CC}$. We then deploy a sparse attention network on top of our bipartite graphs to make dual-view predictions.

### 3.2.1. Bipartite graph generation

More precisely, each bipartite graph $G_{aux \to main}$ is defined as the joint set of nodes $\{V_{CC} \cup V_{MLO}\}$, and one of the two oriented set of edges $\{\varepsilon_{MLO-CC}, \varepsilon_{CC \to MLO}\}$. By definition of a bipartite graph, there are no connections between nodes of the same view. Self-loops are added to each node to account for the main view features when passing messages. Finally, the attributes of each bipartite graph are defined as the concatenation of the features matrices from each view $H_{bip} = H_{CC} \parallel H_{MLO}$. $A_{bip}$ is defined as the adjacency matrix of one of the bipartite oriented graphs $G_{aux \to main}$. By construction, $A_{bip}$ can be re-arranged

<footnote>$^2$ The feature map's spatial dimensions are scaled to match those of the resized mammogram $I_m$, i.e., $H_m \times W_m$, used to obtain the clustering $S_m$.</footnote>
<figure><img src="image_7.png" /><figcaption>Fig. 4. Architecture of the MSGCN. A mono-view graph $\mathcal{G}$ is fed to the network; the model is used to extract features $\mathbf{H}$ at the penultimate layer, local $\hat{\mathbf{y}}$ and global $\hat{\mathbf{Y}}$ probability of malignancy. Nodes's color denotes different scales. Color is recommended for a better visualization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 5. We demonstrate our SBIP network for both bipartite direction with two different colors. Please note that the model is applied a second time for the other direction. First, the graph $G_{bip}$ is fed to the network. Then, the model learned sparse representation of the bipartite correspondences between both views (SAL) and features representation based on the bipartite correspondences (GCL). Finally, the model generated bipartite attention scores $a_{\text{max}-\text{main}}$, and node-wise $\hat{\mathbf{y}}_{\text{main}}$ and view-wise $\hat{\mathbf{Y}}_{\text{main}}$ probabilities of malignancy. Nodes's color denotes different scales. Color is recommended for a better visualization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

as one of the following matrices $[\mathbf{I}_{CC} \quad \mathbf{0} \quad \mathbf{0}]$ or $[\mathbf{0} \quad \mathbf{A}_{CC \to MLO} \quad \mathbf{0}]$ or $[\mathbf{0} \quad \mathbf{I}_{MLO}]$, where $\mathbf{I}_{(\cdot)_{bip}}$ denotes the identity matrix representing the self-loops in one view. In the following, we will use the subscript $(\cdot)_{bip}$ to designate one of the two bipartite graphs, that is $(\cdot)_{bip} \in \{(\cdot)_{CC \to MLO}, (\cdot)_{MLO \to CC}\}$.

Our bipartite graphs explicitly model all possible links between regions of the two views. Therefore, we avoid relying on prior registration, alignment, or detection steps, which are difficult to do under the large deformations induced by mammogram acquisitions.

### 3.2.2. Dual-view sparse attention network

To mitigate the high computational cost induced by considering all bipartite connections, we propose a Sparse BIPartite graph attention network, named hereafter SBIP. During the learning process, the SBIP network aims to preserve or enhance the mono-view classification accuracy while also identifying crucial dual-view connections from a bipartite graph, thereby generating an ipsilateral prediction explained by the most relevant connections between the two views. More precisely, we adapt Ye and Ji (2021) to the bipartite graph case, seeking to reduce the number of bipartite connections that are irrelevant to the classification task (i.e., that does not contribute to malignancy detection) by imposing a sparsity constraint on the bipartite edges. In practice, our SBIP model consists of a sparse mask estimation step, followed by a gated-attention graph convolutional layer parameterized by weights $\mathbf{W}$ (see Fig. 5):

$$ \{\hat{\mathbf{y}}_{\text{main}}, \hat{\mathbf{Y}}_{\text{main}}, \tilde{\mathbf{A}}_{\text{bip}}\} = \text{SBIP}_{\text{W}, \text{Z}_{\text{bip}}} (\mathbf{H}_{\text{bip}}, \mathbf{A}_{\text{bip}}), \quad (2) $$

where $\hat{\mathbf{y}}_{\text{main}} \in (\mathbb{R}^{+})^{N_{\text{main}}}$ is the prediction vector for all nodes in the main graph, and $\hat{\mathbf{Y}}_{\text{main}} \in \mathbb{R}^{+}$ is a probability of malignancy of the main view. The model is parameterized by a binary mask matrix $\mathbf{Z}_{\text{bip}}$ and convolutional weights $\mathbf{W}$ explained later in this section.

Node-wise predictions for each view in the main role, i.e., $\hat{\mathbf{y}}_{\text{main}} = \hat{\mathbf{y}}_{CC}$ and $\hat{\mathbf{y}}_{\text{main}} = \hat{\mathbf{y}}_{MLO}$, are obtained by a forward pass of SBIP using the bipartite oriented graphs $G_{MLO \to CC}$ and $G_{CC \to MLO}$ respectively. A total region-wise prediction vector $\hat{\mathbf{y}}_{d}$ is obtained by simple concatenation as $\hat{\mathbf{y}}_{d} = [\hat{\mathbf{y}}_{CC}, \hat{\mathbf{y}}_{MLO}]$. Finally, a max pooling operation over the node predictions: $\hat{\mathbf{y}}_{d} = \max(\hat{\mathbf{y}}_{d})$, provides a graph-wise dual prediction $\hat{\mathbf{Y}}_{d} \in \mathbb{R}^{+}$.

During training, our SBIP model progressively updates the adjacency matrix with the current estimate of the binary mask $\tilde{\mathbf{Z}}_{\text{bip}}$ as $\tilde{\mathbf{Z}}_{\text{bip}} = \Psi(\mathbf{A}_{\text{bip}} \odot \tilde{\mathbf{Z}}_{\text{bip}})$, where $\Psi(\cdot)$ is the custom normalization operation (see Section 3.2.2) and $\odot$ is the element-wise multiplication. In this way, $\tilde{\mathbf{A}}_{\text{bip}}$ inherits the same sparsity pattern as $\hat{\mathbf{Z}}_{\text{bip}}$. For each bipartite graph, the binary mask $\mathbf{Z}_{\text{bip}}$ is composed of binary gates $z_{ij}$, introduced to dynamically control whether a particular edge $e_{ij} \in \mathcal{E}_{\text{aux}-\text{main}}$ is to be considered during the message passing operation. Denoting $\tilde{a}_{ij}$ the elements of the updated adjacency matrix $\tilde{\mathbf{A}}_{\text{bip}}$, the attention-based message passing aggregation function to update the feature vector $\mathbf{h}_{j}$ for node j is:

$$ \mathbf{h}_{j}^{(l+1)} = \sigma\left(\sum_{\{i|e_{ij} \in \mathcal{E}_{\text{bip}}\}} \tilde{a}_{ij} \mathbf{W}^{(l)} \mathbf{h}_{j}^{(l)}\right), \quad (3) $$

where j denotes a node from the main view, $\sigma$ is the sigmoid function, and l is the index of the layer. Note also that we force $z_{jj}$ to 1 to keep self-loops active.
In practice, we learn model parameters W and a joint binary mask $Z_d = Z_{CC} \to MLO + Z_{MLO} \to CC$ by minimizing the following loss function:

$$ \mathcal{L}_d = \lambda (\mathcal{L}(\hat{\mathbf{y}}_d, \mathbf{y}_d) + \mathcal{L}(\hat{\mathbf{Y}}_d, \mathbf{Y}_d)) + \delta \|\mathbf{Z}_d\|_1, \quad (4) $$

where $\| \cdot \|_1$ denotes the $L_1$-norm and $\lambda$ and $\delta$ are adjustable hyper-parameters balancing between data losses and edge sparsity. Given that the elements in $Z_d$ are binary, both terms in Eq. (4) are not differentiable. Therefore, we rely on the variational stochastic optimization presented in Ye and Ji (2021) to compute the weights and gates updates.

Next, for the sake of completeness, we briefly recall the main elements of the optimization scheme proposed by Ye and Ji (2021). Then, we discuss the limitations of the original SGAT normalization function $\Psi(\cdot)$ and introduce an adaption to the context of a highly imbalanced classification problem.

**Variational Stochastic Optimization.** The optimization of the SBIP parameters from the loss in Eq. (4) is similar to the SGAT problem in Ye and Ji (2021), with the differences that (i) we enforce local and global penalties, (ii) we deal with bipartite graphs with oriented edges, (iii) and that we optimize the binary sparsity masks for two bipartite graphs simultaneously.

Following Ye and Ji (2021), we approximate the minimization of Eq. (4) by assuming that the gates $z_{ij}$, instead of being binary, are drawn from a hard-concrete distribution (a continuous surrogate of the discrete Bernoulli distribution). With this approximation, $\hat{z}_{ij}$ takes continuous values within the interval [0, 1], and the optimization becomes stochastic. The goal is to find the hard concrete distribution parameters for each edge on the bipartite graph.

