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Concept Factorization by Joint Locality-constrained and ℓ 2,1-norm Regularization for Image Representation
Wei Jiang, Jie Zhang and Yongqing Zhang

Concept Factorization (CF) is a variation of Nonnegative Matrix Factorization (NMF) that each basis vector can be expressed by linear combination of the data points, each of which can be represented by a linear combination of all the bases. However, existing techniques could not accurately control over the sparseness. To address this issue, we propose a unified criterion, called Concept Factorization by Joint Locality-constrained and 𝓁2,1-norm regularization (CF2L), which is designed to simultaneously perform concept factorization and locality constraint as well as to achieve the row sparsity. We reformulate the non-negative local coordinate factorization problem and use 𝓁2,1-norm on the coefficient matrix to achieve row sparsity, which leads to selecting relevant features. An efficient multiplicative updating procedure is produced, and its convergence is guaranteed theoretically. Experiments on benchmark face recognition data sets demonstrate the effectiveness of our proposed algorithm in comparison to the state-of-the-art approaches.

Keywords: Concept factorization, feature selection, local constraint, clustering, 𝓁2,1-norm, row sparsity.

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