A new algorithm for solving a class of matrix optimization problem arising in unsupervised feature selection

In this paper, we consider a class of matrix optimization problem in unsupervised feature selection, which has many applications in machine learning, pattern detection and data mining. A sparse graph-constrained matrix optimization model is established and it can preserve the local geometric structure of the feature manifold. Based on the idea of Monte Carlo, the matrix optimization problem is firstly transformed into a stochastic programming problem and then an online optimization algorithm has been designed to solve this model. Different from traditional feature selection methods, the new algorithm can better deal with big data and data stream problems. Numerical results show that the new method is feasible and effective. Especially, some simulation experiments in unsupervised feature selection illustrate that our algorithm is more effective than the existed algorithms.