The hard concrete distribution is commonly parameterized as $\hat{z}_{ij} \sim \text{hardConcrete}(\alpha_{ij}, \beta, \zeta, \gamma)$, where $\zeta$, and $\gamma$ are set to known fix values that determine its conventional stretched and centered shape (Louizos et al., 2017), $\beta$ is a hyperparameter, and $\alpha_{ij}$ is defined as a data-dependent term.<fnref n="3" /> In particular, $\log \alpha_{ij}$ is made to depend on the feature vectors of the nodes j and i, and on a learnable parameter b, such that:

$$ \log \alpha_{ij} = \left[ \text{Wh}_j^{(l)} \| \text{Wh}_i^{(l)} \right] \mathbf{b}^{\top}. \quad (5) $$

In this way, the gate values $\hat{z}_{ij}$ sampled from the distribution are dynamically adapted to each edge, and the loss gradient flows to update b. Finally, with the help of the reparameterization trick<fnref n="4" /> and variational bound estimations, optimizing the large stochastic computation graph via gradient descent becomes possible. Readers can refer to Ye and Ji (2021) and Louizos et al. (2017) for more details on the optimization.

**SGAT Normalization.** At the end of the training, a significant number of $\hat{z}_{ij}$ values approach zero. If a gate is considered disabled, i.e., $\hat{z}_{ij} = 0$, it leads to the dynamic pruning of an edge from the bipartite graph by modifying its oriented adjacency matrix. More concretely, gated attention coefficients $\tilde{a}_{ij}$ are computed as the row-wise normalization $\Psi(\cdot)$ of the gated adjacencies, i.e., $\tilde{A}_{bip} = \Psi(A_{bip} \odot \hat{Z}_{bip})$ with elements:

$$ \tilde{a}_{ij} = \frac{a_{ij} \hat{z}_{ij}}{\sum_{k \in N_{ij}} a_{kj} \hat{z}_{kj}}, \quad \text{and} \quad \tilde{a}_{ii} = 1, \quad (7) $$

where we force $\tilde{a}_{jj}$ to 1 so that each node preserves its own information. In this way, the aggregation rule in Eq. (3) is a gated version of the standard GAT (Velickovic et al., 2018).

$$ \hat{z}_{ij}(\log \alpha_{ij}, u) = g\left(\sigma\left(\left(\log \frac{u}{1-u} + \log \alpha_{ij}\right) / \beta\right)(\zeta - \gamma) + \gamma\right), \quad (6) $$

where u represents a sample drawn from the uniform distribution.

<figure><img src="image_9.png" /><figcaption>Fig. 6. Illustration of the difference between (A) the initial row-wise normalization and (B) our proposed CDBN. The green and red nodes represent normal and malignant breast regions, respectively, and the dotted arrows represent the edge to normalize. Only a small portion of the unbalanced edge classes is represented for illustration purposes. In practice, we have an average factor of approximately 1 edge of type = 1 versus 319 edges of type = 2 and type = 3 for a malignant graph. As the number of unbalanced positive and negative edge classes increases, the gap between negative and positive normalized attention becomes more pronounced with our CDBN. Color is recommended for a better visualization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

## Class-Dependent Batch Normalization.

The row-wise normalization in Eq. (7) does not account for the significant imbalance in the edge's nature in the bipartite graph. Looking at one bipartite graph, we clearly observe more normal edges than malignant edges. To address this issue, we propose a different $\Psi(\cdot)$ based on the node-wise predictions of our mono-view model $\hat{y}$.

More precisely, a node is considered positive if its prediction is higher than a threshold $\hat{y}^{(l)} > \tau$, and negative otherwise. Note that all nodes in a mammogram are identified as negative if the view-wise prediction $\hat{Y}$ of the MSGCN is negative. In practice, in a bipartite-oriented graph, we can identify three types of edges: edges connecting positive to positive nodes (type 1), those connecting negative to negative nodes (type 2), and edges connecting a positive to a negative region (type 3).

Our custom normalization function $\Psi(\cdot)$ aims at penalizing the importance given to bipartite edges of type 2 and 3, as the negative (normal) regions are numerous compared to positive edges. During the training, we consider all the bipartite edges in a batch of graphs to leverage the balance between negative and positive edges.

We normalize the gated adjacencies for a type t as:

$$ \tilde{a}_{ij} = \frac{\frac{1}{|t|} a_{ij} \hat{z}_{ij}}{\sum_{l'=1}^{3} \frac{1}{|t'|} \sum_{e_{kj} \in \mathcal{T}} a_{kj} \hat{z}_{kj}}, \quad (8) $$

where $|t|$ is the number of edges per type in a batch of graphs and $\mathcal{T}$ is the set of edges of type $t'$ directed to the node j.

The principle is illustrated in Fig. 6, normalizing the dotted edge. The original normalization (Fig. 6-A.) of the gated attention would consider all edges, diluting the information of the positive edges (dotted). Instead, our proposed normalization is computed over a batch of similar connections only (for type $t = 1$ in our example, Fig. 6-B.).

As shown later in the experiments, with the proposed modification, the sparsity of SBIP focuses the gated attention coefficients on pairs of regions from the two views that are suspected to be malignant, as only those regions contribute to the correct final classification.

**Salience and Contribution Maps.** In order to provide explainability to our model, we can visualize the predicted malignancy scores for the regions in the main view or the contribution of regions in the auxiliary view to the final decision score. Recall that the SBIP generates two local node-level informations: a classification score $\hat{y}_d^{(j)}$ (i.e., a probability of a node j to be malignant) and attention scores $\{\tilde{a}_{ij}\}$ denoting the

<footnote n="3">³ hardConcrete($\alpha_{ij}, \beta, \zeta, \gamma$) = $g(\sigma(\frac{\log \alpha_{ij}}{\beta})(\zeta - \gamma) + \gamma)$, with $g(\cdot)$ the hardtanh activation function, $\sigma(\cdot)$ the sigmoid function, $\gamma = -0.1$, $\zeta = 1.1$, and $\beta = 2/3$ as in Ye and Ji (2021).</footnote>

<footnote n="4">⁴ During training, the hard concrete distribution is adapted with the reparameterization trick, such that:</footnote>
<caption>Table 1</caption>

Description of the dataset used in our experiments. The labels “Cancer” and “No Cancer” indicate a BI-RADS Score > 3 and BI-RADS Score ≤ 3, respectively. X stands for no pixel-wise annotations, and ✓ stands for pixel-wise annotations.

<table><thead><tr><th rowspan="2">Datasets</th><th colspan="3">Images</th><th colspan="3">Breasts</th><th rowspan="2">Pixel-level annotations</th></tr><tr><th>Number</th><th>Cancer</th><th>No Cancer</th><th>Number</th><th>Cancer</th><th>No Cancer</th></tr></thead><tbody><tr><td>D<sub>HMI<sub>TR</sub></sub></td><td>2016</td><td>1038</td><td>978</td><td>614</td><td>315</td><td>299</td><td>✓</td></tr><tr><td>D<sub>VINDR<sub>TR</sub></sub></td><td>2201</td><td>1564</td><td>637</td><td>582</td><td>284</td><td>298</td><td>✓</td></tr><tr><td>D<sub>CBIS<sub>TR</sub></sub></td><td>2371</td><td>788</td><td>1583</td><td>956</td><td>311</td><td>645</td><td>✓</td></tr><tr><td>D<sub>HMI<sub>TE</sub></sub></td><td>504</td><td>243</td><td>261</td><td>59</td><td>29</td><td>30</td><td>✓</td></tr><tr><td>D<sub>RINB<sub>TE</sub></sub></td><td>402</td><td>302</td><td>100</td><td>185</td><td>135</td><td>50</td><td>✓</td></tr><tr><td>D<sub>SINB<sub>TE</sub></sub></td><td>108</td><td>78</td><td>30</td><td>50</td><td>35</td><td>15</td><td>✓</td></tr><tr><td>D<sub>CMMD<sub>TE</sub></sub></td><td>3744</td><td>1112</td><td>2632</td><td>1872</td><td>556</td><td>1316</td><td>X</td></tr><tr><td>D<sub>VINDR<sub>TE</sub></sub></td><td>3540</td><td>3495</td><td>45</td><td>1671</td><td>1651</td><td>20</td><td>✓</td></tr><tr><td>D<sub>CBIS<sub>TE</sub></sub></td><td>628</td><td>238</td><td>390</td><td>253</td><td>85</td><td>168</td><td>✓</td></tr><tr><td>D<sub>DDSM<sub>TE</sub></sub></td><td>322</td><td>126</td><td>196</td><td>-</td><td>-</td><td>-</td><td>✓</td></tr></tbody></table>

contribution of a set of regions in the auxiliary view, to the final decision score of the node j.

In the main view, we compute a saliency map to show the probability of malignancy in the breast regions and generate a binary segmentation to evaluate lesion detection performances. To this end, we first generate a 3-dimensional (3D) multi-scale heatmap $K \in \mathbb{R}^{H \times W \times M}$ for the main view by assigning a predicted node-wise malignancy score of a node j to all the pixels of the superpixel $s_j$ in the multi-scale heatmap. Then, we compute a multi-scale binary segmentation $K_b$ by thresholding the 3D heatmap $K$ as $K_b = (K > \tau)$. Next, we then find the maximum number of scales $M_{max}$ where one pixel is activated. Finally, the binary detection map $K_f$ is obtained by setting to 1 the pixels when they are activated in $M_{max}$ different scales of $K_f$. This approach reduces the oversegmentation generated from our multi-scale clustering, as abnormalities can have overlapping activation of different sizes at different scales in $K_f$.

In the auxiliary view, we generate a contribution map for a set of suspicious regions $J$ in the main view. First, we calculate the contribution for each node i in the auxiliary view (i.e., all pixels of the superpixel $s_i$) by assigning the value of the maximum gated attention score $c_i = \max_{j \in J}(\tilde{a}_{ij})$. This results in a 3D multi-scale contribution map C. Next, we obtain the final contribution map by computing a normalized sum of the contributions across scales in the auxiliary view.

