Spectral descriptors have received much attention in recent years due in large part to their versatility
as well as their ability to capture either local or global geometric information of data. While the overwhelming
majority of work on spectral descriptors has concentrated primarily on image/shape retrieval
and object recognition, the goal of this work is to introduce efficient algorithms for data classification
and clustering in the spectral graph-theoretic setting. In addition to exploiting the dependence among
the features of spectral descriptors, we perform clustering and classification on sparse codes, thereby
seamlessly capturing the similarity between these features.
Unlike classification in which objects are assigned to predefined classes, clustering is different
in the sense that the number (and labels) of clusters or the cluster structure are not known in advance.
In this thesis, we propose a spectral graph-theoretic clustering and classification framework,
called GraphFDD, which uses the Fermi density descriptor (FDD) in conjunction with graph regularized
sparse coding. We also propose a unified framework for data clustering using the spectral graph
wavelet descriptor, which has a strong discriminative power and good performance in capturing neighborhood
information. To further enhance the effectiveness of the proposed algorithms, we not only
optimize the parameters, but also determine the proper matching normalization technique.
To assess the performance of the proposed algorithms, we use several validity measures and indices,
including the average clustering accuracy, normalized mutual information, confusion matrix
and classification accuracy. Our experiments on different standard benchmarks not only show that the
proposed approaches outperform state-of-the-art methods, but also provide attractive scalability and
robustness in terms of computational efficiency.