Enhancing Breast Cancer Diagnosis in Mammography: Evaluation and Integration of Convolutional Neural Networks and Explainable AI

Interpretability in ML is about comprehending how a model operates, especially when predicting variables. It provides insight into the model’s prediction mechanisms without necessarily unraveling the causal relationships behind those predictions. While interpretability contributes to a model’s overall explainability, not every interpretable model can be deemed fully explainable. It also encompasses the evaluation of hypothetical scenarios, allowing us to speculate on the outcomes had certain inputs been altered. The aim is to achieve a thorough understanding of the ML model, factoring in both visible and hidden elements, to construct a broad explanation of its functionality. The opaque nature of many AI models often obscures the rationale behind their outputs, complicating efforts to understand their decision-making processes. However, interpretability primarily concerns grasping the model’s functional details, whereas explainability extends this by elucidating how the model reacts to new data and the implications of specific changes in its predictions. This distinction becomes particularly significant in healthcare, where the stakes of decision-making are high. A deep comprehension of how AI algorithms derive their suggestions is essential. Without such transparency, healthcare practitioners may hesitate to rely on and embrace AI technologies, fearing the inability to confirm the validity of their recommendations [15]. Thus, explainability and interpretability are essential for verifying the reliability and fairness of AI systems, especially in areas like healthcare, finance, and the legal system where decision-making has significant consequences.

XAI models are primarily divided into two main categories: intrinsic and post-hoc. Intrinsic models, also known as transparent models, are naturally understandable and explainable.

Conversely, post-hoc explainability techniques are further divided into model-specific and model-agnostic methods. Models lacking inherent transparency utilize post-hoc or surrogate models to clarify their decision-making processes. Model-specific explanations are custom-made to fit a model’s unique architecture, with Grad-CAM and saliency maps being notable examples. In contrast, model-agnostic explanations are more versatile and can be applied across different models to explain the prediction process, with SHAP and LIME being widely recognized methods in this category. XAI explanations can also be distinguished as local or global. Local explanations focus on understanding individual decisions made by a model, while global explanations provide insight into the overall behavior and rules of the model across all scenarios.

The subsequent sections delve into various XAI models, with an emphasis on those most commonly applied alongside ML/Deep Learning (DL) models in the context of breast cancer research. A thorough discussion of XAI models follows, including an overview of relevant research within the breast cancer domain.

Introduced by Lundberg, SHAP [16] offers a coherent framework for the interpretation of model predictions, attributing significance to each feature in the context of a specific prediction. SHAP elucidates the influence of individual features on the output of any ML model, providing a tool for both global and local model understanding.

Game theory, particularly as seen through Shapley values, serves as the foundation for the SHAP methodology. It aims to distribute the prediction outcome fairly among the features, akin to dividing a payout among players based on their contribution.

SHAP Formalism: The SHAP value equation is presented as follows:

Here, $\phi(f,x)$ symbolizes the SHAP value for a model prediction $f$ with input $x$, where $z^{\prime}$ denotes a subset of features, $M$ the total number of features, and $f_{x}(z^{\prime})$ and $f_{x}(z^{\prime}\setminus i)$ represent the model’s predictions for the subset $z^{\prime}$ and for the subset excluding a specific feature, respectively.

Key principles of SHAP include:

1. 1.

   Local Accuracy:  This principle asserts that the output from the explanation model $g(x^{\prime})$ should align with the original model’s output $f(x)$ for any given input $x$, as follows:

   $$f(x)=g(x^{\prime})=\phi_{0}+\sum_{i=1}^{M}\phi_{i}x^{\prime}_{i}$$

   (2)

   Here, $\phi_{0}$ is the model’s base value, and $\phi_{i}$ are the SHAP values associated with each feature.

2. 2.

   Missingness: According to this principle, an absent feature (with a value of zero) in the input should not influence the model’s prediction, formalized as:

   $$x^{\prime}_{i}=0\Rightarrow\phi_{i}=0$$

   (3)

3. 3.

