Improving the Locality Preserving Projection for dimensionality reduction

Locality Preserving Projection (LPP) is a recently proposed approach for dimensionality reduction that preserves the neighbourhood information and is widely used for finding the intrinsic dimensionality of the data which is usually of high dimension. A new proposal called Extended LPP (ELPP) has been introduced in which a weighing scheme is designed that pays importance to the data points which are at a moderate distance, in addition to the nearest points. This helps to resolve the ambiguity occurring at the overlapping regions as well as increase the reducibility capacity. The proposal is further extended to the supervised version of LPP (SLPP) that uses the known class labels of data points to enhance the discriminating power along with inheriting the properties of ELPP. Both proposals are tested on variety of datasets leading towards significant improvement in the results.