## 4. Experimental evaluation

We conducted experiments on several datasets to demonstrate SBIP's ability to identify important bipartite edges for feature aggregation from disassortative graphs (i.e., graphs with a high number of neighbor noise) and improve mono-view performances. First, we compare our performances with state-of-the-art algorithms (Chen et al., 2024; Pathak et al., 2024; Vu et al., 2023; Chen et al., 2022; Stadnick et al., 2021; Liu et al., 2020) in cancer classification and detection tasks. Then, we performed ablation of the different parts of our method. Next, we compared the explainability of our model (i.e., how our model decision is based on salient areas over the image that highlight important regions) against two weakly supervised algorithms and one fully supervised algorithm: GLAM<fnref n="5" /> (Liu et al., 2021a), GMIC top-5 ensemble<fnref n="6" /> (Shen et al., 2019b), and DMV<fnref n="7" /> (Wu et al., 2020). Finally, we quantitatively analyze the detection performance and the contribution maps of the auxiliary views generated by our approach.

### 4.1. Experimental setup

**Datasets.** In our experiments, we used diverse bilateral mammogram datasets regarding patient populations, geographic locations, and

mammography system vendors. We utilized six datasets in total. The first is our private dataset, including 1128 patients and 3162 FFDM (Full-Field Digital Mammography) images from four vendors (Fujifilm, GE, Hologic, and Planmed) and which is used for both training ($D_{HMI_{TR}}$) and evaluation ($D_{HMI_{TE}}$). The second is the publicly available CMMD dataset (Chunyan et al., 2021) containing 1775 patients and 3744 FFDM images acquired with the GE Senographe DS mammography system (denoted as $D_{CMMD_{TE}}$). The third is the INbreast dataset (Moreira et al., 2012) consisting of 108 patients and 410 FFDM images acquired with the Siemens mammography system. We used the subsets of the INbreast dataset proposed by Ribli et al. (2018) ($D_{RINB_{TE}}$<fnref n="8" />) and Shen et al. (2019a) ($D_{SINB_{TE}}$) for testing our model and fair comparison. The fourth is VinDr (Nguyen et al., 2023), a large-scale public benchmark dataset of FFDM from several manufacturers comprising 5000 patients and 20 000 mammograms. We used two subsets of the official split for training and evaluation (denoted as $D_{VINDR_{TR}}$ and $D_{VINDR_{TE}}$). In addition, we also used two digitized mammogram datasets: DDSM (Heath et al., 1998) and CBIS-DDSM (Lee et al., 2017). DDSM consists of 2243 patients and 9571 mammograms with normal, benign, and malignant images, and CBIS-DDSM comprises 1508 patients and 2921 mammograms with only malignant and benign images. We used a similar test set of DDSM as Liu et al. (2021b, 2020) and the official split of CBIS-DDSM to generate train and test set denoted as $D_{DDSM_{TE}}$, $D_{CBIS_{TR}}$, and $D_{CBIS_{TE}}$, respectively. For some datasets, the image labels are provided. For others, the available BI-RADS (Breast Imaging-Reporting And Data System) score (D'Orsi, 2014) is used to define the image labels. Positive mammograms have pixel-level and region-level annotations (except for CMMD). The statistics of the different datasets are detailed in Table 1.

**Training Strategy.** Our models used two training strategies. First, we initially trained our models (denoted in the following sections as $B_{18}$, $MSGCN_{18}$, and $SBIP_{18}$) with global and local annotations using $D_{HMI_{TR}}$. For the mono-view models (i.e., $B_{18}$ and $MSGCN_{18}$), we use all available mammograms, and we trained our $SBIP_{18}$ with mammograms having at least one ipsilateral view (evaluations are performed similarly). Then, we train a second version of our models (denoted as $B_{19}$, $MSGCN_{19}$, and $SBIP_{19}$) following the first approach with more data. We added $D_{VINDR_{TR}}$ to increase the number of FFDM, and we included digitized images from $D_{CBIS_{TR}}$ to train our models on this type of image. However, VinDr is an unbalanced dataset (approximately 1/20 images are malignant), so $D_{VINDR_{TR}}$ corresponds to a subsample of the official train set, excluding PlanMed images due to the poor image quality. Concerning the annotations, we chose to perform in-house delimitations of the lesions as the initial annotations lack precision as they are bounding boxes. For the test set ($D_{VINDR_{TE}}$), we used the official split, and we removed images that were also in the training set. Furthermore, we found duplicated mammograms with different

<footnote n="5">⁵ https://github.com/nyukat/GLAM.</footnote>

<footnote n="6">⁶ https://github.com/nyukat/GMIC.</footnote>

<footnote n="7">⁷ https://github.com/nyukat/breast_cancer_classifier.</footnote>

<footnote n="8">⁸ It's worth noting that only 4 of the eight exams described by Ribli et al. (2018) were retained, as they weren't precise exams identifiers.</footnote>
<caption>**Table 2**</caption>

Comparison of our approaches against the state-of-the-art methods using image-wise AUC-ROC on $D_{\text{INB}}_{\text{TE}}$ and $D_{\text{CMMD}}_{\text{TE}}$ with 95% bootstrap confidence intervals (CI) and 2000 bootstrap replicates. It is worth noting that the dataset used by Wang et al. (2024) has been split into train and test sets, i.e., the subset used for testing is dissimilar to ours. n.a. stands for not available.

<table><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">AUC</th><th colspan="5">Models</th></tr><tr><th><i>B</i><sub>18</sub><br>In-house</th><th><i>MSGCN</i><sub>18</sub><br>In-house<br>Pelluet et al. (2022)</th><th><i>SBIP</i><sub>18</sub><br>In-house</th><th>GlobalNet<br>Wang et al. (2024)</th><th>LLSA<br>Li et al. (2025)</th></tr></thead><tbody><tr><td><b><i>D</i><sub>RINB</sub><sub>TE</sub></b></td><td>ROC</td><td>0.93<br>(0.90–0.96)</td><td>0.95<br>(0.92–0.97)</td><td><b>0.95</b><br>(<b>0.94–0.99</b>)</td><td>n.a.<br>n.a.</td><td>0.95<br>(0.86–1.00)</td></tr><tr><td><b><i>D</i><sub>CMMD</sub><sub>TE</sub></b></td><td>ROC</td><td>0.81<br>(0.79–0.83)</td><td>0.81<br>(0.80–0.85)</td><td>0.82<br>(0.81–0.85)</td><td><b>0.89</b><br>(<b>0.88–0.90</b>)</td><td>n.a.<br>n.a.</td></tr></tbody></table>

identifiers in the VinDr dataset. We removed these duplicates, which are both in the test set and the training set. Please refer to the GitHub page<fnref n="9" /> for a list of patient identifiers used in the different splits for the public datasets. Both versions of our pipeline were trained using a stratified split of our private dataset with 84% of the images for training ($D_{\text{HMI}}_{\text{TR}}$) and 16% of the images for testing ($D_{\text{HMI}}_{\text{TE}}$).

All mammograms are cleaned from image artifacts (particularly the digitized mammograms) and are pre-processed using the following steps: (1) using the triangle algorithm (Zack et al., 1977) to extract the background; (2) truncating the image histogram at the first and last percentile; (3) flipping the breast to normalize the alignment to the left; (4) cropping the mammogram to the bounding box around the breast; (5) resizing the cropped image with linear interpolation to a size of 2048 × 1280; (6) stretching the intensity to 0.995 of maximum value and rescaling between 0 and 1. We regrouped the mammograms by breast for breast-wise evaluation and case for case-wise evaluation. Some cases contain more than two ipsilateral views, so we chose to generate all ipsilateral combinations (e.g., for a breast exam that contains one CC and two MLOs, we generate two pairs).

**Implementation Details.** The number of scales *M* was set to 4. The $A_{\text{min}}$, $A_{\text{max}}$ are set to 15 mm and 3689 mm for multi-scale oversegmentation to cover lesions size range (the interval is generated from InBreast pixel-wise annotated lesions, except for the asymmetries which were excluded from the experimentation). In the generated multi-scale and bipartite graphs, each node is assigned a malignancy label of 1 if the corresponding superpixel overlaps with the annotations by at least 5% and that the corresponding region has a BI-RADS > 3, and 0 otherwise. For the training of our *MSGCN* and *SBIP*, we use a local and global weighted cross-entropy loss to deal with unbalanced data based on the binary proportional distribution (i.e., BI-RADS ≤ 3) of the malignant and normal mammograms or regions in the training dataset. Adam optimizer (Kingma and Ba, 2014) was used with an initial learning rate of $5e^{-4}$, weight decay of $1e^{-5}$. The loss and regularization functions were balanced using two parameters $\alpha = 1$ and $\delta = 0.1$, and the number of epochs for training was set to 15000. The parameters are identical for *MSGCN* and *SBIP*, except for the batch size, set to 32 for *MSGCN* and 4 for *SBIP* due to the large size of the bipartite graphs. A dropout with a probability of 0.1 was applied on each layer, and *ReLU* was used as activation layers for the Sparse Attention Layer and the Graph Convolutional Layers. Regarding the heatmaps, we used an adaptive threshold of Li on the breast for $\tau$, and we applied morphological closing and opening to smooth $K_h$, reducing the number of false positives generated. All experiments were implemented using Deep Graph Library (Wang et al., 2019) and PyTorch (Paszke et al., 2019) and conducted on an NVIDIA A100 GPU.