   Consistency: The consistency principle states that SHAP values should accurately reflect a feature’s impact. If a feature’s presence or constancy enhances the model’s output, its SHAP value should not decrease. For any two models, $f$ and $f^{\prime}$, if

   $$f_{x}^{\prime}(z^{\prime})-f_{x}^{\prime}(z^{\prime}\setminus i)\geq f_{x}(z^{\prime})-f_{x}(z^{\prime}\setminus i)$$

   (4)

   for all inputs $z^{\prime}\in\{0,1\}^{M}$, then $\phi_{i}(f^{\prime},x)\geq\phi_{i}(f,x)$.

SHAP thus provides a mathematically rigorous framework for fair and consistent feature importance attribution, enhancing the interpretability of ML models.

Grad-CAM [17], introduced by Selvaraju et al., serves as a visual explanation method for a wide spectrum of CNN models. It operates by identifying and illuminating significant areas within an input image that are pivotal for the model’s class predictions. This is achieved by calculating the gradients of any target class relative to the activations in the final convolutional layer, thereby creating a heatmap of these key regions. Distinguished from CAM, Grad-CAM boasts adaptability across various CNN architectures, enabling model interpretability without necessitating architectural modifications. As a method that discriminates between classes, Grad-CAM conducts gradient calculations and manipulates the feature maps of the concluding convolutional layer to produce meaningful visualizations.

Grad-CAM Computation Steps:

1. 1.

   Gradient Calculation: The first step of Grad-CAM involves the calculation of the gradient of the loss concerning the final convolutional layer’s activations:

   $$\frac{\partial L}{\partial A^{k}}$$

   (5)

   This step discerns the contribution of each segment within the activation maps towards the model’s loss, delineating their significance in the decision-making process.

2. 2.

   Global Average Pooling (GAP) of Gradients: Following, a Global Average Pooling (GAP) operation is applied to these gradients to ascertain the importance weights ($\alpha_{k}$) for each channel within the activation maps:

   $$\alpha_{k}=\frac{1}{Z}\sum_{i}\sum_{j}\frac{\partial L}{\partial A^{k}_{i,j}}$$

   (6)

   Herein, $Z=H\times W$ represents the total count of elements in the activation map $A^{k}$, with $\alpha_{k}$ elucidating the weightage of each channel’s impact on the model’s output.

3. 3.

   Final Grad-CAM Equation: The construction of the Grad-CAM heatmap is then achieved by applying these weights to the activation maps and incorporating the ReLU function:

   $$\text{Grad-CAM}_{c}=\text{ReLU}\left(\sum_{k}\alpha_{k}A^{k}\right)$$

   (7)

This formula emphasizes the collaborative effect of the weighted activation maps on illuminating the predictive regions of the input image. The ReLU ensures visualization of only those features positively affecting the target class, thereby aiding in the interpretability of the model’s predictive behavior.

Ribeiro et al. introduced Local Interpretable Model-Agnostic Explanations (LIME) [18], which generate explanations that are both locally accurate and comprehensible for individual predictions by simulating the model’s decision boundary to be linear in the proximity of the instance being explained. It explicates an instance by fitting an interpretable model to a perturbed dataset around the input instance, shedding light on the prediction mechanisms of the original model.

LIME Formalism:

1. 1.

   Interpretable Data Representations:  The distinction between the actual features used by the model and those used for explanations is pivotal. For comprehensibility, explanations utilize representations that are understandable to humans, which might be different from the complex features the model employs. For text classification, this could be a binary vector denoting word presence, and for image classification, it might indicate the presence or absence of super-pixels, despite the model using complex features like word embeddings or pixel tensors.

   $$x\in{R}^{d}$$

   (8)

   This represents the original instance, and

   $$x^{\prime}\in\{0,1\}^{d^{\prime}}$$

   (9)

   This is its binary vector form for interpretable representation.

2. 2.

