Adaptive reweighted quaternion sparse learning for data recovery and classification

doi:10.1016/j.patcog.2023.109653

Adaptive reweighted quaternion sparse learning for data recovery and classification

2023-10-01

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DOI：10.1016/j.patcog.2023.109653

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Sparse representation (SR) methods in quaternion space have been attracting increasing interests recently. However, most existing quaternion SR methods adopt the quaternion L 1 norm, which penalizes all the entries of the quaternion sparse vector equally and ignores the differences and significance of different entries. Ideally, the entries with large magnitude should be less penalized while those with small mag-nitude (such as zero entries) should be more penalized. Therefore, we propose an Adaptive Weighted Quaternion Sparse Representation (AWQSR) method in this paper, which can learn weights for distinct entries of the quaternion sparse entries in an adaptive manner. Due to the noncommutativity of quater-nion multiplication, it is difficult to tackle the resulting optimization problem of AWQSR. For this reason, we devise an effective iteratively reweighted optimization algorithm based on quaternion operators. To further improve the classification performance, we also develop a Supervised AWQSR based Classifica-tion (SAWQSRC) method by leveraging the label information of training samples to learn discriminative weights. Theoretical analysis of SAWQSRC has also been established to show that SAWQSRC succeeds in classification under appropriate conditions. The experiments on simulated data and real data prove the validity of the proposed methods for quaternion signal recovery and classification.(c) 2023 Elsevier Ltd. All rights reserved.

Keywords:

Quaternion sparse representation

Weight learning

Supervised learning

vector

Adaptive reweighted quaternion sparse learning for data recovery and classification

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