Scalable unsupervised feature selection via matrix learning and bipartite graph theory

With the rapid spread of technology, large volumes of unlabeled data with large dimensions needed to be processed. To reduce the dimensions, unsupervised feature selection is known as an important pre-step before machine learning tasks. In this paper, an unsupervised feature selection method is proposed. The method works dynamically and is scalable based on matrix graphs and weighted matrices. To improve the performance of this method, instead of using the Lagrange function to construct a weight matrix, a bipartite graph theory is applied. Feature selection is done on the matrix graph. This graph is constructed using k nearest neighbors, which makes the method more robust to noise. The global structure of the original data is also preserved by constructing a Reconstruction Weight Matrix with low-rank constraint. In addition, the feature score, which explicitly reflects the strength of the features, is modeled using the Frobenius norm function. The proposed method is compared with similar methods in three criteria of classification accuracy, parameter sensitivity and complexity. Experiments show that the classification accuracy of the method presented in this paper has improved by an average of 2.83%. Its complexity has also been reduced to max{O(n2d),O(nm)}, where n is the number of samples, d is the number of features and m is the number of anchor points.