   Fidelity-Interpretability Trade-off:  The explanation model, $g\in G$, where $G$ encompasses models such as linear models, decision trees, or lists, is chosen for its simplicity. The domain of $g$ is $\{0,1\}^{d^{\prime}}$, acting over the binary vector. The complexity of an explanation model, $\Omega(g)$, varies; for instance, it might be the depth of a decision tree or the count of non-zero weights in a linear model. The fidelity function, $L(f,g,\pi_{x})$, assesses how accurately the explanation model approximates the original model $f$ near instance $x$, with $\pi_{x}(z)$ defining proximity to $x$. To balance interpretability and local fidelity, the optimal explanation minimizes:

   $$\xi(x)=\arg\min_{g\in G}L(f,g,\pi_{x})+\Omega(g)$$

   (10)

3. 3.

   Sampling for Local Exploration:  LIME approximates the loss $L(f,g,\pi_{x})$, weighted by $\pi_{x}$, by sampling around $x^{\prime}$ without presupposing any structure for $f$. This sampling constructs a dataset $Z$ of perturbed samples with labels generated by the model $f$. Optimizing equation (10) with dataset $Z$ yields a locally faithful explanation $\xi(x)$, emphasizing the need for a balance between simplicity and fidelity.

4. 4.

   Sparse Linear Explanations:    Considering $G$ as the class of linear models and $L$ as the locally weighted square loss, the aim is to derive a sparse linear model that remains interpretable. This is facilitated using a kernel function $\pi_{x}(z)$ to stress local proximity around $x$:

   $$L(f,g,\pi_{x})=\sum_{z,z^{\prime}\in Z}\pi_{x}(z)(f(z)-g(z^{\prime}))^{2}$$

   (11)

   To ensure interpretability, limitations on the number of features in the explanation are imposed, typically achieved through regularization methods like Lasso for feature selection, followed by least squares for weight determination, known as K-LASSO.

   $$\Omega(g)=\infty 1[||w_{g}||_{0}>K]$$

   (12)

LIME strategically creates explanations that are both locally accurate and interpretable, offering insights into the operational behaviors of complex models through interpretable approximations.

The Curated Breast Imaging Subset of the Digital Database for Screening Mammography (CBIS-DDSM) is an updated and standardized version of the DDSM, containing 2,620 mammography studies categorized into malignant, benign, and normal classifications as depicted in Table 1 . This extensive dataset includes 10,239 images, totaling 163.6 GB, featuring mammograms coupled with accurate pathology annotations through ROI segmentation and bounding boxes. Its comprehensive scale and verified annotations establish CBIS-DDSM as the preferred dataset for this study.

In this study, 2,129 mammograms were selected from the dataset, with each corresponding mammogram’s ROI extracted and converted from DICOM to PNG format. The number of ROIs varies across images, with each highlighting the critical features. All ROIs from an individual mammogram were merged into a single composite image, resulting in a dataset of 2,129 paired mammograms and ROI images.

An illustration of this process can be seen in Figure 3, which displays a composite of five ROIs from one mammogram. Accompanying CSV files classify these images into benign and malignant categories, comprising 1,229 benign and 900 malignant cases. Figure 2 exemplifies a benign and a malignant mammogram alongside their respective ROIs from the dataset.

Preprocessing is crucial in optimizing the efficacy and computational efficiency of DL models applied to medical imaging. For this research, the mammographic images within the dataset were standardized to a resolution of 224x224 pixels. This dimensionality adjustment is followed by a rigorous preprocessing pipeline meticulously designed to expunge extraneous details while simultaneously amplifying diagnostically relevant features within the images. The preprocessing regimen encompasses three principal components: artifact reduction, line removal, and image enhancement, each underpinned by data augmentation strategies to expand the dataset beyond its original volume of 2,129 images.

In the domain of ML applications within medical imaging analysis, data augmentation emerges as a critical preprocessing step, especially in tasks involving mammogram classification. The essence of data augmentation lies in its capacity to augment the training dataset through a series of transformations, such as flipping, rotating, and adjusting image properties. This process introduces a broader range of scenarios for the model to learn from, significantly enhancing its robustness and preventing overfitting. It is vital in medical imaging, where the ability to accurately recognize diverse patterns and anomalies can dramatically affect diagnostic outcomes. The goal of implementing specific augmentation strategies is to enrich the dataset with complexities and variabilities reflective of real-world conditions, thereby improving the model’s diagnostic performance.

