Globally and locally consistent unsupervised projection

In this paper, we propose an unsupervised projection method for feature extraction to preserve both global and local consistencies of the input data in the projected space. Traditional unsupervised feature extraction methods, such as principal component analysis (PCA) and locality preserving projections (LPF), can only explore either the global or local geometric structures of the input data, but not the both at the same time. In our new method, we introduce a new measurement using the neighborhood data variances to assess the data locality, by which we propose to learn an optimal projection by rewarding both the global and local structures of the input data. The formulated optimization problem is challenging to solve, because it ends up a trace ratio minimization problem. In this paper, as an important theoretical contribution, we propose a simple yet efficient optimization algorithm to solve the trace ratio problem with theoretically proved convergence. Extensive experiments have been performed on six benchmark data sets, where the promising results validate the proposed method.