Zhenzhen Sun

Zhenzhen Sun, Yuanlong Yu

This paper proposes a homotopy coordinate descent (HCD) method to solve the $l_0$-norm regularized least square ($l_0$-LS) problem for compressed sensing, which combine the homotopy technique with a variant of coordinate descent method. Differs from the classical coordinate descent algorithms, HCD provides three strategies to speed up the convergence: warm start initialization, active set updating, and strong rule for active set initialization. The active set is pre-selected using a strong rule, then the coordinates of the active set are updated while those of inactive set are unchanged. The homotopy strategy provides a set of warm start initial solutions for a sequence of decreasing values of the regularization factor, which ensures all iterations along the homotopy solution path are sparse. Computational experiments on simulate signals and natural signals demonstrate effectiveness of the proposed algorithm, in accurately and efficiently reconstructing sparse solutions of the $l_0$-LS problem, whether the observation is noisy or not.

Zhenzhen Sun, Yuanlong Yu

Feature selection is an important data preprocessing in data mining and machine learning which can be used to reduce the feature dimension without deteriorating model's performance. Since obtaining annotated data is laborious or even infeasible in many cases, unsupervised feature selection is more practical in reality. Though lots of methods for unsupervised feature selection have been proposed, these methods select features independently, thus it is no guarantee that the group of selected features is optimal. What's more, the number of selected features must be tuned carefully to obtain a satisfactory result. To tackle these problems, we propose a joint adaptive graph and structured sparsity regularization unsupervised feature selection (JASFS) method in this paper, in which a $l_{2,0}$-norm regularization term with respect to transformation matrix is imposed in the manifold learning for feature selection, and a graph regularization term is incorporated into the learning model to learn the local geometric structure of data adaptively. An efficient and simple iterative algorithm is designed to solve the proposed optimization problem with the analysis of computational complexity. After optimized, a subset of optimal features will be selected in group, and the number of selected features will be determined automatically. Experimental results on eight benchmarks demonstrate the effectiveness and efficiency of the proposed method compared with several state-of-the-art approaches.

Zhenzhen Sun, Yuanlong Yu

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.