Before the augmentation process begins, a crucial step involves dividing the collection of mammographic images into training and testing groups, adhering to a 90:10 split. This division is essential for ensuring a balanced representation of both benign and malignant cases in the training and testing phases and maintaining the integrity of the dataset. A balanced representation aids in preventing model bias, ensuring that the diagnostic capabilities of the ML model are developed uniformly across different types of cases.

Upon establishing a structured and balanced dataset, the focus shifts to enhancing the robustness and generalizability of the model. This enhancement is achieved by applying a series of data augmentation techniques to the training set. The deployment of these techniques aims to increase the size of the training dataset by generating modified versions of the images, thereby reducing overfitting and improving the model’s ability to generalize from training to unseen data.

To address this, seven distinct data augmentations were implemented on the training dataset. which include horizontal flipping, vertical flipping, and combined flipping in both directions and rotations (both positive and negative 30 degrees), with and without subsequent flipping as shown in Figure 6. Such comprehensive augmentation ensures the model is exposed to a wide array of image orientations and variations, mirroring the diversity encountered in real-world diagnostic settings.

The approach involves the use of models pre-trained on large datasets, which are then slightly adjusted or fine-tuned to perform specific tasks, such as identifying abnormalities in mammogram images. Transfer learning is particularly beneficial in situations where annotated medical datasets are scarce. By leveraging knowledge acquired from related tasks, it allows for the efficient training of robust models on smaller datasets, simply by modifying the model’s final layers to adapt to the new task. This technique’s capacity to overcome the challenges posed by limited data availability has been well documented in the literature of [39]. The ability to transfer learned patterns from one domain to another significantly enhances model performance and accelerates the development process in data-constrained environments. Convolutional neural Networks (CNNs) are at the forefront of image analysis technologies, with several architectures standing out for their performance. Notable examples include VGG [40], Res-Net [41], Dense-Net [42], Inception [43], and Alex-Net [44]. Each architecture offers distinct advantages, making them suitable for a wide range of applications in deciphering image data. This study aimed to evaluate the performance of various transfer learning models on a dataset curated for mammographic image analysis. The models tested were VGG16, Inception V3, Res-Net18, and Res-Net50. Consistency in dataset usage and data split ratios ensured the reliability of performance comparisons. The objective was to identify the model that The evaluations revealed variations across the tested models, with Res-Net50 emerging as the most effective, achieving a test accuracy of 72%. Enhancement of this model through fine-tuning—a process of re-adjusting pre-trained weights for specific tasks as detailed in [45]—led to improved accuracy of 76% as displayed in Table 2.

The fine-tuned Res-Net50 model is instrumental in the integration of XAI within the mammographic analysis. XAI aims to increase transparency in AI decision-making processes, making AI-driven diagnoses more understandable. This is particularly important in the medical sector, where clear diagnostic reasoning can significantly affect patient outcomes. The research findings demonstrate the significant impact of transfer learning on improving the accuracy of AI models for medical image analysis. Additionally, this study lays the foundation for advancements in Explainable AI (XAI) to bridge the gap between AI’s capabilities and human interpretability. This increased understanding has the potential to encourage better collaboration between healthcare professionals and AI systems, ultimately leading to improved patient care.

To ensure the safety and security of any AI system, it is important to consider how much knowledge about the model itself is revealed by the information provided in the explanation. An example of information leakage can be the explanations of a k-nearest neighbor model, which can reveal the information of the training data points of the model. However, when this factor is considered for our model, it is not a concern as we use DL models, which are essentially black-box models and require explanations to understand the results. The explanations provided by our chosen methods of Grad-CAM, LIME, and SHAP also do not reveal any information about the architecture of the model itself; instead, they help us understand the regions of interest chosen by the model in each sample image. Each output of the models provides visual information that highlights the most important regions in the image.

