Papers › Online Estimation of Similarity Matrices with Incomplete Data
Online Estimation of Similarity Matrices with Incomplete Data
Fangchen Yu, Yicheng Zeng, Jianfeng Mao, Wenye Li
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 https://github.com/CUHKSZ-Yu/OnMC.
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