Locality preserving score for joint feature weights learning

Locality preserving measurement criterion is frequently used for assessing the quality of features. However, locality preserving criterion based unsupervised feature selection algorithms have two widely acknowledged weaknesses: (1) The performance of feature selection heavily depends on the effectiveness of the similarity matrix, which is defined in the original space, and thus it is probably inconsistent with the one in the weighted space. (2) Greedy searching strategy neglects the correlation and redundancy among features. To alleviate these deficiencies, we propose a novel unsupervised feature selection algorithm by jointly learning adaptive nearest neighbors in the weighed space. An effective iterative algorithm is developed to solve the proposed formulation, where each iteration reduces to a convex subproblem which can be efficiently solved with some off-the-shelf toolboxes. The results of experiments on the UCI and face data sets demonstrate the effectiveness of the proposed algorithm, for outperforming many state-of-the-art unsupervised and supervised feature selection methods in terms of classification accuracy.