Supervised machine learning explainability has developed rapidly in recent years. However, clustering explainability has lagged behind. Here, we demonstrate the first adaptation of model-agnostic explainability methods to explain unsupervised clustering. We present two novel "algorithm-agnostic" explainability methods - global permutation percent change (G2PC) and local perturbation percent change (L2PC) - that identify feature importance globally to a clustering algorithm and locally to the clustering of individual samples. The methods are (1) easy to implement and (2) broadly applicable across clustering algorithms, which could make them highly impactful. We demonstrate the utility of the methods for explaining five popular clustering methods on low-dimensional synthetic datasets and on high-dimensional functional network connectivity data extracted from a resting-state functional magnetic resonance imaging dataset of 151 individuals with schizophrenia and 160 controls. Our results are consistent with existing literature while also shedding new light on how changes in brain connectivity may lead to schizophrenia symptoms. We further compare the explanations from our methods to an interpretable classifier and find them to be highly similar. Our proposed methods robustly explain multiple clustering algorithms and could facilitate new insights into many applications. We hope this study will greatly accelerate the development of the field of clustering explainability.
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