Dimensionality reduction via preserving local information

Abstract

Dimensionality reduction is an important technique for multimedia data in smart cities. As a significant type of multimedia data, images are being processed frequently using such technique. It is worth noting that finding neighbors is an integral part of graph embedding algorithms in dimensionality reduction. In this paper, we present an effective and efficient metric function, named local similarity preserving (LSP), which can preserve the similarity information of each sample to its homogeneous and heterogeneous neighbors. The proposed LSP function is helpful to enhance the discriminative capability of subsequent feature extractors. Based on LSP function, we also propose two novel algorithms, local similarity preserving discriminant (LSPD) algorithm, which can preserve the local similarity information and LSPD+ algorithm, which can preserve the local similarity and geometric structure information, respectively. The experimental results on digit visualization and face recognition demonstrate the effectiveness and efficiency of the proposed algorithms.