Win-Win: On Simultaneous Clustering and Imputing over Incomplete Data

Abstract

Although clustering methods have shown promising performance in various applications, they cannot effectively handle incomplete data. Existing studies often impute missing values first before clustering analysis and conduct these two processes separately. However, inaccurate imputation does not necessarily contribute positively to the subsequent clustering. Intuitively, accurate imputation and clustering can serve and benefit from each other, where clustering-based imputation methods typically utilize cluster signals to impute incomplete data and accurate fillings are expected to bring more valuable data for clustering. Therefore, in this manuscript, rather than considering two tasks independently or conducting them respectively, we study simultaneous clustering and imputing over incomplete data. The immediate benefit is that such a strategy improves both clustering and imputation performance simultaneously, to get a win-win result. Our major technical highlights include (1) the problem formalization and NP-hardness analysis on computing simultaneous clustering and imputing results, (2) exact solutions by transforming the problem as the integer linear programming (ILP) formulation, and (3) efficient approximation algorithms based on the linear programming (LP) relaxation and local neighbors (LN) solution, with approximation guarantees. Experiments on various real-world datasets demonstrate the superiority of our work in clustering and imputing incomplete data.