  Feature selection is an important data pre-processing in data mining and
machine learning, which can reduce feature size without deteriorating model's
performance. Recently, sparse regression based feature selection methods have
received considerable attention due to their good performance. However, because
the $l_{2,0}$-norm regularization term is non-convex, this problem is very hard
to solve. In this paper, unlike most of the other methods which only solve the
approximate problem, a novel method based on homotopy iterative hard threshold
(HIHT) is proposed to solve the $l_{2,0}$-norm regularization least square
problem directly for multi-class feature selection, which can produce exact
row-sparsity solution for the weights matrix. What'more, in order to reduce the
computational time of HIHT, an acceleration version of HIHT (AHIHT) is derived.
Extensive experiments on eight biological datasets show that the proposed
method can achieve higher classification accuracy (ACC) with fewest number of
selected features (No.fea) comparing with the approximate convex counterparts
and state-of-the-art feature selection methods. The robustness of
classification accuracy to the regularization parameter and the number of
selected feature are also exhibited.
