Scan Statistics and Applications

Glaz, Joseph; Naus, Joseph

doi:10.1002/0471667196.ess3207

Cited by 8 publications

(9 citation statements)

References 58 publications

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“…Chi-squared statistic is a simple and well used measure, and we are currently investigating the possibility of decomposing it into orthogonal components to examine the moments of the observed frequencies (Rayner and Best, 2001). A recent statistical research direction directly applicable to query by content and anomaly detection has been moved toward scan statistics (Glaz and Balakrishnan, 1999;Glaz et al, 2001). Scan statistics relate to distributions over sliding windows.…”

Section: Statistical Tests For Rle Clipped Seriesmentioning

confidence: 99%

A Bit Level Representation for Time Series Data Mining with Shape Based Similarity

Bagnall

Ratanamahatana

Keogh

et al. 2006

Data Min Knowl Disc

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Clipping is the process of transforming a real valued series into a sequence of bits representing whether each data is above or below the average. In this paper, we argue that clipping is a useful and flexible transformation for the exploratory analysis of large time dependent data sets. We demonstrate how time series stored as bits can be very efficiently compressed and manipulated and that, under some assumptions, the discriminatory power with clipped series is asymptotically equivalent to that achieved with the raw data. Unlike other transformations, clipped series can be compared directly to the raw data series. We show that this means we can form a tight lower bounding metric for Euclidean and Dynamic Time Warping distance and hence efficiently query by content. Clipped data can be used in conjunction with a host of algorithms and statistical tests that naturally follow from the binary nature of the data. A series of experiments illustrate how clipped series can be used in increasingly complex ways to achieve better results than other popular representations. The usefulness of the proposed representation is demonstrated by the fact that the results with clipped data are consistently better than those achieved with a Wavelet or Discrete Fourier Transformation at the same compression ratio for both clustering and query by content. The flexibility of the representation is shown by the fact that we can take advantage of a variable Run Length Encoding of clipped series to define an approximation of the Kolmogorov complexity and hence perform Kolmogorov based clustering

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Section: Statistical Tests For Rle Clipped Seriesmentioning

confidence: 99%

A Bit Level Representation for Time Series Data Mining with Shape Based Similarity

Bagnall

Ratanamahatana

Keogh

et al. 2006

Data Min Knowl Disc

View full text Add to dashboard Cite

show abstract

“…(Wallenstein 2009). Two books (Glaz and Balakrishnan 1999;Glaz et al 2001) cover the scan statistic with the emphasis on the one-dimensional version. Among the two-dimensional versions of the scan statistic, the circular scan statistic proposed and developed by Kulldorff and Nagarwalla (1995), Kulldorff (1997) is a milestone.…”

Section: Introductionmentioning

confidence: 99%

PULSE, progressive upper level set scan statistic for geospatial hotspot detection

Patil

Joshi

Koli³

2010

Environ Ecol Stat

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This paper presents a scan statistic, progressive upper level set (PULSE) scan statistic, for geospatial hotspot detection and its software implementation. Like ULS, the PULSE scan statistic is based on the arbitrarily shaped scan window and can be adapted for a network setting. PULSE is a refinement of the upper level set (ULS) scan statistic. Like some other likelihood based scanning devices, the ULS scan statistic identifies maximum likelihood estimate (MLE) zones that tend to be 'stringy' and sprawling. Its search path increases possibility of inclusion of extraneous cells in its MLE zones and, to a smaller extent, of exclusion of cells that belong to a true hotspot from its MLE zone. The PULSE scan statistic achieves improvement over the ULS scan statistic in two ways. First, it begins its search for a most likely zone with a large population of candidate zones obtained by modifying the ULS tree structure and continues its search using a genetic algorithm. Secondly, to reduce chances of generating an MLE that is excessively stringy and that includes extraneous cells in the MLE zone, PULSE uses cardinality and compactness of zones along with their 123 150 Environ Ecol Stat (2010) 17:149-182 likelihoods as the fitness function in the genetic algorithm and uses several pertinent criteria including evenness of intra-zone cellular response ratios to determine the MLE zone. To reduce computation, Gumbel distribution of extreme values is used to determine the p-value of the MLE zone. Better results come at the cost of increased processing time. An evaluative performance study is presented.

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“…The concept of runs and scans has been used effectively in a wide range of areas such as reliability theory, hypothesis testing, start-up demonstration tests, and statistical quality control (see Balakrishnan and Koutras, 2002;Balakrishnan et al, 1997;Chao et al, 1995;Glaz and Balakrishnan, 1999;Inoue and Aki, 2005;Shmueli and Cohen, 2000;and references therein). Distribution theory of runs and scans has been developed in various situations by many authors (see Aki et al, 1996;Glaz et al, 2001;Hirano et al, 1997;Inoue and Aki, 2003;Uchida, 1998).…”

Section: Introductionmentioning

confidence: 99%

Distributions of Runs and Scans on Higher-Order Markov Trees

Inoue

Aki

2009

Communications in Statistics - Theory and Methods

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In this article, we consider the distributions of the number of success runs of specified length and scans on a higher-order Markov tree under three different enumeration schemes (the "non overlapping", the "at least", and the "overlapping" scheme). Recursive formulae for the evaluation of their probability generating functions are established. We provide a proper framework for extending the exact distribution theory of runs and scans from based on sequences to based on directed trees. Some numerical results for the run and scan statistics are given in order to illustrate the computational aspects and the feasibility of our theoretical results. Finally, two special reliability systems are considered, which are closely related to our general results.

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Scan Statistics and Applications

Abstract: Library of Congress Cataloging-in-Publication Data Scan statistics and applications / [edited by] Joseph Glaz, N. Balakrishnan. p. cm.-(Statistics for industry and technology) Includes bibliographical references and index.

Cited by 8 publications

References 58 publications

A Bit Level Representation for Time Series Data Mining with Shape Based Similarity

A Bit Level Representation for Time Series Data Mining with Shape Based Similarity

PULSE, progressive upper level set scan statistic for geospatial hotspot detection

Distributions of Runs and Scans on Higher-Order Markov Trees

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