document: Unsupervised feature selection for multi-cluster data In many data analysis tasks , one is often confronted with very high dimensional data . Feature selection techniques are designed to find the relevant feature subset of the original features which can facilitate clustering , classification and retrieval . In this paper , we consider the feature selection problem in unsupervised learning scenario , which is particularly difficult due to the absence of class labels that would guide the search for relevant information . The feature selection problem is essentially a combinatorial optimization problem which is computationally expensive . Traditional unsupervised feature selection methods address this issue by selecting the top ranked features based on certain scores computed independently for each feature . These approaches neglect the possible correlation between different features and thus can not produce an optimal feature subset . Inspired from the recent developments on manifold learning and L1-regularized models for subset selection , we propose in this paper a new approach , called Multi-Cluster Feature Selection ( MCFS ) , for unsupervised feature selection . Specifically , we select those features such that the multi-cluster structure of the data can be best preserved . The corresponding optimization problem can be efficiently solved since it only involves a sparse eigen-problem and a L1-regularized least squares problem . Extensive experimental results over various real-life data sets have demonstrated the superiority of the proposed algorithm .
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