## 4.2. Evaluation of the proposed framework

**Classification and Detection Performance.** The classification performance is assessed using the Area Under the Curve for the Receiver

Operating Characteristic (AUC-ROC) and the Area Under the Curve for the Precision-Recall (AUC-PR). We also report 95% bootstrap Confidence Intervals (CI) with 2000 bootstrap replicates. Evaluations are based on image, breast, and case levels. We used a max operator for aggregation of the breast and case levels. The detection performance is assessed on the heatmaps generated by our models and on the merged heatmaps obtained using an average operator, denoted as $[\cdot, \cdot]_{av}$. The True Positive Rate (TPR) and False Positive Per Image (FPPI) metrics are utilized to evaluate the local detection performance.

Table 2 shows a comparison of the AUC-ROC and Table 3 shows a comparison of the AUC-ROC and AUC-PR based on the first version of our models (·)$_{18}$ against state-of-the-art methods. First, we evaluate our learning scheme on $D_{\text{RINB}}_{\text{TE}}$. Then, we used the smaller subset defined by Shen et al. (2019a), $D_{\text{SINB}}_{\text{TE}}$. We also compare our results on $D_{\text{CMMD}}_{\text{TE}}$. While our *SBIP*$_{18}$ generates state-of-the-art classification at an image-wise and breast-wise level on $D_{\text{RINB}}_{\text{TE}}$ in terms of AUC-ROC (0.95 image-wise and 0.96 breast-wise) and AUC-PR (0.90 breast-wise), it also produces similar state-of-the-art results at a breast-level (0.99 AUC-ROC and 0.99 AUC-PR) with the method presented by Chen et al. (2022) on $D_{\text{SINB}}_{\text{TE}}$, showing the importance of dual-view analysis. On $D_{\text{CMMD}}_{\text{TE}}$, our approaches produced competitive results in terms of breast-wise AUC-ROC compared to Chen et al. (2022) and Ribli et al. (2018) while having a higher AUC-PR (0.92), showing that the metrics are more robust as they provide insights into how well the model captures positive instances while minimizing false positives. Regarding the image-wise metrics presented by Wang et al. (2024), they achieved good results compared to ours (AUC-ROC of 0.82) with an AUC-ROC of 0.89. However, their method is trained on a subset of $D_{\text{CMMD}}_{\text{TE}}$.

Another analysis of our model trained with the second strategy (·)$_{19}$ is performed (on Table 4). We compare the results against state-of-the-art methods on two datasets: $D_{\text{VINDR}}_{\text{TE}}$ and $D_{\text{CBIS}}_{\text{TE}}$. For $D_{\text{VINDR}}_{\text{TE}}$, we show state-of-the-art results on the breast-level analysis (0.91) and case-level analysis (0.92). Our *SBIP*$_{19}$ improves the classification compared to *MSGCN*$_{19}$, which generates more false positives. Moreover, our *SBIP*$_{19}$ also improves the initial performances of the backbone on both levels. Regarding $D_{\text{CBIS}}_{\text{TE}}$, we show a better AUC-ROC at the breast level with our bipartite approach than the other methods (0.80 versus 0.79 and 0.78). However, our *SBIP*$_{19}$ achieved a lower AUC-ROC score than our *MSGCN*$_{19}$ (0.84), suggesting that our bipartite approach does not correctly model relevant correspondences on digitized mammograms.

Regarding the model's ability to localize abnormalities, we chose to evaluate our detection performance against state-of-the-art methods on $D_{\text{RINB}}_{\text{TE}}$ and $D_{\text{DDSM}}_{\text{TE}}$. Tables 5 and 6 report the experimental performance on $D_{\text{RINB}}_{\text{TE}}$ with all abnormalities and $D_{\text{DDSM}}_{\text{TE}}$ comprising masses only. A detection is considered correct if the overlap between the detected regions and the ground truth annotation exceeds 10% for $D_{\text{RINB}}_{\text{TE}}$ and 20% for the $D_{\text{DDSM}}_{\text{TE}}$. Results reported in Table 6 are from Vu et al. (2023) and Liu et al. (2020).

For the FFDM images (Table 5), our *MSGCN*$_{18}$ improves the initial $B_{18}$ performance detection, increasing the TPR from 0.67 to 0.93 while having a higher number of FPPI (from 0.08 to 0.33). The high pair-wise correspondences between mammography views and the

<footnote n="9">⁹ https://github.com/GuillaumeP2705/SBip.git.</footnote>
<caption>**Table 3**</caption>

Comparison of our approaches against the state-of-the-art methods using breast-wise AUC-ROC and AUC-PR on the different datasets with 95% bootstrap confidence intervals (CI) and 2000 bootstrap replicates. n.a. stands for not available.

<table><caption>**Table 4**</caption><thead><tr><th rowspan="2">Dataset</th><th rowspan="2"></th><th rowspan="2">AUC</th><th colspan="6">Models</th></tr><tr><th>B<sub>18</sub><br>In-house</th><th>MSGCN<sub>18</sub><br>In-house<br>Pelluet et al.<br>(2022)</th><th>SBIP<sub>18</sub><br>In-house</th><th>Faster<br>(R-CNN)<br>Ribli et al.<br>(2018)</th><th>GMIC<br>(Top-5 ensemble)<br>Shen et al.<br>(2019b)</th><th>DMV-CNN<br>Wu et al. (2020)</th><th>GLAM<br>Liu et al. (2021a)</th><th>BRAIxMVCCL<br>(Single)<br>Chen et al.<br>(2022)</th></tr></thead><tbody><tr><td rowspan="4">D<sub>RINB<sub>TE</sub></sub></td><td rowspan="2">ROC</td><td>0.93<br>(0.91–0.97)</td><td>0.95<br>(0.92–0.98)</td><td><strong>0.96</strong><br>(<strong>0.93–0.98</strong>)</td><td>0.92<br>(0.88–0.96)</td><td>0.65<br>(0.81–0.94)</td><td>0.80<br>(0.73–0.87)</td><td>0.88<br>(0.55–0.75)</td><td>n.a.<br>n.a.</td></tr><tr><td>0.81<br>(0.67–0.93)</td><td>0.88<br>(0.79–0.94)</td><td><strong>0.90</strong><br>(<strong>0.79–0.94</strong>)</td><td>0.82<br>(0.71–0.91)</td><td>0.82<br>(0.81–0.95)</td><td>0.56<br>(0.40–0.71)</td><td>0.47<br>(0.32–0.62)</td><td>n.a.<br>n.a.</td></tr><tr><td rowspan="2">PR</td><td>0.97<br>(0.95–1.00)</td><td>0.98<br>(0.97–1.00)</td><td><strong>0.99</strong><br>(<strong>0.99–1.00</strong>)</td><td>0.97<br>(0.92–1.00)</td><td>0.98<br>(0.94–1.0)</td><td>0.80<br>(0.65–0.93)</td><td>0.61<br>(0.43–0.79)</td><td><strong>0.99</strong><br>(<strong>0.99–1.00</strong>)</td></tr><tr><td>0.923<br>(0.85–1.00)</td><td>0.98<br>(0.97–1.00)</td><td><strong>0.99</strong><br>(<strong>0.98–1.00</strong>)</td><td>0.94<br>(0.81–1.00)</td><td>0.96<br>(0.86–1.00)</td><td>0.74<br>(0.51–0.91)</td><td>0.53<br>(0.28–0.74)</td><td><strong>0.99</strong><br>(0.97–1.00)</td></tr><tr><td rowspan="4">D<sub>SINB<sub>TE</sub></sub></td><td rowspan="2">ROC</td><td>0.82<br>(0.80–0.84)</td><td>0.82<br>(0.81–0.85)</td><td>0.83<br>(0.81–0.85)</td><td>0.81<br>(0.79–0.82)</td><td>0.83<br>(0.82–0.85)</td><td>0.74<br>(0.72–0.76)</td><td>0.79<br>(0.77–0.80)</td><td><strong>0.85</strong><br>(<strong>0.84–0.86</strong>)</td></tr><tr><td>0.91<br>(0.90–0.93)</td><td><strong>0.92</strong><br>(<strong>0.91–0.94</strong>)</td><td><strong>0.92</strong><br>(<strong>0.91–0.94</strong>)</td><td>0.84<br>(0.83–0.86)</td><td>0.86<br>(0.84–0.88)</td><td>0.79<br>(0.80–0.84)</td><td>0.82<br>(0.76–0.80)</td><td>0.88<br>(0.86–0.89)</td></tr><tr><td rowspan="2">PR</td><td>0.923<br>(0.85–1.00)</td><td>0.98<br>(0.97–1.00)</td><td><strong>0.99</strong><br>(<strong>0.98–1.00</strong>)</td><td>0.94<br>(0.81–1.00)</td><td>0.96<br>(0.86–1.00)</td><td>0.74<br>(0.51–0.91)</td><td>0.53<br>(0.28–0.74)</td><td><strong>0.99</strong><br>(0.97–1.00)</td></tr><tr><td>0.91<br>(0.90–0.93)</td><td><strong>0.92</strong><br>(<strong>0.91–0.94</strong>)</td><td><strong>0.92</strong><br>(<strong>0.91–0.94</strong>)</td><td>0.84<br>(0.83–0.86)</td><td>0.86<br>(0.84–0.88)</td><td>0.79<br>(0.80–0.84)</td><td>0.82<br>(0.76–0.80)</td><td>0.88<br>(0.86–0.89)</td></tr></tbody></table>

Comparison of our approaches against the state-of-the-art methods using AUC-ROC on $D_{VINDR_{TE}}$ at different levels, and $D_{CBIS_{TE}}$ at the image level. For the comparison at a case and breast level against DMV-CNN, GMIC-R18, and Resnet34, we followed the instructions in Pathak et al. (2024). n.a. stands for not available.

