Semi-supervised Robust Feature Selection with ℓ_q-Norm Graph for Multiclass Classification

Flexible manifold embedding (FME) is a semi-supervised dimension reduction framework. It has been extended into feature selection by using different loss functions and sparse regularization methods. However, these kind of methods used the quadratic form of graph embedding, thus the results are sensitive to noise and outliers. In this paper, we propose a general semisupervised feature selection model that optimizes an ℓ_q-norm of FME to decrease the noise sensitivity. Compare to the fixed parameter model, the ℓ_q-norm graph brings flexibility to balance the manifold smoothness and the sensitivity to noise by tuning its parameter. We present an efficient iterative algorithm to solve the proposed ℓ_q-norm graph embedding based semi-supervised feature selection problem, and offer a rigorous convergence analysis. Experiments performed on typical image and speech emotion datasets demonstrate that our method is effective for the multiclass classification task, and outperforms the related state-of-the-art methods.