Robust multi-view learning with incomplete information has received significant attention due to issues such as incomplete correspondences and incomplete instances that commonly affect real-world multi-view applications. Existing approaches heavily rely on paired samples to realign or impute defective ones, but such preconditions cannot always be satisfied in practice due to the complexity of data collection and transmission. To address this problem, we present a novel framework called SeMantic Invariance LEarning (SMILE) for multi-view clustering with incomplete information that does not require any paired samples. To be specific, we discover the existence of invariant semantic distribution across different views, which enables SMILE to alleviate the cross-view discrepancy to learn consensus semantics without requiring any paired samples. The resulting consensus semantics remains unaffected by cross-view distribution shifts, making them useful for realigning/imputing defective instances and forming clusters. We demonstrate the effectiveness of SMILE through extensive comparison experiments with 13 state-of-the-art baselines on five benchmarks. Our approach improves the clustering accuracy of NoisyMNIST from 19.3%/23.2% to 82.7%/69.0% when the correspondences/instances are fully incomplete. We will release the code after acceptance.

Fair clustering aims to divide data into distinct clusters while preventing sensitive attributes (e.g., gender, race, RNA sequencing technique) from dominating the clustering. Although a number of works have been conducted and achieved huge success recently, most of them are heuristical, and there lacks a unified theory for algorithm design. In this work, we fill this blank by developing a mutual information theory for deep fair clustering and accordingly designing a novel algorithm, dubbed FCMI. In brief, through maximizing and minimizing mutual information, FCMI is designed to achieve four characteristics highly expected by deep fair clustering, i.e., compact, balanced, and fair clusters, as well as informative features. Besides the contributions to theory and algorithm, another contribution of this work is proposing a novel fair clustering metric built upon information theory as well. Unlike existing evaluation metrics, our metric measures the clustering quality and fairness as a whole instead of separate manner. To verify the effectiveness of the proposed FCMI, we conduct experiments on six benchmarks including a single-cell RNA-seq atlas compared with 11 state-of-the-art methods in terms of five metrics. The code could be accessed from https://pengxi.me.