Unsupervised feature selection via low-rank approximation and structure learning

Feature selection is an important research topic in machine learning and computer vision in that it can reduce the dimensionality of input data and improve the performance of learning algorithms. Low-rank approximation techniques can well exploit the low-rank property of input data, which coincides with the internal consistency of dimensionality reduction. In this paper, we propose an efficient unsupervised feature selection algorithm, which incorporates low-rank approximation as well as structure learning. First, using the self-representation of data matrix, we formalize the feature selection problem as a matrix factorization with low-rank constraints. This matrix factorization formulation also embeds structure learning regularization as well as a sparse regularized term. Second, we present an effective technique to approximate low-rank constraints and propose a convergent algorithm in a batch mode. This technique can serve as an algorithmic framework for general low-rank recovery problems as well. Finally, the proposed algorithm is validated in twelve publicly available datasets from machine learning repository. Extensive experimental results demonstrate that the proposed method is capable to achieve competitive performance compared to existing state-of-the-art feature selection methods in terms of clustering performance.