Data mining applications place special requirements on clustering algorithms including: the ability to find clusters embedded in subspaces of high dimensional data, scalability, end-user comprehensibility of the results, non-presumption of any canonical data distribution, and insensitivity to the order of input records. We present CLIQUE, a clustering algorithm that satisfies each of these requirements. CLIQUE identifies dense clusters in subspaces of maximum dimensionality. It generates cluster descriptions in the form of DNF expressions that are minimized for ease of comprehension. It produces identical results irrespective of the order in which input records are presented and does not presume any specific mathematical form for data distribution. Through experiments, we show that CLIQUE efficiently finds accurate clusters in large high dimensional datasets.

Dyadic data refers to a domain with two finite sets of objects in which observations are made for dyads, i.e., pairs with one element from either set. This includes event co-occurrences, histogram data, and single stimulus preference data as special cases. Dyadic data arises naturally in many applications ranging from computational linguistics and information retrieval to preference analysis and computer vision. In this paper, we present a systematic, domain-independent framework for unsupervised learning from dyadic data by statistical mixture models. Our approach covers different models with flat and hierarchical latent class structures and unifies probabilistic modeling and structure discovery. Mixture models provide both, a parsimonious yet flexible parameterization of probability distributions with good generalization performance on sparse data, as well as structural information about data-inherent grouping structure. We propose an annealed version of the standard Expectation Maximization algorithm for model fitting which is empirically evaluated on a variety of data sets from different domains.

Abstract—Texture features that are based on the local power spectrum obtained by a bank of Gabor filters are compared. The features differ in the type of nonlinear post-processing which is applied to the local power spectrum. The following features are considered: Gabor energy, complex moments, and grating cell operator features. The capability of the corresponding operators to produce distinct feature vector clusters for different textures is compared using two methods: the Fisher criterion and the classification result comparison. Both methods give consistent results. The grating cell operator gives the best discrimination and segmentation results. The texture detection capabilities of the operators and their robustness to nontexture features are also compared. The grating cell operator is the only one that selectively responds only to texture and does not give false response to nontexture features such as object contours. Index Terms—Classification, complex moments, discrimination,

A range query applies an aggregation operation over all selected cells of an OLAP data cube where the selection is specified by providing ranges of values for numeric dimensions. We present fast algorithms for range queries for two types of aggregation operations: SUM and MAX. These two operations cover techniques required for most popular aggregation operations, such as those supported by SQL. For range-sum queries, the essential idea is to precompute some auxiliary information (prefix sums) that is used to answer ad hoc queries at run-time. By maintaining auxiliary information which is of the same size as the data cube, all range queries for a given cube can be answered in constant time, irrespective of the size of the sub-cube circumscribed by a query. Alternatively, one can keep auxiliary information which is 1/b d of the size of the d-dimensional data cube. Response to a range query may now require access to some cells of the data cube in addition to the access to the auxiliary ...

In this paper we present a n O(k 1\Gamma1=d ) time algorithm for solving the k-center problem in R d , under L1 and L 2 metrics. The algorithm extends to other metrics, and can be used to solve the discrete k-center problem, as well. We also describe a simple (1 + ffl)-approximation algorithm for the k-center problem, with running time O(n log k) + (k=ffl) O(k 1\Gamma1=d ) . Finally, we present a n O(k 1\Gamma1=d ) time algorithm for solving the L-capacitated k-center problem, provided that L = \Omega\Gamma n=k 1\Gamma1=d ) or L = O(1). We conclude with a simple approximation algorithm for the L-capacitated k-center problem. The work on this paper was partially supported by a National Science Foundation Grant CCR-93--01259, by an Army Research Office MURI grant DAAH04-96-1-0013, by a Sloan fellowship, by an NYI award and matching funds from Xerox Corporation, and by a grant from the U.S.-Israeli Binational Science Foundation. y Department of Computer Science, Box ...

A theory for detecting general curve families by means of symmetry measurements in the coordinate transformed originals is presented. Symmetries are modeled by iso-gray curves of conjugate harmonic function pairs which also define the coordinate transformations. Harmonic function pair coordinates render the target curve patterns as parallel lines, which is defined here as linear symmetry. Detecting these lines, or generalized linear symmetry fitting as it will be called, corresponds to finding invariants of Lie groups of transformations. A technique based on least square error minimization for estimating the invariance parameters is presented. It uses the Lie infinitesimal operators to construct feature extraction methods that are efficient and simple to implement. The technique, which is shown to be an extension of the generalized Hough transform, enables detection by voting and accumulating evidence for the searched pattern. In this approach complex valued votes are permitted, where ...

This paper introduces a novel statistical mixturemodel for probabilistic grouping of distributional (histogram) data. Adopting the Bayesian framework, we propose to perform annealed maximum a posteriori estimation to compute optimal clustering solutions. In order to accelerate the optimization process, an efficient multiscale formulation is developed. We present a prototypical application of this method for the unsupervised segmentation of textured images based on local distributions of Gabor coefficients. Benchmark results indicate superior performance compared to K-means clustering and proximity-based algorithms.

We propose an approach to texture boundary detection that only requires a line-search in the direction normal to the edge. It is therefore very fast and can be incorporated into a real-time 3--D pose estimation algorithm that retains the speed of those that rely solely on gradient properties along object contours but does not fail in the presence of highly textured object and clutter.

Quadtree-like pyramids have the advantage of resulting in a multiresolution representation where each pyramid node has four unambiguous parents. Such a centered topology guarantees a clearly defined up-projection of labels. This concept has been successfully and extensively used in applications of contour detection, object recognition and segmentation. Unfortunately, the quadtree-like type of pyramid has poor approximation powers because of the employed piecewise-constant image model. This paper deals with the construction of improved centered image pyramids in terms of general approximation functions. The advantages of the centered topology such a symmetry, consistent boundary conditions and accurate up-projection of labels are combined with a more faithful image representation at coarser pyramid levels. We start by introducing a general framework for the design of least squares pyramids using the standard filtering and decimation tools. We give the most general explicit formulas for the computation of the filter coefficients by any (well behaving) approximation function in both the continuous (L2 ) and the discrete (l 2 ) norm. We then define centered pyramids and provide the filter coefficients for odd spline approximation functions. Finally, we compare the centered pyramid to the ordinary one and highlight some applications.

Texture is an inherently non-local image property. All common texture descriptors, therefore, have a significant spatial support which renders classical edge detection schemes inadequate for the detection of texture boundaries.