Clustering algorithms have the annoying characteristic of finding clusters in random data. A theoretical analysis of the threshold of the mutual neighborhood clustering algorithm (MNCA) under the hypothesis of random data is presented. This yields a theoretical minimum value of this threshold below which even unclustered data are broken into separate clusters. To derive the threshold, a theorem about mutual near neighbors in a Poisson process is stated and proved. Simple experiments demonstrate the usefulness of the theoretical thresholds.>

The author gives a mathematical description of resource availability. He defines a naive algorithm for computing availability, and then describes method to maintain availability information as new reservations/assignments are made. An approach for using for storing resource availability information is presented. It is shown that availability queries are then efficient and that updates can be done in time logarithmic in the size of the availability information. An algorithm is given for calculating the availability of sets of resources which is linear in the number of previously schedule operations. It is shown that this algorithm is optimal.>

A test is described for multivariate normality that is useful in pattern recognition. The test is based on the Friedman-Rafsky (1979) multivariate extension of the Wald-Wolfowitz runs test. The test data are combined with a multivariate swarm of points following the normal distribution generated with mean vector and covariance matrix estimated from the test data. The minimal spanning tree of this resultant ensemble of points is computed and the count of the interpopulation edges in the minimal spanning tree is used as a test statistic. The simulation studied both the null case of the test and one simple deviation from normality. Two conclusions are made from this study. First, the test can be conservatively applied by using the asymptotic normality of the test statistic, even for small sample sizes. Second, the power of the test appears reasonable, especially in high dimensions. Monte Carlo experiments were performed to determine if the test is reliable in high dimensions with moderate sample size. The method is compared to other such tests available in the literature.>

Testing for uniformity in multidimensional data is important in exploratory pattern analysis, statistical pattern recognition, and image processing. The goal of this paper is to determine whether the data follow the uniform distribution over some compact convex set in K-dimensional space, called the sampling window. We first provide a simple, computationally efficient method for generating a uniformly distributed sample over a set which approximates the convex hul of the data. We then test for uniformity by comparing this generated sample to the data by using Friedman-Rafsky's minimal spanning tree (MST) based test. Experiments with both simulated and real data indicate that this MST-based test is useful in deciding if data are uniform.

This paper describes a procedure for segmenting muscle cell pictures. The segmentation procedure is broken into two logical parts. The first part segments the picture into regions composed of cells or clumps of cells using a number of low-level operations. The second part of the procedure involves the segmentation of the cell clumps into individual cells. This is done by using a hierarchical clustering algorithm to group together those boundary points of a cell clump that belong to the same globally convex sections of the boundary. The dissimilarity measure used by the clustering algorithm is based only on information about the shape of the boundary, where this information is derived from line segments interior to the boundary. This procedure has given us satisfactory results on a number of test pictures.