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Outlier-robust segmentation solution - Model-based approach

Model Assisted Statistics and Applications 2009年第3期4卷 203-213页

作者： Nowakowska, Ewa GfK Polonia 00-389 Warszawa ul. Smulikowskiego 4 Poland

Undiscovered presence of outlying observations in a dataset is likely to result in misleading conclusions. The problem is vital for cluster analysis, where undetected contamination usually causes significant decrease in stability and reproducibility, leading to distortions in the segment profiles. Based on the ML-approach proposed by Gallegos and Ritter [9], we have implemented an effective algorithm, which allows for simultaneous detection of outliers and estimation of the structure in the remaining data. In contrast to standard pre clustering procedures, it detects contamination in relation to the identified data structure. This paper compares the performance of the new robust algorithm with a standard pre clustering outlier detection procedure by means of simulation study. The results indicate that the robust method in certain situations may lead to more distinct cluster structure and less biased segment profiles. The method applications in market research are also discussed. © 2009 IOS Press. All rights reserved.

关键词： Between-segments heterogeneity Cluster analysis effective algorithm Maximum likelihood estimation Outlying observations Reproducibility Segmentation research Stability Within-segments homogeneity

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Joint detection of a given number of reference fragments in a quasi-periodic sequence and its partition into segments containing series of identical fragments

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Computational Mathematics and Mathematical Physics 2006年第1期46卷 165-181页

作者： Mikhailova, L.V. Sobolev Institute of Mathematics Siberian Division Russian Academy of Sciences Novosibirsk 630090 pr. Akademika Koptyuga 4 Russian Federation

The problem of joint a posteriori detection of reference fragments in a quasi-periodic sequence and its partition into segments containing series of recurring fragments from the reference tuple is solved. It is assumed that (i) an ordered reference tuple of sequences to be detected is given, (ii) the number of desired fragments is known, (iii) the index of the sequence term corresponding to the beginning of a fragment is a deterministic (not random) value, and (iv) a sequence distorted by an additive uncorrelated Gaussian noise is available for observation. It is established that the problem consists in testing a set of hypotheses about the mean of a random Gaussian vector. The cardinality of the set grows exponentially as the vector dimension (i.e., the sequence length) increases. An efficient a posteriori algorithm producing a maximum-likelihood optimal solution to the problem is substantiated. Time and space complexity bounds related to the parameters of the problem are derived. The results of numerical simulation are presented. © MAIK "Nauka/Interperiodica" (Russia), 2006.

关键词： A posteriori noise-proof processing Detecting effective algorithm Numerical sequence Partitioning Quasi-periodic fragment Series

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AN EFFICIENT algorithm FOR GRAPH ISOMORPHISM

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JOURNAL OF THE ACM 1970年第1期17卷 51-&页

作者： CORNEIL, DG GOTLIEB, CC University of Toronto Department of Computer Science Toronto Ontario Canada University of Toronto Department of Computer Science Toronto Ontario Canada

A procedure for determining whether two graphs are isomorphic is described. During the procedure, from any given graph two graphs, the representative graph and the reordered graph, are derived. The representative graph is a homomorphic image of the original graph;the reordered graph is constructed from the representative graph to be isomorphic to the given graph. Unique labels are assigned to the vertices of both derived graphs. It follows that two representative graphs or two reordered graphs are isomorphic if and only if they are identical. A conjecture states that the representative graphs exhibit the automorphism partitioning of the given graph. The representative graphs form a necessity condition for isomorphism;namely, if the representative graphs are not identical, then the given graphs are not isomorphic. The converse is true for trees and follows from the conjecture for other types of graphs. It is also shown that the reordered graphs form a sufficiency condition for isomorphism;namely, if the reordered graphs are identical, then the given graphs are isomorphic. The converse follows from the conjecture. The time required to determine both derived graphs depends on a power of n, the order of the given graph. This power is a function of an adjacency property known as the strong regularity of the given graph. For graphs that do not contain a strongly regular transitive subgraph, the power is, at worst, five. © 1970, ACM. All rights reserved.

关键词： automorphism partitioning automorphisms coding of graphs deterministic algorithm effective algorithm efficient algorithm graph graph isomorphism heuristic procedure isomorphism strongly regular graph transitive graphs transitive subgraphs

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