The factor of information misuse comes into consideration based on the information in the model that is leaked via explanations. A model can be stolen or replicated if considerable information about it can be gathered through the explanations. However, this factor does not apply to our model, as our methods of explanation do not leak any information regarding the architecture of the model.

The third factor in the dimension of safety is explanation invariance. The primary objective of explanations is to develop an understanding of humans for each sample. Hence, an explainable system is expected to be stable and consistent.

The factor of stability defines that explanations of the same prediction by a model generated multiple times should result in the same explanation as well. This was evaluated in our model as well by implementing the three XAI techniques multiple times on the same image. An explanation generated by LIME results from the process of random perturbation, which generates simulated data in the surroundings of an instance for a simple linear classifier to predict and results in instability as it leads to the generation of different explanations for the same prediction [46]. Hence, while Grad-CAM and SHAP are stable and produce the same explanation for each prediction, the explanation provided by LIME is unstable, which has been shown in Figure 10.

The factor of consistency defines that explanations of a fixed model for similar data points should also be similar. We have evaluated the consistency of our model by using the ROI data provided in the original CBIS DDSM dataset and checking whether images with similar regions of interest have similar XAI results. The Figure 11 shows two similar ROI images with similar Grad-CAM results, which shows the consistency of Grad-CAM. SHAP works by assigning each feature an importance value for a particular prediction [47]. Hence, similar datapoints are assigned similar importance values, which shows the consistency of SHAP. The instability of LIME also makes LIME inconsistent as it generates different explanations for the same prediction; hence, comparison of similar data points does not produce similar explanations.

The final safety measure is the explanation quality, which emphasizes the correctness of the explanation provided. While we have achieved the explainability of the model, it is necessary to analyze the correctness of the explanations provided by the different XAI functions to understand the performance of the black-box DL model. To analyze the explanations provided by XAI techniques for the performance of our model, the ROI images of the CBIS DDSM dataset have been used to compare the areas of importance highlighted by verified pathologists with the areas highlighted by XAI techniques. The ratio of similarity between the results of XAI and the original ROI images indicated how well the model is detecting the correct parts of the images for its classification. To create this ratio, we have created binary masks of the explanations provided by Grad-CAM and LIME which are shown in Figure 12.

Figure 13 shows the original mammogram, the pre-processed image, the Grad-CAM output, the mask generated from the Grad-CAM heatmap, and the original ROI from the dataset.

Figure 14 shows the original mammogram, the pre-processed image, the LIME output, the mask generated from the LIME segments, and the original ROI from the dataset.

The binary masks are then compared to the ROI images using Hausdorff distance. Hausdroff distance is a common measure for comparing the dissimilarity between image segmentation and point sets [48]. This method is commonly used in the medical domain to evaluate segmentation in medical images such as computed tomography (CT) and magnetic resonance imaging (MRI) [49]. The Hausdorff distance $\check{H}$ between two point sets $A$ and $B$ is the maximum distance between each point, as shown in the following equation [48].

The degree of resemblance is greater when the value of the Hausdroff distance between two shapes is smaller [50]. The range of Hausdorff distance values depends on the size and complexity of the images being compared. In general, the Hausdorff distance values range from 0 to infinity, where a value of 0 indicates that the two binary masks are identical, and larger values indicate increasing differences between the two masks. After the Hausdroff distance for each image is calculated, the mean distance is calculated to analyze the performance of the model. A lower mean Hausdorff distance indicates a higher level of similarity between all the images, while a higher mean Hausdorff distance indicates a greater level of dissimilarity.
When comparing the ROI images with the masks produced by Grad-CAM, the Hausdorff distance values of our dataset range from 1 to 133, with the mean Hausdorff value being 18. When comparing the ROI images with the masks produced by Grad-CAM, the Hausdorff distance values of our dataset range from 1 to 160, with the mean Hausdorff value being 86. This indicates that the performance of the Grad-CAM explainability technique is better than the explainability provided by LIME.