Similarity Preserving Dimensionality Reduction for Image Data

Abstract

Data collection and storage capabilities have increased manifold in last few decades,leading to information overload. Number of variables used to represent each data observation newlineis called dimension of the data and dealing with large dimensions is a challenging task. Images have become a source of such large data which is increasing day by day with advances in image capturing devices and demand of high resolution images. newlineImages typically consist of large dimensions and processing that becomes very di cult even for machines. Dimensionality reduction techniques learn a compact representation of such data by exploring the properties such as correlation, pairwise newlinedistances, neighborhood structure etc. The idea is to retain these properties in lower dimensional representation as well, inducing minimum information loss. Early age newlinetechniques of dimensionality reduction preserve the global structure of the data, but,many a times, local manifold structure is more important than the global Euclidean newlinestructure. This thesis is an attempt to develop robust and powerful dimensionality reduction technique based on similarity preservation for image data. In particular,the thesis emphasizes on the dimensionality reduction techniques those are linear in newlinenature and are based on preserving the local relationship of the image data.In this work, Locality Preserving Projection (LPP), that preserves the local structure newlineof data is studied and its various extensions are proposed. LPP works on the concept that neighboring data points in the high dimensional space should remain newlineneighbors in the low dimensional space as well. Ambiguities in regions having data points from di erent classes close by, less reducibility capacity, data dependent parameters, newlineignorance of discriminant information, non-orthogonality of the basis, vectorized processing are some of the issues with conventional LPP. Some of the variants newlineof LPP have been introduced that try to resolve these problems. Discriminant information, if considered, can play vital role...