Unsupervised Discriminative Projection for Feature Selection

Feature selection is one of the most important techniques to deal with the high-dimensional data for a variety of machine learning and data mining tasks, such clustering, classification, and retrieval, etc. Fuzziness is a widespread nature of data in nature human society. However, most existing feature selection methods ignore the existence of fuzziness in the data, resulting in sub-optimal feature subsets. To address the problem, we propose a novel unsupervised feature selection method, called Unsupervised Discriminative Projection for Feature Selection (UDPFS) to select discriminative features by conducting fuzziness learning and sparse learning, simultaneously. Specifically, we use projection matrix transform data as its low-dimensional representation, which are partitioned into clusters by using membership matrix with sparse constraint. In addition, $\ell _{2, 1}$-norm regularization is applied to the projection matrix. Then, a discriminative projection matrix with row sparse is obtained by perform fuzziness learning and sparse learning, simultaneously. An effective alternative optimization algorithm is proposed to solve the objective function. Evaluate experimental results on several real-world datasets show the effectiveness and superiority of the proposed unsupervised feature selection method.

1 Introduction

With the rapid growth of high dimensional data, feature selection plays an increasingly important role in many field, such as text mining [1], image search [2], person re-identification [3], visual classification [4], bioinformatics [5], etc. It is a very important and challenging task that mine valuable information in complex high-dimensional data. Due to there are many redundant features, noise and outliers in complex high-dimensional data [6], [7], high-dimensional data demands more computing costs and storage requirements in the process of data processing [8], [9], [10]. High-dimensional data will adversely affect the performance of subsequent data processing tasks such as clustering, classification due to curse of dimensionality [11], [12], [13]. Feature selection is a process that obtain relevant low-dimensional feature subsets from original high-dimensional feature set and remove redundant feature and outliers to improve performance of subsequent data processing tasks [14]. Feature selection is an effective solution to deal with high-dimensional data and feature selection methods have received more and more attention in recent years.