Explainable Classification of Brain Networks via Contrast Subgraphs

Abstract

Mining human-brain networks to discover patterns that can be used to discriminate between healthy individuals and patients affected by some neurological disorder, is a fundamental task in neuroscience. Learning simple and interpretable models is as important as mere classification accuracy. In this paper we introduce a novel approach for classifying brain networks based on extracting contrast subgraphs, i.e., a set of vertices whose induced subgraphs are dense in one class of graphs and sparse in the other. We formally define the problem and present an algorithmic solution for extracting contrast subgraphs. We then apply our method to a brain-network dataset consisting of children affected by Autism Spectrum Disorder and children Typically Developed. Our analysis confirms the interestingness of the discovered patterns, which match background knowledge in the neuroscience literature. Further analysis on other classification tasks confirm the simplicity, soundness, and high explainability of our proposal, which also exhibits superior classification accuracy, to more complex state-of-the-art methods.

Counterfactual Graphs for Explainable Classification of Brain Networks

“…Still in the context of brain network classification, Lanciano et al [17] propose a method based on contrast subgraph, i.e., a set of vertices whose induced subgraph is very dense in one class of graphs and very sparse in the other class. This approach produces very simple classifiers which are transparent and self-explanatory.…”

“…While [17,41] propose methods that have some explainability bydesign, here we study how to produce local post-hoc explanations of any black-box graph classifier, by means of graph counterfactuals.…”

“…Their proposal is an explanatory agent based on reinforcement learning which has access to the internal representation of the black-box and leverages domain knowledge to constrain the generated explanations to be valid molecules. The main difference with our work is in the type of graph classification assumed: our graphs, in fact, enjoy node identity awareness [15,17], i.e., the fact that a specific vertex id is unique in a graph and corresponds to the same brain ROI through all the input networks. Conversely, molecules are small graphs where the vertices are atoms, the same vertex can thus appear many times in the same graph, and the links are labeled with the type of bond.…”

“…Besides the importance of explainability, classification of brain networks distinguishes from other graph classification tasks for other aspects. As discussed by other authors, e.g., [15,17], brain networks enjoy node identity awareness, i.e., the fact that a specific vertex id is unique in a graph and corresponds to the same brain ROI through all the input networks, which are all thus defined over the same vertices 𝑉 . This is different from other graph classification tasks and other application domains (e.g., prediction of functional and structural properties of molecules in cheminformatics) where vertices can share the same labels and the vertex identity is not a relevant information.…”

“…Thanks to the network representation of the brain, many interesting neuroscience challenges can be tackled as graph mining problems [6]. A prominent example is that of classification of brain networks: given two groups of individuals, a condition group (class 1) and a control group (class 0), where each individual is represented as a brain network, i.e., a graph defined over the same set 𝑉 of vertices corresponding to the brain regions of interest (ROIs), the goal is to infer a model that, given an unseen graph defined over the same vertices 𝑉 , it is able to predict whether the new individual belongs to class 0 or class 1 [17,23,39,41].…”