<table><thead><tr><th rowspan="2">Models</th><th colspan="2">D<sub>VINDR<sub>TE</sub></sub></th><th>D<sub>CBIS<sub>TE</sub></sub></th></tr><tr><th>Breast</th><th>Case</th><th>Image</th></tr></thead><tbody><tr><td>B<sub>19</sub></td><td>0.86 ± 0.05</td><td>0.89 ± 0.04</td><td>0.73 ± 0.04</td></tr><tr><td>MSGCN<sub>19</sub></td><td>0.82 ± 0.07</td><td>0.78 ± 0.08</td><td><strong>0.84 ± 0.02</strong></td></tr><tr><td>SBIP<sub>19</sub></td><td><strong>0.91 ± 0.04</strong></td><td><strong>0.92 ± 0.02</strong></td><td>0.80 ± 0.03</td></tr><tr><td>DMV-CNN (Wu et al., 2020)</td><td>n.a.</td><td>0.75 ± 0.04</td><td>n.a.</td></tr><tr><td>GMIC-R18 (Shen et al., 2021)</td><td>n.a.</td><td>n.a.</td><td>0.79 ± 0.02</td></tr><tr><td>ResNet-34 (Shen et al., 2021)</td><td>n.a.</td><td>n.a.</td><td>0.78 ± 0.01</td></tr><tr><td>GMIC-R18 (Pathak et al., 2024)</td><td>n.a.</td><td>0.83 ± 0.02</td><td>n.a.</td></tr><tr><td>ResNet-34<sup>a</sup> (Truong et al., 2023)</td><td>0.75 ± n.a.</td><td>n.a.</td><td>n.a.</td></tr><tr><td>SBIP<sub>19</sub><sup>a</sup></td><td><strong>0.89 ± 0.04</strong></td><td>0.87 ± 0.05</td><td>n.a.</td></tr></tbody></table>

<caption>**Table 5**</caption>

Comparison against state-of-the-art in terms of detection performance on $D_{RINB_{TE}}$.

<table><thead><tr><th>Authors</th><th>Models</th><th>TPR@FPPI</th></tr></thead><tbody><tr><td>Ribli et al. (2018)</td><td>Faster R-CNN</td><td>0.90@0.30</td></tr><tr><td>Shen et al. (2019a)</td><td>ResNet-50</td><td><strong>0.97@1.94</strong></td></tr><tr><td>Ours</td><td>B<sub>18</sub></td><td>0.67@0.08</td></tr><tr><td>Ours</td><td>MSGCN<sub>18</sub></td><td>0.86@0.19</td></tr><tr><td>Ours</td><td>SBIP<sub>18</sub></td><td>0.93@0.33</td></tr><tr><td>Ours</td><td>[B<sub>18</sub>, MSGCN<sub>18</sub>]av</td><td>0.94@0.29</td></tr><tr><td>Ours</td><td>[B<sub>18</sub>, SBIP<sub>18</sub>]av</td><td><strong>0.97@0.33</strong></td></tr></tbody></table>

redundancy of the mono-view oversegmentation can explain a higher number of FPPI for our MSGCN<sub>18</sub>. We observe similar results with B<sub>19</sub> with digitized mammograms. When averaging our heatmaps with the backbone heatmaps that have a low number of FPPI, we improve the TPR by +0.04 for the SBIP<sub>18</sub>. Compared to the state-of-the-art detection performance, our method achieves a competitive number of FPPI (0.33 against 0.30 for Ribli et al. (2018)) while preserving a higher number of true positives (0.97 against 0.90). Shen et al. (2019a) achieved a TPR of 0.97, equivalent to our own TPR, at the expense of a higher FPPI (1.94 versus 0.33 for us), which is less suitable for clinical analysis. In Section 4.5, we qualitatively analyze our method with examples of detection for several cases extracted from $D_{RINB_{TE}}$ to better understand how the proposed model benefits from the correspondence reasoning mechanism. Our method can delineate malignant regions

<caption>**Table 6**</caption>

Comparison against state-of-the-art methods in terms of mass detection performance on $D_{DBSM_{TE}}$. Our split is 100 bootstrap replicates and averaged over 126 normal images from the test set and 196 malignant images containing only masses, following a similar distribution of the test set in Liu et al. (2020).

<table><thead><tr><th>Authors</th><th>Models</th><th>TPR@FPPI</th></tr></thead><tbody><tr><td>Ma et al. (2021)</td><td>Faster R-CNN</td><td>0.73@1.20</td></tr><tr><td>Ma et al. (2021)</td><td>CVR-RCNN</td><td>0.85@1.20</td></tr><tr><td>Liu et al. (2020)</td><td>BG-RCNN</td><td>0.80@0.50</td></tr><tr><td>Liu et al. (2021b)</td><td>AG-RCNN</td><td><strong>0.82@0.50</strong></td></tr><tr><td>Zhao et al. (2022)</td><td>CL-Net</td><td>0.83@0.50</td></tr><tr><td>Vu et al. (2023)</td><td>M&M</td><td><strong>0.87@0.50</strong></td></tr><tr><td>Ours</td><td>B<sub>19</sub></td><td>0.63@0.37</td></tr><tr><td>Ours</td><td>MSGCN<sub>19</sub></td><td>0.53@1.07</td></tr><tr><td>Ours</td><td>SBIP<sub>19</sub></td><td>0.40@1.08</td></tr><tr><td>Ours</td><td>[B<sub>19</sub>, MSGCN<sub>19</sub>]av</td><td>0.79@0.63</td></tr><tr><td>Ours</td><td>[B<sub>19</sub>, SBIP<sub>19</sub>]av</td><td>0.81@0.69</td></tr></tbody></table>

more accurately and find the suspicious areas missed by the B<sub>18</sub>. Thanks to the relevant contributions and correspondences retrieved with the ipsilateral view, our approach exhibits better generalization ability to datasets from unseen manufacturers (e.g., Siemens from $D_{RINB_{TE}}$) than other deep learning based methods.

Regarding the digitalized images (Table 6), a higher detection performance is achieved with our $[B<sub>19</sub>, SBIP<sub>19</sub>]av$ at the cost of a higher number of FPPI compared to other approaches such as BG-RCNN of Liu et al. (2020), where final heatmaps are fed to a mask R-CNN (He et al., 2017). We exceed their performances with a TPR@FPPI at 0.81@0.69 versus 0.80@0.5, improving their detection rate. However, they showed in their other work (Liu et al., 2021b) that using the bilateral view in the model allows a contrastive analysis, improving their performance to 0.82@0.5 with their AG-RCNN (Liu et al., 2021b). Compared to other approaches such as Zhao et al. (2022) (0.83@0.5) and Vu et al. (2023) (0.87@0.5), the proposed models achieved a competitive TPR at the expense of a higher number of false positives (FPPI). The latter can be explained by the fact that detections are not processed individually using a top model such as the RPN (Chen et al., 2024) or the Mask R-CNN (Liu et al., 2021b, 2020) to avoid the selection of imprecise region proposals.

## 4.3. Ablation study

**Modules Ablation.** To confirm the importance of both multi-scale topological information and inter-view correlations, we performed ablation of our dual-view model on $D_{RINB_{TE}}$. We used the node-wise labels to define the edge types (i.e., types are based on the predicted

<footnote>a Denotes evaluation using a subset of $D_{VINDR_{TE}}$ composed of BI-RADS 2 versus BI-RADS 4&5.</footnote>
<figure><img src="image_10.png" /><figcaption>Fig. 7. Evolution of the correspondences determined by our SBIP<sub>18</sub> (left) and the number of removed bipartite edges (right) on D<sub>RINB<sub>TE</sub></sub>. The low opacity curve represents the raw results collected at each epoch, while the solid curve is the smoothed version for visualization. Color is recommended for a better visualization.</figcaption></figure>

<caption>**Table 7**</caption>

Ablation study with breast-wise AUC-ROC on the D<sub>RINB<sub>TE</sub></sub> X stands for no pixel-wise annotations, and ✓ stands for pixel-wise annotations.

<table><thead><tr><th rowspan="2">Dataset</th><th colspan="3">Models</th><th rowspan="2">AUC</th><th rowspan="2">Δ<sub>a</sub></th></tr><tr><th>B<sub>18</sub></th><th>MSGCN<sub>18</sub></th><th>SBIP<sub>18</sub></th></tr></thead><tbody><tr><td rowspan="4">D<sub>RINB<sub>TE</sub></sub></td><td>✓</td><td>✗</td><td>✗</td><td>0.93</td><td>✗</td></tr><tr><td>✓</td><td>✓</td><td>✗</td><td>0.95</td><td>✗</td></tr><tr><td>✓</td><td>✗</td><td>✓</td><td>0.95</td><td>0.0003</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td><strong>0.96</strong></td><td><strong>0.0284</strong></td></tr></tbody></table>

label of the source and destination nodes). We can see in Table 7 that our MSGCN<sub>18</sub> improves the initial performance of the backbone B<sub>18</sub> (from 0.93 to 0.95), leveraging multi-scale topological and semantic information but without taking into account the cross-view correlation. The performance increased to 0.96 when using our dual-view approach, which successfully embeds the ipsilateral information. To show the interest of the proposed method, we also computed the gap Δ<sub>a</sub> between the average of all attention scores of positive (type 1) and non-positive (type 2 and 3) bipartite edges. We observe a high gap in the case of SBIP, with 0.0284. However, suppose we do not use our mono-view backbone to encode topological information first. In that case, the difference falls to 0.0003, showing that the topological information has to be encoded with the backbone features X to produce discriminate bipartite correspondences. Fig. 10 shows a qualitative visual comparison between our backbone model B<sub>18</sub> and our SBIP<sub>18</sub>. We can clearly see that the gated message passing between both views improves the detection relying on the inter-view correlations.

