Discriminative and Uncorrelated Feature Selection With Constrained Spectral Analysis in Unsupervised Learning

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Abstract
The existing unsupervised feature extraction methods frequently explore low-redundant features by an uncorrelated constraint. However, the constrained models might incur trivial solutions, due to the singularity of scatter matrix triggered by high-dimensional data. In this paper, we propose a regularized regression model with a generalized uncorrelated constraint for feature selection, which leads to three merits: 1) exploring the low-redundant and discriminative features; 2) avoiding the trivial solutions and 3) simplifying the optimization. Besides that, the local cluster structure is achieved via a novel constrained spectral analysis for the unsupervised learning, where Must-Links and Cannot-Links are transformed into a intrinsic graph and a penalty graph respectively, rather than incorporated into a mixed affinity graph. Accordingly, a discriminative and uncorrelated feature selection with constrained spectral analysis (DUCFS) is proposed with adopting σ -norm regularization for interpolating between F-norm and l2,1 -norm. Due to the flexible gradient and global differentiability, our model converges fast. Extensive experiments on benchmark datasets among several state-of-the-art approaches verify the effectiveness of the proposed method.
Funding Information
  • Northwestern Polytechnical University (CX201918)
  • China Postdoctoral Science Foundation (2018M643765, 2019T120960)
  • Xi’an Postdoctoral Innovation Base Funding
  • National Natural Science Foundation of China (61871470, 61761130079, 61751202, 61772427)
  • National Basic Research Program of China (2018AAA0101902)

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