Statement of Research

Currently, I am especially interested in the problem of identifying similarities between high-dimensional datasets. Very often, data may be collected by a number of sources, which may be unable to share their entire datasets for reasons like confidentiality agreements, dataset location and size, etc. If there exists some similar substructure between distinct datasets, this may be exploited. For example, two consumer markets (A and B) differing in geography, economy, political orientation or some other way, may have some unusually similar consumer profiles. This may prompt sales managers in B to use successful sales strategies employed by sales managers in A for consumer profiles in which they are unusually similar. This problem has many application domains including computational biology (finding common structure among proteins given the 3-d coordinates of their amino acids), computer vision (object recognition), dataset evolution, etc. To solve this problem, we have taken a 2-stage approach [8]. The first stage involves generating a condensed model (a graph) for each dataset. The second stage involves the identification of similarities between the condensed models of the datasets, at a central location. The first stage requires identification of the components (vertices in the graph) making up the condensed model and the intra-model inter-component relationships (edge weights). The existing algorithms used to find the model components, use non-intuitive parameters. We have designed a new algorithm SCHISM [6], using statistically sound and intuitive interestingness thresholds. Our paper underlines the inherent drawback of a constant threshold support, as employed by Apriori [1]-based algorithms. SCHISM unifies the intuition underlying pioneering subspace mining algorithms, CLIQUE[2] and MAFIA[3] . It provides insight into the setting of thresholds for Apriori-based algorithms. We have extended such ideas to finding interesting sequences [9]. In the second stage, to find inter-model similarities between components (vertices) in different datasets (graphs), we use network-flow based algorithms, which propagate similarities in structure between the two datasets. These algorithms have been shown to perform better than some of the state of the art algorithms [8]. In the future, I hope to use nonlinear dimensionality reduction techniques to learn underlying manifolds or subspaces. We are also currently working on extending such techniques as used in SCHISM[6] to mining of other interesting patterns, like graphs and trees. I am also interested in the problem of mining temporal sequences. I hope to extend my earlier work [4], which dealt with