Robust Self-expression Learning with Adaptive Noise Perception

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Self-expression learning methods often obtain a coefficient matrix to measure the similarity between pairs of samples. However, directly using the raw data to represent each sample under the self-expression framework may not be ideal, as noise points are inevitably involved in the process of representing clean samples. To address this issue, this work proposes a novel self-expression model called robust Self-Expression learning with adaptive Noise Perception (SENP). SENP decomposes each sample into a clean part and a noisy part, and samples with large self-expression losses can be recognized as the noise points. A reliable coefficient matrix can then be learned by using only the clean points to reconstruct the clean part of each sample. By simultaneously detecting the noisy part of each sample and noise points, and adaptively mitigating their negative impacts, the representative ability of the generated coefficient matrix is improved. Moreover, inspired by the solution of non-negative matrix factorization (NMF), an effective algorithm is formed to optimize SENP. Extensive experiments on well-known benchmark datasets demonstrate the superiority of SENP compared to several state-of-the-art methods.