Unsupervised Feature Selection Using Nonnegative Spectral Analysis

In this paper, a new unsupervised learning algorithm, namely Nonnegative Discriminative Feature Selection (NDFS), is proposed. To exploit the discriminative information in unsupervised scenarios, we perform spectral clustering to learn the cluster labels of the input samples, during which the feature selection is performed simultaneously. The joint learning of the cluster labels and feature selection matrix enables NDFS to select the most discriminative features. To learn more accurate cluster labels, a nonnegative constraint is explicitly imposed to the class indicators. To reduce the redundant or even noisy features, `2,1-norm minimization constraint is added into the objective function, which guarantees the feature selection matrix sparse in rows. Our algorithm exploits the discriminative information and feature correlation simultaneously to select a better feature subset. A simple yet efficient iterative algorithm is designed to optimize the proposed objective function. Experimental results on different real world datasets demonstrate the encouraging performance of our algorithm over the state-of-the-arts.  The dimension of data is often very high in many domains (Jain and Zongker 1997; Guyon and Elisseeff 2003), such as image and video understanding (Wang et al. 2009a; 2009b), and bio-informatics. In practice, not all the features are important and discriminative, since most of them are often correlated or redundant to each other, and sometimes noisy (Duda, Hart, and Stork 2001; Liu, Wu, and Zhang 2011). These features may result in adverse effects in some learning tasks, such as over-fitting, low efficiency and poor performance (Liu, Wu, and Zhang 2011). Consequently, it is necessary to reduce dimensionality, which can be achieved by feature selection or transformation to a low dimensional space. In this paper, we focus on feature selection, which is to choose discriminative features by eliminating the ones with little or no predictive information based on certain criteria. Many feature selection algorithms have been proposed, which can be classified into three main families: filter, wrapper, and embedded methods. The filter methods (Duda, Hart, ; He, Cai, and Niyogi 2005; Zhao and Liu 2007; Masaeli, Fung, and Dy 2010; Liu, Wu, and Zhang 2011; Yang et al. 2011a) use statistical properties of the features to filter out poorly informative ones. They are usually performed before applying classification algorithms. They select a subset of features only based on the intrinsic properties of the data. In the wrapper approaches (Guyon and Elisseeff 2003; Rakotomamonjy 2003), feature selection is “wrapped” in a learning algorithm and the classification performance of features is taken as the evaluation criterion. Embedded methods (Vapnik 1998; Zhu et al. 2003) perform feature selection in the process of model construction. In contrast with filter methods, wrapper and embedded methods are tightly coupled with in-built classifiers, which causes that they are less generality and computationally expensive. In this paper, we focus on the filter feature selection algorithm. Because of the importance of discriminative information in data analysis, it is beneficial to exploit discriminative information for feature selection, which is usually encoded in labels. However, how to select discriminative features in unsupervised scenarios is a significant but hard task due to the lack of labels. In light of this, we propose a novel unsupervised feature selection algorithm, namely Nonnegative Discriminative Feature Selection (NDFS), in this paper. We perform spectral clustering and feature selection simultaneously to select the discriminative features for unsupervised learning. The cluster label indicators are obtained by spectral clustering to guide the feature selection procedure. Different from most of the previous spectral clustering algorithms (Shi and Malik 2000; Yu and Shi 2003), we explicitly impose a nonnegative constraint into the objective function, which is natural and reasonable as discussed later in this paper. With nonnegative and orthogonality constraints, the learned cluster indicators are much closer to the ideal results and can be readily utilized to obtain cluster labels. Our method exploits the discriminative information and feature correlation in a joint framework. For the sake of feature selection, the feature selection matrix is constrained to be sparse in rows, which is formulated as `2,1-norm minimization term. To solve the proposed problem, a simple yet effective iterative algorithm is proposed. Extensive experiments are conducted on different datasets, which show that the proposed approach outperforms the state-of-the-arts in different applications.