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36
A Generalized Approach For Connectionist AutoAssociative Memories: Interpretation, Implication Illustration For Face Processing
 In J. Demongeot (Ed.) Artificial
, 1988
"... this paper and Jim Anderson for support. This paper has been written during a visiting professorship in Brown University made possible by a Fullbright scholarship (19861988). Correspondence about this paper should be adressed to: Herv'e Abdi, The University of Texas at Dallas, Program in Cognition ..."
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Cited by 29 (20 self)
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this paper and Jim Anderson for support. This paper has been written during a visiting professorship in Brown University made possible by a Fullbright scholarship (19861988). Correspondence about this paper should be adressed to: Herv'e Abdi, The University of Texas at Dallas, Program in Cognition, MS:GR4.1., Richardson, TX750830688, USA. email: herve@utdallas.edu .
The Gifi System Of Descriptive Multivariate Analysis
 STATISTICAL SCIENCE
, 1998
"... The Gifi system of analyzing categorical data through nonlinear varieties of classical multivariate analysis techniques is reviewed. The system is characterized by the optimal scaling of categorical variables which is implemented through alternating least squares algorithms. The main technique of h ..."
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Cited by 18 (3 self)
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The Gifi system of analyzing categorical data through nonlinear varieties of classical multivariate analysis techniques is reviewed. The system is characterized by the optimal scaling of categorical variables which is implemented through alternating least squares algorithms. The main technique of homogeneity analysis is presented, along with its extensions and generalizations leading to nonmetric principal components analysis and canonical correlation analysis. A brief account of stability issues and areas of applications of the techniques is also given.
Two purposes for matrix factorization: A historical appraisal
 SIAM Review
"... Abstract. Matrix factorization in numerical linear algebra (NLA) typically serves the purpose of restating some given problem in such a way that it can be solved more readily; for example, one major application is in the solution of a linear system of equations. In contrast, within applied statistic ..."
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Abstract. Matrix factorization in numerical linear algebra (NLA) typically serves the purpose of restating some given problem in such a way that it can be solved more readily; for example, one major application is in the solution of a linear system of equations. In contrast, within applied statistics/psychometrics (AS/P), a much more common use for matrix factorization is in presenting, possibly spatially, the structure that may be inherent in a given data matrix obtained on a collection of objects observed over a set of variables. The actual components of a factorization are now of prime importance and not just as a mechanism for solving another problem. We review some connections between NLA and AS/P and their respective concerns with matrix factorization and the subsequent rank reduction of a matrix. We note in particular that several results available for many decades in AS/P were more recently (re)discovered in the NLA literature. Two other distinctions between NLA and AS/P are also discussed briefly: how a generalized singular value decomposition might be defined, and the differing uses for the (newer) methods of optimization based on cyclic or iterative projections.
Energy Partitions and Image Segmentation
, 2004
"... We address the issue of lowlevel segmentation for realvalued images. The proposed approach relies on the formulation of the problem in terms of an energy partition of the image domain. In this framework, an energy is defined by measuring a pseudometric distance to a source point. Thus, the choic ..."
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Cited by 11 (1 self)
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We address the issue of lowlevel segmentation for realvalued images. The proposed approach relies on the formulation of the problem in terms of an energy partition of the image domain. In this framework, an energy is defined by measuring a pseudometric distance to a source point. Thus, the choice of an energy and a set of sources determines a tessellation of the domain. Each energy acts on the image at a different level of analysis; through the study of two types of energies, two stages of the segmentation process are addressed. The first energy considered, the path variation, belongs to the class of energies determined by minimal paths. Its application as a presegmentation method is proposed. In the second part, where the energy is induced by a ultrametric, the construction of hierarchical representations of the image is discussed.
An Introduction to Symbolic Data Analysis and the Sodas Software
 Journal of Symbolic Data Analysis
, 2003
"... ..."
The remarkable simplicity of very high dimensional data: application to modelbased clustering
 Journal of Classication
, 2009
"... An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a hierarchical embedding. Such hierarchical structure can be global in the data set, or local. By quantifying extent or degree of ultrametricity in a d ..."
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Cited by 4 (1 self)
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An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a hierarchical embedding. Such hierarchical structure can be global in the data set, or local. By quantifying extent or degree of ultrametricity in a data set, we show that ultrametricity becomes pervasive as dimensionality and/or spatial sparsity increases. This leads us to assert that very high dimensional data are of simple structure. We exemplify this finding through a range of simulated data cases. We discuss also application to very high frequency time series segmentation and modeling.