**Analysis of the Edge Pruning Process.** We further analyze the importance of edge removal for correspondence evaluation. Fig. 7 illustrates the evolution of the correspondences between views and the number of edges kept on D<sub>RINB<sub>TE</sub></sub> at each epoch of the training. As we can see, the SBIP<sub>18</sub> rapidly pruned 49.5% of the negative edges (type 3), 67% of the edges of type 2, and 83.5% of the positive edges (type 1), indicating that the model removed a significant number of redundant and noisy edges resulting from the superpixel multi-scale oversegmentation. Ye and Ji (2021) have presented a similar behavior of the edge pruning process with their SGAT on disassortative graphs.

To demonstrate the relevance of bipartite edges correspondences in dual-view analysis, we use three different strategies to measure the evolution of the dual-view classification while removing auxiliary nodes that contribute the most to the final classification for the graphs classified as malignant only:

<figure><img src="image_11.png" /><figcaption>Fig. 8. Evolution of the image-wise malignancy probability performance with our SBIP<sub>18</sub> on the images classified as malignant from D<sub>RINB<sub>TE</sub></sub> when different percentages of auxiliary nodes are detected by the network as important (i.e., nodes from the auxiliary view are detected as important for the main view when they have a high attention score) are removed from the dual-view graph. Three strategies for selecting nodes for removal are considered: (green) Top-k; (blue) Rand-k; (red) Bot-k. Color is recommended for a better visualization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

1. top-k sorted descending by their contribution value c<sub>i</sub>

2. uniformly rand-k removal

3. bot-k sorted descending by their contribution value c<sub>i</sub>

Using the removal strategy, we remove nodes on the auxiliary view with the most important contributions to any node in the main view, i.e., we hypothesized that highly contributive auxiliary nodes should correspond to malignant nodes. Then, we revert the main and auxiliary views for inference and measured the image-wise AUC to see the evolution over iterations, which should decrease with a top-k% strategy. At each iteration, we remove 1% of the total number of nodes on each scale until 20% of the information in each scale is removed. Fig. 8 illustrates the evolution of the classification performance on the D<sub>RINB<sub>TE</sub></sub> dataset when different percentages of nodes are removed from the graph with different strategies. As we can see, SBIP<sub>18</sub> accurately identifies a percentage of essential correspondences between views, as removing them from the graph incurs a more important average malignancy probability loss than bot-k or rand-k node removal. However, after 5% of auxiliary nodes are removed, the average malignancy probability slowly increases, showing that contribution from the auxiliary view contains false positive nodes. Regarding the other strategies, we
<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Comparison of the explicability of our models with weakly supervised and fully supervised models on malignant mammograms from $D_{RINB_{TE}}$. Color is recommended for a better visualization.</figcaption></figure>

can see a low difference between bot-k and rand-k as the random approach eliminates negative nodes, which are more prevalent than positive nodes in the graph.

### 4.4. Explainability of the proposed models

We compare the explainability of our model against weakly and fully supervised state-of-the-art models from Stadnick et al. (2021). We used a masking strategy based on a grid of tile 32 × 32 over the image for the state-of-the-art methods to generate larger areas to analyze (Zafeiriou et al., 2023). There are two reasons to prefer larger areas over pixels. The first reason is efficiency, as mammograms are high-resolution images. The second reason is that a region perturbation allows for observable changes contrary to single pixel perturbation. For our graphs, we used a pruning strategy to perturb semantic information and graph topology similarly to the edge pruning process presented earlier. The analysis is constrained to 20% of the number of patches or nodes by scales in the breast removed with a top-k% strategy, as relevant information should not surpass 20% of the breast area. We removed only the nodes in the main view for our bipartite model, as the auxiliary view is not used for prediction but only for its contribution. In this section, we work exclusively on a subset of $D_{RINB_{TE}}$ which contains only malignant images (denoted as $D_{POS}$) to evaluate how the model is confident on its prediction. We based our evaluation on two hypotheses: (i) The bigger and steeper the average malignancy probability drop is, the more accurate the importance ordering of the image regions and, consequently, the model is more explainable (Zafeiriou et al., 2023); (ii) A false negative prediction should remain false negative when removing important regions.

In our iterative process to compare the explainability between models, we removed at each iteration $j$, 1% of the patches or nodes in the descending order of their malignancy, as these are scored by importance by the heatmap itself. Note that we kept only patches overlapping with the breast by at least 10%, and nodes are removed for each scale independently. Then, the average malignancy probability $P$ is computed as $P(j) = \frac{p(j)}{p(0)}$ over the images, with $p(j) = \sum_{I_j \in D_{POS}} Q(I_j)$ and $Q$ a model. To enable a fair comparison between different models, the average probability is normalized between [0, 1] with a min-max scaler.

Fig. 9 displays our results. While DMV (Wu et al., 2020) and our schemes predict one probability for the malignancy, the two other methods predict two independent probabilities for both benign and malignant classes. For a fair comparison, we only observe the normalized

<figure><img src="image_13.png" /><figcaption>**Fig. 10.** Visualization of the detections (first and third columns) and contribution maps (second and fourth columns) obtained by the backbone network $B_{18}$ and our bipartite model $SBIP_{18}$ (red and blue delimitations, respectively) on $D_{RINB_{TE}}$. Green delimitations show lesion annotations. Color is recommended for a better visualization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

proportional evolution of the malignancy probability. Compared to the GMIC approach (GMIC top-5 ensemble) (Shen et al., 2019b), GLAM (Liu et al., 2021a) converges rapidly to a malignancy probability of 0.37 in a few epochs, showing that GLAM produces more explainable results. Still, it took longer than the other methods to reach its minimum, meaning the model is interpretable even though it is less precise. On the other side, our methods ($MSGCN_{18}$ and $SBIP_{18}$) converge to a local minimum before removing 12% of information, similarly to DMV (Wu et al., 2020) which suggests that supervised methods are more explainable, which is of no surprise as they carefully use pixel-wise annotations. However, we can see that $SBIP_{18}$ produces less explainable predictions than $MSGCN_{18}$, as our bipartite graphs are disassortative, which means that a large number of bipartite edges results in a higher number of false positives in the main view compared to the $MSGCN_{18}$, as shown in Table 5.

### 4.5. Qualitative analysis

To qualitatively evaluate our method, we show in Fig. 10 three examples of detections in three different breast cases on FFDM images. We can see that the bipartite graph focuses on the malignant regions of the auxiliary view and thus learns complementary feature representations to detect malignant areas in the main view. Our model provides radiologists with a relatively precise delineation of suspicious regions, aiding clinical interpretation. Moreover, the third row shows that $SBIP_{18}$ can detect and rectify an area partially missed by the $B_{18}$. Indeed, finding correspondences in the second view not only enhanced the initial mono-view classification and detection performance but also provided an explainable decision with the provided contribution maps.
<figure><img src="image_14.png" /><figcaption>**Fig. 11.** Visualization of a successful model prediction on a benign case (first row), and two malignant cases missed by our models (second and last rows). Our backbone networks (red and blue delimitations in the images, respectively) were applied to the FFDM images from $D_{RINB_{TE}}$. For the last row, we used $B_{19}$ and $SBIP_{19}$ to analyze digitized images from $D_{CBIS_{TE}}$. Green delimitations show lesion ground truth annotations. Color is recommended for a better visualization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

On the other side, Fig. 11 shows a true negative case and limits of our approach on positive cases for FFDM and digitalized images. On the first row, we can see the true negative case without correspondences as no detection was found (mammograms were correctly classified as negative as they do not contain any malignant abnormalities, only benign lesions). The second row shows an example of a missed correspondence from the MLO view (auxiliary) to the CC view (main), where only one lesion was correlated with the detections. The last row on digitized examples shows the correct correspondence between the MLO lesions. However, the lesion on the CC view was missed, resulting in a false positive activation. But the $SBIP_{19}$ correctly found a correspondence between the false positive and the malignant auxiliary region.

## 4.6. Discussion

**Limitations.** Despite the promising results, our method has some limitations. First, the performance on digitized mammograms is lower than on FFDM images, suggesting that further adaptation is needed for heterogeneous data sources and more specific pre-processing could be done. Moreover, the current implementation of our method requires a significant amount of memory to process a dual-view multi-scale graph built upon high-resolution images, and therefore relies on the availability of a high-end GPU, e.g., A100 GPU with 40 GB of memory, which limits its practical deployment for radiologists in typical clinical environments. Additionally, while our bipartite approach improves detection, it can introduce more false positives due to its disassortative nature as shown in Table 6.

