Abstract — This paper targets the identification of faulty sensors and detection of the reach of events in sensor networks with faulty sensors. Typical applications include the detection of the transportation front line of a contamination and the diagnosis of network health. We propose and analyze two novel algorithms for faulty sensor identification and fault-tolerant event boundary detection. These algorithms are purely localized and thus scale well to large sensor networks. Their computational overhead is low, since only simple numerical operations are involved. Simulation results indicate that these algorithms can clearly detect the event boundary and can identify faulty sensors with a high accuracy and a low false alarm rate when as many as 20 % sensors become faulty. Our work is exploratory in that the proposed algorithms can accept any kind of scalar values as inputs, a dramatic improvement over existing works that take only 0/1 decision predicates. Therefore, our algorithms are generic. They can be applied as long as the “events ” can be modelled by numerical numbers. Though designed for sensor networks, our algorithms can be applied to the outlier detection and regional data analysis in spatial data mining.

We provide a new characterization of the Dirichlet distribution. Let ` ij , 1 i k; 1 j n, be positive random variables that sum to unity. Define ` i\Delta = P n j=1 ` ij , `I \Delta = f` i\Delta g k\Gamma1 i=1 , ` jji = ` ij = P j ` ij , and ` Jji = f` jji g n\Gamma1 j=1 . We prove that if f`I \Delta ; ` Jj1 ; : : : ; ` Jjk g are mutually independent and f` \DeltaJ ; ` Ij1 ; : : : ; ` Ijn g are mutually independent (where ` \DeltaJ and ` Ijj are defined analogously), and assuming strictly positive pdfs, then the pdf of ` ij is Dirichlet. 1 Introduction Suppose s and t are two discrete random variables having finite domains, fs i g k i=1 and ft j g n j=1 , respectively. We wish to infer the joint probability p(s; t) from a sample of pairs of values (s i ; t j ) of s and t. The standard Bayesian approach to this statistical inference problem is to associate with p(s i ; t j ) a parameter ` ij (often called the multinomial parameter), assign f` ij j1 i k; 1 j ng a p...

Abstract We give a tutorial overview of several geometric methods for feature extraction and dimensional reduction. We divide the methods into projective methods and methods that model the manifold on which the data lies. For projective methods, we review projection pursuit, principal component analysis (PCA), kernel PCA, probabilistic PCA, and oriented PCA; and for the manifold methods, we review multidimensional scaling (MDS), landmark MDS, Isomap, locally linear embedding, Laplacian eigenmaps and spectral clustering. The Nyström method, which links several of the algorithms, is also reviewed. The goal is to provide a self-contained review of the concepts and mathematics underlying these algorithms.

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Current methods for inferring population structure from genetic data do not provide formal significance tests for population differentiation. We discuss an approach to studying population structure (principal components analysis) that was first applied to genetic data by Cavalli-Sforza and colleagues. We place the method on a solid statistical footing, using results from modern statistics to develop formal significance tests. We also uncover a general ‘‘phase change’ ’ phenomenon about the ability to detect structure in genetic data, which emerges from the statistical theory we use, and has an important implication for the ability to discover structure in genetic data: for a fixed but large dataset size, divergence between two populations (as measured, for example, by a statistic like F ST) below a threshold is essentially undetectable, but a little above threshold, detection will be easy. This means that we can predict the dataset size needed to detect structure.

The method we used is based on our Self-Organizing Hierarchical Optimal Subspace Learning and Inference Framework (SHOSLIF). It uses the theories of linear discriminant projection for automatic optimal feature selection in each of the internal nodes of a SpaceTessellation Tree. We demonstrate the technique on a relatively large image database of human faces and widely varying real-world objects taken in natural settings, and show the applicability of the approach for variability in position, size, and 3D orientation. In the work presented here, we require "well-framed" images as input for recognition. By well-framed images we mean that only a relatively small variation in the size, position, and orientation of the objects in the input images is allowed. We report the experimental results that show the performance difference between the subspaces of linear discriminant analysis and the principle component analysis and the effect of using a tree as opposed to a flat eigenspace.

Speedup learning systems are typically evaluated by comparing their impact on a problem solver's performance. The impact is measured by running the problem solver, before and after learning, on a sample of problems randomly drawn from some distribution. Often, the experimenter imposes a bound on the CPU time the problem solver is allowed to spend on any individual problem. Segre et al. [1991] argue that the experimenter's choice of time bound can bias the results of the experiment. To address this problem, we present statistical hypothesis tests specifically designed to analyze speedup data and eliminate this bias. We apply the tests to the data reported in [Etzioni, 1990a], and show that most (but not all) of the speedups observed are statistically significant. y The statistical tests described in this paper are encoded as Common Lisp routines. The routines, and the data analyzed in the paper, are available by sending mail to etzioni@cs.washington.edu. We hope that other researchers...

Two stochastic programming decision models are presented. In the rst one, we use probabilistic constraints, and constraints involving conditional expectations further incorporate penalties into the objective. The probabilistic constraint prescribes a lower bound for the probability of simultaneous occurrence of events, the number of which can be in nite in which casestochastic processes are involved. The second one is a variant of the model: two-stage programming under uncertainty, where we require the solvability of the second stage problem only with a prescribed (high) probability. The theory presented in this paper is based to a large extent on recent results of the author concerning logarithmic concave measures. 1

this technical claim is that in order to find all positive integrable functions that satisfy Eq. 9, it is permissible to take any derivative at any point in the domain because it exists. By setting z ij = 1=k, for all i and j, in Equation 9 we get that f 0 (y 1 ; : : : ; y n\Gamma1 ) is proportional to

1 Comprehensive visual learning is the treatment of theories and techniques for computer vision systems to automatically learn to understand comprehensive visual information with minimal human-imposed rules about the visual world. This article discusses some major performance difficulties encountered by currently prevailing approaches to computer vision and introduces the promising direction of comprehensive learning towards overcoming these difficulties. It also indicates why the direction may have a profound impact on the performance of computer vision algorithms for real world problems. Some example techniques for comprehensive visual learning are presented. 1 Introduction An image of a real-world scene depends on a series of factors, illumination, object shape, surface reflectance, viewing geometry, sensor type, etc. The image is a result of compound interactions among these factors. In the real world, change in these factors is ubiquitous and mostly is not known a priori. This ...