Coupled locality discriminant analysis with globality preserving for dimensionality reduction

Dimensionality reduction plays a key role in pattern recognition. It can preserve essential and inherent feature information while reducing noise and redundant information contained in the high-dimensional raw data, which achieve performance improvement in subsequent tasks (e.g., classification and clustering). Locality preserving projection (LPP), as a typical method for dimensionality reduction, can explore the local sub-manifold of the raw data with the aid of K-nearest neighbor (KNN). However, LPP has some serious limitations: (1) the neighbor parameter is artificially set, and this leads to the problem that the size of the neighbor parameter may affect the performance of LPP in the application; (2) LPP, as a single-view method, cannot function in multi-view data; (3) LPP ignores both the discriminative information and the global linear relationship of the raw data. In response to these limitations, we propose a novel multi-view dimensionality reduction method called coupled locality discriminant analysis with globality preserving (CLDA-GP). CLDA-GP can learn a couple of optimal mappings so that different multi-view raw spaces can be mapped into a low-dimensional uniform elastic subspace while keeping the local sub-manifold and global linear relationship. It is also worth mentioning that CLDA-GP gives another strategy called local similarity self-learning (LSSL) to excavate the local manifold information of the multi-view data. By utilizing the LSSL strategy, CLDA-GP casts off the limitation of the neighbor parameter. Besides, CLDA-GP further introduces the supervision information of the raw data, which enables its discriminant power. The experiment results on the artificial and benchmark (COIL-20, GT, and Umist) datasets prove CLDA-GP outperforms the comparative methods, which also illustrate the effectiveness and feasibility of CLDA-GP.