**Future work.** In future studies, our work will focus on three points. First, transformers (Vaswani et al., 2017) will be explored to enhance the correspondence mechanism between ipsilateral nodes, allowing for more robust and flexible modeling of the relationships between views. This should enable the model to capture complex patterns better and improve the overall performance of the framework. Second, our work could be expanded to ipsilateral and bilateral analysis as the work presented by Liu et al. (2021b), since asymmetry is also a malignant clue that is looked at by the radiologist. Additionally, we could use correspondence analysis between different modalities, e.g., enabling the study of mammography and MRI, as they provide complementary information in diagnosis (our method is dimensionally invariant). Lastly, approaches similar to the multi-scale decomposition presented by Wang et al. (2025) can be explored based on the multi-scale properties of our baseline network to reduce the computational cost of our method and improve the performances.

## 5. Conclusion

In this work, we propose a new method for dual-view mammography classification and lesion detection relying on a unified graph framework independent from spatial constraints, which combines an initial backbone model and a multi-scale single-view backbone with a dual bipartite graph. Our method features (i) a mono-view graph representation, allowing the capture of topological and semantic information at different scales, (ii) a cross-view pair-wise correlation in an unregistered setting, and (iii) a sparse graph attention network capable of exploiting different edge classes and accurately removing unreliable edges. Thanks to its ability to explore the complementarity between different views and multiple scales, the proposed approach outperforms most state-of-the-art methods in classification and detection. Furthermore, with the sparse graph attention paradigm, we can visualize the main view's malignancy heatmap and the auxiliary view's contributions, making the model more interpretable for clinical diagnosis.

## CRediT authorship contribution statement

**Guillaume Pelluet:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Resources, Methodology, Formal analysis, Data curation, Conceptualization. **Mira Rizkallah:** Validation, Supervision, Resources, Project administration, Methodology, Conceptualization. **Mickael Tardy:** Writing – review & editing, Writing – original draft, Validation, Supervision, Software, Resources, Project administration, Methodology, Formal analysis, Data curation, Conceptualization. **Diana Mateus:** Writing – review & editing, Writing – original draft, Validation, Supervision, Resources, Project administration, Methodology, Investigation, Data curation, Conceptualization.

## Funding

This work was supported by Hera-MI SAS, and the ANRT grant 2020/1124.

## Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Guillaume Pelluet reports financial support was provided by National Association of Technical Research. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
## Acknowledgments

The authors acknowledge Dr. Clement Bailly, Dr. Bruno Cheffer, M. Paul Terrassin, and Dr. Nathan Lauzeral for helping annotate the private dataset and contributing to the design of the baselines used in this work. We would also like to thank the GLiCID team for providing the computational resources for this research.

## Data availability

Training data are private but we used public datasets to compare our performances against StateOfTheArt methods. Moreover, subsets details are available on a git link.

## References

Chen, Y., Liu, Y., Wang, C., Elliott, M., Kwok, C.F., Peña-Solorzano, C., Tian, Y., Liu, F., Frazer, H., McCarthy, D.J., et al., 2024. BRAIxDet: Learning to detect malignant breast lesion with incomplete annotations. Med. Image Anal. 96, 103192.

Chen, Y., Wang, H., Wang, C., Tian, Y., Liu, F., Liu, Y., Elliott, M., McCarthy, D.J., Frazer, H., Carneiro, G., 2022. Multi-view local co-occurrence and global consistency learning improve mammogram classification generalisation. Int. Conf. Med. Image Comput. Comput. Assist. Interv. (MICCAI) http://dx.doi.org/10.1007/978-3-031-16437-8_1, URL: https://link.springer.com/chapter/10.1007/978-3-031-16437-8_1.

Chunyan, C., Li, L., Hongmin, C., Zhihao, F., Ling, Z., Tingting, D., et al., 2021. The Chinese mammography database (CMMD): An online mammography database with biopsy confirmed types for machine diagnosis of breast. Cancer Imaging Arch. http://dx.doi.org/10.7937/tcia.eqdde-4b16.

D'Orsi, C.J., 2014. ACR BI-RADS atlas: Breast imaging reporting and data system - acr. URL: https://books.google.co.in/books?vid=ISBN155903016X&redir=()esc=y.

Du, H., Feng, J., Feng, M., 2019. Zoom in to where it matters: a hierarchical graph based model for mammogram analysis. arXiv preprint arXiv:1912.07517.

Du, H., Yao, M.M.S., Liu, S., Chen, L., Chan, W.P., Feng, M., 2023. Automatic calcification morphology and distribution classification for breast mammograms with multi-task graph convolutional neural network. IEEE J. Biomed. Heal. Inform. 27 (8), 3782-3793. http://dx.doi.org/10.1109/JBHI.2023.3249404.

George, M., Chen, Z., Zwiggelaar, R., 2019. Multiscale connected chain topological modelling for microcalcification classification. Comput. Biol. Med. 114, 103422. http://dx.doi.org/10.1016/j.combiomed.2019.103422, URL: https://www.sciencedirect.com/science/article/pii/S0010482519302999.

He, K., Gkioxari, G., Dollár, P., Girshick, R., 2017. Mask R-CNN. IEEE/CVF Int. Conf. Comput. Vis. (ICCV) 2980-2988. http://dx.doi.org/10.1109/ICCV.2017.322.

Heath, M., Bowyer, K., Kopans, D., Kegelmeyer, Jr., P., Moore, R., Chang, K., Munishkumaran, S., 1998. Current status of the digital database for screening mammography. Digit. Mammogr.: Nijmegen, 1998 457-460.

Henriksen, E.L., Carlsen, J.F., Vejborg, I.M., Nielsen, M.B., Lauridsen, C.A., 2019. The efficacy of using computer-aided detection (CAD) for detection of breast cancer in mammography screening: a systematic review. Acta Radiol. 60 (1), 13-18.

Huang, H., Lin, L., Tong, R., Hu, H., Zhang, Q., Iwamoto, Y., Han, X., Chen, Y.-W., Wu, J., 2020. Unet 3+: A full-scale connected unet for medical image segmentation. IEEE Int. Conf. Acoust. Speech Signal Process. (ICASSP) 1055-1059.

Ibrahim, R., Shafiq, M.O., 2023. Explainable convolutional neural networks: A taxonomy, review, and future directions. ACM Comput. Surv. 55 (10), http://dx.doi.org/10.1145/3563691.

Kingma, D.P., Ba, J., 2014. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980.

Lee, R.S., Gimenez, F., Hoogi, A., Miyake, K.K., Gorovoy, M., Rubin, D.L., 2017. A curated mammography data set for use in computer-aided detection and diagnosis research. Sci. Data 4 (1), 1-9.

Lei Lei, Y., Tian, Y., Shan, H., Zhang, J., Wang, G., Kalra, M.K., 2020. Shape and margin-aware lung nodule classification in low-dose CT images via soft activation mapping. Med. Image Anal. 60, 101628.

Li, P., Zhong, J., Chen, H., Hong, J., Li, H., Li, X., Shi, P., 2025. An explainable and comprehensive BI-RADS assisted diagnosis pipeline for mammograms. Phys. Medica 132, 104994. http://dx.doi.org/10.1016/j.ejpmp.2025.104994, URL: https://www.sciencedirect.com/science/article/pii/S1120179725000596.

Liu, K., Shen, Y., Wu, N., Chłędowski, J., Fernandez-Granda, C., Geras, K.J., 2021a. Weakly-supervised high-resolution segmentation of mammography images for breast cancer diagnosis. Proc. Mach. Learn. Res. 143, 268-285, arXiv:2106.07049.

Liu, Y., Zhang, F., Chen, C., Wang, S., Wang, Y., Yu, Y., 2021b. Act like a radiologist: Towards reliable multi-view correspondence reasoning for mammogram mass detection. IEEE Trans. Pattern Anal. Mach. Intell. (TPAMI) 44 (10), 5947-5961. http://dx.doi.org/10.1109/TPAMI.2021.3085783.

Liu, Y., Zhang, F., Zhang, Q., Wang, S., Wang, Y., Yu, Y., 2020. Cross-view correspondence reasoning based on bipartite graph convolutional network for mammogram mass detection. Proc. IEEE/CVF Int. Conf. Comput. Vis. Pattern Recognit. (CVPR) 3811-3821. http://dx.doi.org/10.1109/CVPR42600.2020.00387.

Loizidou, K., Elia, R., Pitris, C., 2023. Computer-aided breast cancer detection and classification in mammography: A comprehensive review. Comput. Biol. Med. 153 (December 2022), 106554. http://dx.doi.org/10.1016/j.combiomed.2023.106554.

Lopez, E., Grassucci, E., Valleriani, M., Comminiello, D., 2022. Multi-view breast cancer classification via hypercomplex neural networks. arXiv preprint arXiv:2204.05798. arXiv:2204.05798. URL: http://arxiv.org/abs/2204.05798.

Louizos, C., Welling, M., Kingma, D.P., 2017. Learning sparse neural networks through L0 regularization. arXiv preprint arXiv:1712.01312.

LoweKamp, B.C., Chen, D.T., Yaniv, Z., Yoo, T.S., 2018. Scalable Simple Linear Iterative Clustering (SSLIC) Using a Generic and Parallel Approach. Kitware, Inc..

Ma, J., Li, X., Li, H., Wang, R., Menze, B., Zheng, W.-S., 2021. Cross-view relation networks for mammogram mass detection. Int. Conf. Pattern Recognit. (ICPR) 8632-8638.

Min, H., Chandra, S.S., Crozier, S., Bradley, A.P., 2019. Multi-scale sifting for mammographic mass detection and segmentation. Biomed. Phys. Express 5, http://dx.doi.org/10.1088/2057-1976/aafc07.

