Locality Sensitive Semi-Supervised Dimensionality Reduction on Multimodal Data

A special kind of data is considered in this paper called multimodal data. It has the property that samples in a class are from several separate clusters. Locality Preserving Projection (LPP) can work well with multimodal data due to its locality preserving property. However, the label information is not used to improve the learning performance due to the unsupervised character of LPP. In this paper, we propose a method called Locality Sensitive Semi-Supervised Dimensionality Reduction (semi-LSDR). It takes both the discriminant information and geometry structure into account. Specifically, we construct a between-class graph on labeled samples and a nearest neighbor graph both from the perspective of locality. A directly mapping can be achieved by solving a generalized eigenvalue problem. Effectiveness of the proposed method is showed through simulations with benchmark data sets.