Constrained Homogeneity Analysis With Applications To Hierarchical Data
 Hierarchical Data,” UCLA Statistical Series, #207
, 1996
"... . In this paper we extend the techniques of homogeneity analysis and nonlinear principal components analysis to a multilevel sampling design framework. We also propose some models that take advantage of the multilevel nature of the sampling design, and allow us to make withingroups and betweengrou ..."
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Cited by 3 (3 self)
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. In this paper we extend the techniques of homogeneity analysis and nonlinear principal components analysis to a multilevel sampling design framework. We also propose some models that take advantage of the multilevel nature of the sampling design, and allow us to make withingroups and betweengroups comparisons. Furthermore, it is shown that several models proposed in the literature for panel and event history data, can be casted naturally into our framework. A data set from the National Educational Longitudinal Study (NELS:88) is used to illustrate the techniques introduced in the paper. 1 2 GEORGE MICHAILIDIS AND JAN DE LEEUW 1. Introduction to Homogeneity Analysis The basic technique studied in this paper is known under many different names. For example, we have principal components of scale analysis [19, 20], factorial analysis of qualitative data [7], second method of quantification [21], multiple correspondence analysis [2, 17, 27] and homogeneity analysis [10, 15]. The tec...
Generalized Voronoi Tessellations for VectorValued Image Segmentation Abstract
"... We address the issue of lowlevel segmentation for vectorvalued images, focusing on color images. The proposed approach relies on the formulation of the problem as a generalized Voronoi tessellation of the image domain. In this context, the issue is transferred to the definition of an appropriated p ..."
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Cited by 3 (1 self)
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We address the issue of lowlevel segmentation for vectorvalued images, focusing on color images. The proposed approach relies on the formulation of the problem as a generalized Voronoi tessellation of the image domain. In this context, the issue is transferred to the definition of an appropriated pseudometric and the selection of a set of sources. Two types of pseudometrics are considered; the first one is based on energy minimizing paths and the second is associated to the families of nested partitions of the image domain. We discuss specific applications of our approach to presegmentation, edge detection and hierarchical segmentation on color images. 1
Ontology from local hierarchical structure in text
, 701
"... We study the notion of hierarchy in the context of visualizing textual data and navigating text collections. A formal framework for “hierarchy” is given by an ultrametric topology. This provides us with a theoretical foundation for concept hierarchy creation. A major objective is scalable annotation ..."
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Cited by 2 (2 self)
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We study the notion of hierarchy in the context of visualizing textual data and navigating text collections. A formal framework for “hierarchy” is given by an ultrametric topology. This provides us with a theoretical foundation for concept hierarchy creation. A major objective is scalable annotation or labeling of concept maps. Serendipitously we pursue other objectives such as deriving common word pair (and triplet) phrases, i.e., word 2 and 3grams. We evaluate our approach using (i) a collection of texts, (ii) a single text subdivided into successive parts (for which we provide an interactive demonstrator), and (iii) a text subdivided at the sentence or line level. While detailing a generic framework, a distinguishing feature of our work is that we focus on locality of hierarchic structure in order to extract semantic information.
Knowledge Discovery From Symbolic Data And The Sodas Software
 Conf. on Principles and Practice of Knowledge Discovery in Databases, PPKDD2000
, 2000
"... The data descriptions of the units are called "symbolic" when they are more complex than the standard ones due to the fact that they contain internal variation and are structured. Symbolic data happen from many sources, for instance in order to summarise huge Relational Data Bases by their under ..."
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The data descriptions of the units are called "symbolic" when they are more complex than the standard ones due to the fact that they contain internal variation and are structured. Symbolic data happen from many sources, for instance in order to summarise huge Relational Data Bases by their underlying concepts. "Extracting knowledge" means getting explanatory results, that why, "symbolic objects" are introduced and studied in this paper. They model concepts and constitute an explanatory output for data analysis. Moreover they can be used in order to define queries of a Relational Data Base and propagate concepts between Data Bases. We define "Symbolic Data Analysis" (SDA) as the extension of standard Data Analysis to symbolic data tables as input in order to find symbolic objects as output. In this paper we give an overview on recent development on SDA. We present some tools and methods of SDA and introduce the SODAS software prototype (issued from the work of 17 teams of nine countries involved in an European project of EUROSTAT). 1