CM-CaFE: A Clustering Method with Causality-based Feature Embedding

Clustering is a fundamental technique widely used for exploring the inherent data structure. Many studies indicate that an appropriate feature representation can effectively improve clustering performance. However, the existing feature representation methods are based on correlation to select or extract features, which makes it hard to deal with spurious correlations. The spurious correlations mislead the correlation-based methods to consider features that have no causal relationship as being correlative, which limits the clustering performance and feature interpretability. To tackle this issue, inspired by causal learning, we propose a new joint optimization Clustering Method with Causal Feature Embedding (CM-CaFE) , which utilizes the causality of features to learn more discriminative representation for clustering. Specifically, to eliminate spurious correlations among features, we first employ any state-of-the-art Markov blanket learning method to learn an undirected causal graph. Next, we extract the maximal fully connected causal subgraphs from the learned undirected causal graph and propose an approach to merge them to generate the causal matrix. Based on the causal matrix, we present an objective function that consists of a clustering loss term and a causal matrix fitting term to learn a causal transformation matrix. The causal transformation matrix is utilized to map the original data into a new space for clustering. Finally, we comprehensively compare the proposed method with some state-of-the-art clustering approaches on several datasets to demonstrate the effectiveness and interpretability of the proposed method.