Three graph theoretical statistics are considered for the problem of estimating the intrinsic dimension of a data set. The first is the ‘‘reach’’ statistic, r j,k, proposed in Brito et al. (2002) [4] for the problem of identification of Euclidean dimension. The second,Mn, is the sample average of squared degrees in the minimum spanning tree of the data, while the third statistic, Uk n , is base...

A novel video-object segmentation algorithm is proposed, which takes the previously estimated 2-D dense motion vector field as input and uses the generalized recursive shortest spanning tree method to approximate each component of the motion vector field as a piecewise planar function. The algorithm is successful in capturing 3-D planar objects in the scene correctly, with acceptable accuracy a...

Computing energy efficient broadcast trees is one of the most prominent operations in wireless networks. For stations embedded in the Euclidean plane, the best analytic result known to date is a 6.33-approximation algorithm based on computing an Euclidean minimum spanning tree. We improve the analysis of this algorithm and show that its approximation ratio is 6, which matches a previously known...

A t-spanner of a weighted undirected graph G = (V,E), is a subgraph H such that dH(u, v) ≤ t · dG(u, v) for all u, v ∈ V . The sparseness of the spanner can be measured by its size (the number of edges) and weight (the sum of all edge weights), both being important measures of the spanner’s quality – in this work we focus on the latter. Specifically, it is shown that for any parameters k ≥ 1 an...

In addition to the well-known edit operations, the alignment of minisatellite maps includes duplication events. We model these duplications using a special kind of spanning trees and deduce an optimal duplication scenario by computing the respective minimum spanning tree. Based on best duplication scenarios for all substrings of the given sequences, we compute an optimal alignment of two minisa...

We investigate Prim’s standard ‘tree-growing’ method for finding a minimum spanning tree, when applied to a network in which all degrees are about d and the edges e have independent identically distributed random weights w(e). We find that when the kth edge ek is added to the current tree, where k = o( √ d), the probability that this edge ek is incident to the node that was most recently added ...

In this paper a correction factor for Jennrich’s statistic is introduced in order to be able not only to test the stability of correlation structure, but also to identify the time windows where the instability occurs. If Jennrich’s statistic is only to test the stability of correlation structure along predetermined non-overlapping time windows, the corrected statistic provides us with the histo...

Cardiovascular diseases (CVDs) are the worldwide leading cause of deaths. Based on ultrasound, primary assessment of CVDs is measurement of carotid intima-media thickness and brachial endothelial function. In this work we propose improvements to a state of the art automatic methodology for arterial lumen detection, based on graphs and edge detection, fundamental for cited tests. We propose a ba...

We advance the approach initiated by Chawla et al. for sanitizing (census) data so as to preserve the privacy of respondents while simultaneously extracting “useful” statistical information. First, we extend the scope of their techniques to a broad and rich class of distributions, specifically, mixtures of highdimensional balls, spheres, Gaussians, and other “nice” distributions. Second, we ran...

A .new multiple classifier approach for spectralspatial classification of hyperspectral images is proposed. Several classifiers are used independently to classify an image. For every pixel, if all the classifiers have assigned this pixel to the same class, the pixel is kept as a marker, i .e., a seed of the spatial region, with the corresponding class label. We propose to use spectral-spatial c...