Min, H., Chandra, S.S., Dhungel, N., Crozier, S., Bradley, A.P., 2017. Multi-scale mass segmentation for mammograms via cascaded random forests. In: IEEE Int. Symp. on Biomedical Imaging. ISBI, pp. 113-117. http://dx.doi.org/10.1109/ISBI.2017.7950481.

Moreira, I.C., Amaral, I., Domingues, I., Cardoso, A., Cardoso, M.J., Cardoso, J.S., 2012. INbreast: Toward a full-field digital mammographic database. Academic Radiol. 19 (2), 236-248. http://dx.doi.org/10.1016/j.acra.2011.09.014.

Nauta, M., Trienes, J., Pathak, S., Nguyen, E., Peters, M., Schmitt, Y., Schlötterer, J., van Keulen, M., Seifert, C., 2023. From anecdotal evidence to quantitative evaluation methods: A systematic review on evaluating explainable AI. ACM Comput. Surv. 55 (13s).

Nguyen, H.T., Nguyen, H.Q., Pham, H.H., Lam, K., Le, L.T., Dao, M., Vu, V., 2023. VinDr-Mammo: A large-scale benchmark dataset for computer-aided diagnosis in full-field digital mammography. Sci. Data 10 (1), 277.

Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, et al., 2019. PyTorch: An Imperative Style, High-Performance Deep Learning Library. Curran Associates, Inc., pp. 8024-8035, URL: http://papers.neurips.cc/paper/9015-pytorch-an-imperative-style-high-performance-deep-learning-library.pdf.

Pathak, S., Schlötterer, J., Veltman, J., Geerdink, J., van Keulen, M., Seifert, C., 2024. Prototype-based interpretable breast cancer prediction models: Analysis and challenges. In: Longo, L., Lapuschkin, S., Seifert, C. (Eds.), Explainable Artificial Intelligence. Springer Nature Switzerland, Cham, pp. 21-42.

Pelluet, G., Rizkallah, M., Acosta, O., Mateus, D., 2021. Unsupervised multimodal supervoxel merging towards brain tumor segmentation. Int. Brain Lesion (BrainLes) Work. Conjunction MICCAI 88-99.

Pelluet, G., Rizkallah, M., Tardy, M., Acosta, O., Mateus, D., 2022. Multi-scale graph neural networks for mammography classification and abnormality detection. Int. Conf. Med. Image Underst. Anal. (MIUA) 636-650.

Ribli, D., Horváth, A., Unger, Z., Pollner, P., Csabai, I., 2018. Detecting and classifying lesions in mammograms with deep learning. Sci. Rep. 8 (1), 1-7. http://dx.doi.org/10.1038/s41598-018-22437-z, arXiv:1707.08401.

Shapiro, S., Coleman, E.A., Broeders, M., Codd, M., de Koning, H., Fracheboud, J., Moss, S., Paci, E., Stachenko, S., Ballard-Barbash, R., et al., 1998. Breast cancer screening programmes in 22 countries: current policies, administration and guidelines. Int. J. Epidemiol. 27 (5), 735-742.

Shen, L., Margolies, L., Rothstein, J., Fluder, E., McBride, R., Sieh, W., 2019a. Deep learning to improve breast cancer detection on screening mammography. Sci. Rep. 9, 1-12. http://dx.doi.org/10.1038/s41598-019-48995-4.

Shen, Y., Wu, N., Phang, J., Park, J., Kim, G., Moy, L., Cho, K., Geras, K.J., 2019b. Globally-aware multiple instance classifier for breast cancer screening. Int. Work. Mach. Learn. Med. Imaging (MLMI), Conjunction MICCAI 18-26.

Shen, Y., Wu, N., Phang, J., Park, J., Liu, K., Tyagi, S., Heacock, L., Kim, S.G., Moy, L., Cho, K., et al., 2021. An interpretable classifier for high-resolution breast cancer screening images utilizing weakly supervised localization. Med. Image Anal. 68, http://dx.doi.org/10.1016/j.media.2020.101908, arXiv:2002.07613.

Siegel, R.L., Miller, K.D., Fuchs, H.E., Jemal, A., 2022. Cancer statistics, 2022. CA: Cancer J. Clin. 72 (1), 7-33. http://dx.doi.org/10.3322/caac.21708.

Stadnick, B., Witowski, J., Rajiv, V., Chłędowski, J., Shamout, F.E., Cho, K., Geras, K.J., 2021. Meta-repository of screening mammography classifiers. http://dx.doi.org/10.48550/arxiv.2108.04800, arXiv:2108.04800, arXiv:2108.04800.

Truong, T.T., Nguyen, H.T., Lam, T.B., Nguyen, D.V., Nguyen, P.H., 2023. Delving into ipsilateral mammogram assessment under multi-view network. Int. Work. Mach. Learn. Med. Imaging (MLMI), Conjunction MICCAI 367-376.

Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A.N., Kaiser, L., Polosukhin, I., 2017. Attention is all you need. Adv. Neural Inf. Process. Syst. 30.

Velickovic, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y., 2018. Graph attention networks. Int. Conf. Learn. Represent. (ICLR) 1-12, arXiv:1710.10903.

Vu, Y.N., Guo, D., Taha, A., Su, J., Matthews, T.P., 2023. M&M tackling false positives in mammography with a multi-view and multi-instance learning sparse detector. Int. Conf. Med. Image Comput. Comput. Assist. Interv. (MICCAI) 778-788.
Wang, C., Chen, Y., Liu, F., Elliott, M., Kwok, C.F., Peña-Solorzano, C., Frazer, H., McCarthy, D.J., Carneiro, G., 2024. An interpretable and accurate deep-learning diagnosis framework modeled with fully and semi-supervised reciprocal learning. IEEE Trans. Med. Imaging (TMI) 43 (1), 392–404. http://dx.doi.org/10.1109/TMI.2023.3306781.

Wang, C., Guo, Y., Chen, H., Guo, Q., He, H., Chen, L., Zhang, Q., 2025. ABUS-net: Graph convolutional network with multi-scale features for breast cancer diagnosis using automated breast ultrasound. Expert Syst. Appl. 273, 126978. http://dx.doi.org/10.1016/j.eswa.2025.126978, URL: https://www.sciencedirect.com/science/article/pii/S0957417425006001.

Wang, M., Zheng, D., Ye, Z., Gan, Q., Li, M., Song, X., Zhou, J., Ma, C., Yu, L., Gai, Y., Xiao, T., He, T., Karypis, G., Li, J., Zhang, Z., 2019. Deep graph library: Towards efficient and scalable deep learning on graphs. CoRR abs/1909.01315. arXiv:1909.01315.

Warner, E., 2011. Breast-cancer screening. N. Engl. J. Med. 365 (11), 1025–1032.

Wu, N., Phang, J., Park, J., Shen, Y., Huang, Z., Zorin, M., Jastrzębski, S., Févry, T., Katsnelson, J., Kim, E., Wolfson, S., Parikh, et al., 2020. Deep Neural Networks Improve Radiologists' Performance in Breast Cancer Screening. IEEE Trans. Med. Imaging (TMI) 39 (4), 1184–1194. http://dx.doi.org/10.1109/TMI.2019.2945514, arXiv:1903.08297.

Yan, Y., Conze, P.-H., Lamard, M., Quellec, G., Cochener, B., Coatrieux, G., 2020. Multitasking siamese networks for breast mass detection using dual-view mammogram matching. Int. Work. Mach. Learn. Med. Imaging (MLMI), Conjunction MICCAI (September), 312–321. http://dx.doi.org/10.1007/978-3-030-59861-7_32.

Yang, Z., Cao, Z., Zhang, Y., Tang, Y., Lin, X., Ouyang, R., Wu, M., Han, M., Xiao, J., Huang, L., Wu, S., Chang, P., Ma, J., 2021. MommiNet-v2: Mammographic multi-view mass identification networks. Med. Image Anal. 73, http://dx.doi.org/10.1016/j.media.2021.102204.

Yang, Y., Wang, S., Liu, L., Hickman, S., Gilbert, F.J., Schönlieb, C.-B., Aviles-Rivero, A.I., 2023. MammoDG generalisable deep learning breaks the limits of cross-domain multi-center breast cancer screening. arXiv preprint arXiv:2308.01057.

Ye, Y., Ji, S., 2021. Sparse graph attention networks. IEEE Trans. Knowl. Data Eng. 35 (1), 905–916.

Zack, G.W., Rogers, W.E., Latt, S.A., 1977. Automatic measurement of sister chromatid exchange frequency. J. Histochem. Cytochem. 25 (7), 741–753. http://dx.doi.org/10.1177/25.7.70454, PMID: 70454. arXiv:https://doi.org/10.1177/25.7.70454.

Zafeiriou, A., Kallipolitis, A., Maglogiannis, I., 2023. Ensembling to leverage the interpretability of medical image analysis systems. IEEE Access.

Zhao, Z., Wang, D., Chen, Y., Wang, Z., Wang, L., 2022. Check and link: Pairwise lesion correspondence guides mammogram mass detection. Eur. Conf. Comput. Vis. (ECCV) 384–400. http://dx.doi.org/10.1007/978-3-031-19803-8_23, arXiv:2209.05809.

Zhou, J., Cui, G., Hu, S., Zhang, Z., Yang, C., Liu, Z., Wang, L., Li, C., Sun, M., 2020. Graph neural networks: A review of methods and applications. AI Open 1, 57–81. http://dx.doi.org/10.1016/j.aiopen.2021.01.001, URL: https://www.sciencedirect.com/science/article/pii/S266651021000012.