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 is 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. Images 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 distances, neighborhood structure etc. The idea is to retain these properties in lower dimensional representation as well, inducing minimum information loss. Early age techniques of dimensionality reduction preserve the global structure of the data, but,many a times, local manifold structure is more important than the global Euclidean structure. 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 nature and are based on preserving the local relationship of the image data.In this work, Locality Preserving Projection (LPP), that preserves the local structure of 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 neighbors 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, ignorance of discriminant information, non-orthogonality of the basis, vectorized processing are some of the issues with conventional LPP. Some of the variants of LPP have been introduced that try to resolve these problems. Discriminant information, if considered, can play vital role in obtaining separation between di erent classes. Variants of LPP, considering not only the local structure, but also the dissimilarity between the data points are proposed in the rst part of the thesis. Data representation, face and facial expression recognition experiments are performed using the proposed dimensionality reduction frameworks.