Local tangent space alignment via nuclear norm regularization for incomplete data

Abstract

Manifold learning approaches seek to find the low-dimensional features of high-dimensional data. When some values of the data are missing, the effectiveness of manifold learning methods may be greatly limited since they have difficulty in determining the local neighborhoods and discovering the local structures of neighborhoods. In this paper, a novel manifold learning approach called local tangent space alignment via nuclear norm regularization (LTSA–NNR) is proposed to discover the nonlinear features of the incomplete data. The neighbors of each sample point are selected using the cosine similarity measurement. A new nuclear norm regularization model is then proposed to discover the local coordinate systems of the determined neighborhoods. Different with the traditional manifold learning approaches, the dimensions of local coordinate systems are various in a reasonable range. The global coordinates of the incomplete data are finally obtained by aligning the local coordinates together. We demonstrate the effectiveness of our method on real-world data sets.