Information retrieval and mining in high dimensional databases

This dissertation is composed of two parts. In the first part, we present a framework for finding information (more precisely, active patterns) in three dimensional (3D) graphs. Each node in a graph is an undecoraposable or atomic unit and has a label. Edges are links between the atomic units. Patterns are rigid substructures that may occur in a graph after allowing for an arbitrary number of whole-structure rotations and translations as well as a small number (specified by the user) of edit operations in the patterns or in the graph. (When a pattern appears in a graph only after the graph has been modified, we call that appearance approximate occurrence. ) The edit operations include relabeling a node, deleting a node and inserting a node. The proposed method is based on the geometric hashing technique, which hashes node-triplets of the graphs into a 3D table and compresses the label-triplets in the table. To demonstrate the utility of our algorithms, we discuss two applications of them in scientific data mining. First, we apply the method to locating frequently occurring motifs in two families of proteins pertaining to RNA-directed DNA Polymerase and Thymidylate Synthase, and use the motifs to classify the proteins. Then we apply the method to clustering chemical compounds pertaining to aromatic, bicyclicalkanes and photosynthesis. Experimental results indicate the good performance of our algorithms and high recall and precision rates for both classification and clustering. We also extend our algorithms for processing a class of similarity queries in databases of 3D graphs. In the second part of the dissertation, we present an index structure, called MetricMap, that takes a set of objects and a distance metric and then maps those objects to a k-dimensional pseudo-Euclidean space in such a way that the distances among objects are approximately preserved. Our approach employs sampling and the calculation of eigenvalues and eigenvectors. The index structure is a useful tool for clustering and visualization in data intensive applications, because it replaces expensive distance calculations by sum-of-square calculations. This can make clustering in large databases with expensive distance metrics practical. We compare the index structure with another data mining index structure, FastMap, proposed by Faloutsos and Lin, according to two criteria: relative error and clustering accuracy. For relative error, we show that (i) FastMap gives a lower relative error than MetrieMap for Euclidean distances, (ii) MetricMap gives a lower relative error than Fast Map for non-Euclidean distances (i.e., general distance metrics), and (iii) combining the two reduces the error yet further. A similar result is obtained when comparing the accuracy of clustering. These results hold for different data sizes. The main qualitative conclusion is that these two index structures capture complenleiltary information about distance metrics and therefore can be used together to great benefit. The net effect is that multi-day computations can be done in minutes. We have implemented the proposed algorithms and the MetricMap index structure into a toolkit. This toolkit will be useful for data mining, visualization, and approximate retrieval in scientific, multimedia and high dimensional databases

Graph-Based Approaches to Protein StructureComparison - From Local to Global Similarity

The comparative analysis of protein structure data is a central aspect of structural bioinformatics. Drawing upon structural information allows the inference of function for unknown proteins even in cases where no apparent homology can be found on the sequence level. Regarding the function of an enzyme, the overall fold topology might less important than the specific structural conformation of the catalytic site or the surface region of a protein, where the interaction with other molecules, such as binding partners, substrates and ligands occurs. Thus, a comparison of these regions is especially interesting for functional inference, since structural constraints imposed by the demands of the catalyzed biochemical function make them more likely to exhibit structural similarity. Moreover, the comparative analysis of protein binding sites is of special interest in pharmaceutical chemistry, in order to predict cross-reactivities and gain a deeper understanding of the catalysis mechanism. From an algorithmic point of view, the comparison of structured data, or, more generally, complex objects, can be attempted based on different methodological principles. Global methods aim at comparing structures as a whole, while local methods transfer the problem to multiple comparisons of local substructures. In the context of protein structure analysis, it is not a priori clear, which strategy is more suitable. In this thesis, several conceptually different algorithmic approaches have been developed, based on local, global and semi-global strategies, for the task of comparing protein structure data, more specifically protein binding pockets. The use of graphs for the modeling of protein structure data has a long standing tradition in structural bioinformatics. Recently, graphs have been used to model the geometric constraints of protein binding sites. The algorithms developed in this thesis are based on this modeling concept, hence, from a computer scientist's point of view, they can also be regarded as global, local and semi-global approaches to graph comparison. The developed algorithms were mainly designed on the premise to allow for a more approximate comparison of protein binding sites, in order to account for the molecular flexibility of the protein structures. A main motivation was to allow for the detection of more remote similarities, which are not apparent by using more rigid methods. Subsequently, the developed approaches were applied to different problems typically encountered in the field of structural bioinformatics in order to assess and compare their performance and suitability for different problems. Each of the approaches developed during this work was capable of improving upon the performance of existing methods in the field. Another major aspect in the experiments was the question, which methodological concept, local, global or a combination of both, offers the most benefits for the specific task of protein binding site comparison, a question that is addressed throughout this thesis