Online Estimation of Similarity Matrices with Incomplete Data

Fangchen Yu, Yicheng Zeng, Jianfeng Mao, Wenye Li

Keywords: Incomplete Online Data, Similarity Estimation, Matrix Correction, Convex Optimization

TL;DR: The paper proposes a series of matrix correction algorithms that estimate similarity matrices with incomplete data in different online scenarios.

Abstract: The similarity matrix measures pairwise similarities between a set of data points and is an essential concept in data processing, routinely used in practical applications. Obtaining a similarity matrix is typically straightforward when data points are completely observed. However, incomplete observations can make it challenging to obtain a high-quality similarity matrix, which becomes even more complex in online data. To address this challenge, we propose matrix correction algorithms that leverage the positive semi-definiteness (PSD) of the similarity matrix to improve similarity estimation in both offline and online scenarios. Our approaches have a solid theoretical guarantee of performance and excellent potential for parallel execution on large-scale data. Empirical evaluations demonstrate their high effectiveness and efficiency with significantly improved results over classical imputation-based methods, benefiting downstream applications with superior performance. Our code is available at \url{https://github.com/CUHKSZ-Yu/OnMC}.