We present a new approach to clustering, based on the physical properties of an inhomogeneous ferromagnet. No assumption is made regarding the underlying distribution of the data. We assign a Potts spin to each data point and introduce an interaction between neighboring points, whose strength is a decreasing function of the distance between the neighbors. This magnetic system exhibits three phases. At very low temperatures, it is completely ordered; all spins are aligned. At very high temperatures, the system does not exhibit any ordering, and in an intermediate regime, clusters of relatively strongly coupled spins become ordered, whereas different clusters remain uncorrelated. This intermediate phase is identified by a jump in the order parameters. The spin-spin correlation function is used to partition the spins and the corresponding data points into clusters. We demonstrate on three synthetic and three real data sets how the method works. Detailed comparison to the performance of other techniques clearly indicates the relative success of our method. 1

Indexing of multi-dimensional data has been the focus of a considerable amount of research effort over many years but no generally agreed paradigm has emerged to compare with the impact of the B-Tree, for example, on the indexing of one-dimensional data. At the same time, the need for efficient methods is ever more important in an environment where databases become larger and more complex in their structures. Mapping multi-dimensional data to one dimension, thus enabling one-dimensional access methods to be exploited, has been suggested in the literature but for the most part interest has been confined to the Z-order curve. The possibility of using other curves, such as the Hilbert and Gray-code curves, whose characteristics differ from those of the Z-order curve, has also been suggested. In this thesis we design and implement a working le store which is underpinned by the principle of mapping multi-dimensional data to one of a variety of space-filling curves and their variants. Data is then indexed using a B+ Tree which remains compact, regardless of the volume and number of dimensions. The implementation has entailed developing

Image search has been actively studied in recent years. On the other hands, image browsing has received little attention. Image browsing refers to the process of presenting some forms of overview or summary of the image relationships, thus facilitating a user to navigate across the data set and find images of interests. In this paper, we present a new data structure built on the multi-linearization of image attributes for efficient organization of the data set and fast visual browsing of the images. We describe new techniques for multi-linearization based on multiple space-filling curves and hierarchical clustering techniques. In addition to providing fast navigation, our proposed data structure allows computationally efficient insertion and deletion of images from the data set. We then present a novel image navigator and browser built on dual-linearization data structure and intuitive presentation of image relevance and relationships, demonstrate the image navigation process, and repo...