Abstracts E-N

Aïcha El Golli, INRIA-Rocquencourt, Brieuc Conan-Guez, and Fabrice Rossi, University of Paris-Dauphine, ``A Self-Organizing Map for Dissimilarity Data'' Abs: Treatment of complex data (for example symbolic data, semi-structured data, or functional data) cannot be easily done by clustering methods that are based on calculating the center of gravity. We present in this paper an extension of self-organizing maps to dissimilarity data. This extension allows to apply this algorithm to numerous types of data in a convenient way.


José Luis Espinoza, Instituto Technológico de Costa Rice, and Javier Trejos, CIMPA, ``Genetic Variable Selection in Linear Regression'' Abs: We study the application of genetic algorithms in variable selection problems for multiple linear regression, minimizing the least squares criterion. The algorithm is based on a chromosomic representation of variables that are considered in the least squares model. A binary chromosome indicates the presence (1) or absence (0) of a variable in the model. The fitness function is based on the determination coefficient, weighting also the quantity of variables that enter into the model:

$$F = R^2\times (1+\alpha q)$$

where $q$ is the number of absent variables, and $\alpha$ is a parameter. The usual genetic operators, including roulette-wheel selection, crossover, and mutation are implemented. Comparisons are performed with benchmark data sets, and this finds promising results.


Anuska Ferligoj and Vladimir Batagelj, University of Ljubljana, and Patrick Doreian, University of Pittsburgh, ``Blockmodeling as a Clustering Problem'' Abs: The goal of blockmodeling is to reduce a large, potentially incoherent network to a smaller comprehensible structure that can be interpreted more readily. One of the main procedural goals of blockmodeling is to identify, in a given network (defined by a set of units and one or several relations) clusters of units that share structural characteristics defined in terms of the relation. The units within a cluster have the same or similar connection patterns to other units. The set of clusters form a clustering (e.g., a partition, hierachy). The problem of establishing a partition of units in a network in terms of a selected type of equivalence is a special case of clustering problem that can be formulated as an optimization problem: determine the clustering that has the minimal value of a criterion function across all possible feasible clusterings. Criterion functions can be constructed indirectly as a function of a compatible (dis)similarity measure between pairs of units (a classical clustering problem), or directly as a function measuring the fit of a clustering to an ideal one with perfect relations within each cluster and between clusters according to the considered types of connections (equivalence). A local optimization procedure (a relocation algorithm) can be used if the criterion function is defined directly. This optimizational approach permits to generalize equivalences and to consider pre-specification of a blockmodel by starting with a blockmodel that is specified in terms of substance prior to an analysis. In this case given a network, set of types of ideal blocks, and a reduced model, a solution (a clustering) can be determined which minimizes the criterion function. The proposed approach can be applied also to two-mode relational data. The key idea is that the rows and columns of a two-mode matrix are clustered simultaneously but in different ways. Several examples will be given to illustrate the proposed generalized approach to blockmodeling.


Bernard Fichet, University of Aix Marseille II, ``Theory for the Cartesian Product of $\lambda$-Quasi-Hierarchies'' Abs: Quasi-hierarchies, as were introduced by Diatta and Fichet (1994), or Bandelt and Dress (1994), extend the hierarchical structures. The main axiom is the one of Bandelt-Dress weak hierarchies : $H_1\cap H_2\cap H_3\in \left\{ H_1\cap H_2,H_2\cap H_3,H_3\cap H_1\right\} ,$ for every triple $\left( H_1,H_2,H_3\right)$ of clusters. A natural generalisation is given for any integer $\lambda \geq 2:$ ${\cap }_i H_i\in %% \left\{ {\cap }_{i\neq j} H_i\right\} _{j=1,..,\left( \lambda +1\right) }$ for every collection of clusters $H_1,..,H_{\lambda +1},$ see Bandelt and Dress (1994) and Diatta (1997), leading to the so-called $\lambda$-quasi-hierarchies. Pseudo-hierarchies (''pyramids''), the union of two hierarchies after closure and structures associated with additive trees provide some famous examples of quasi-hierarchies $\left( \lambda =2\right) .$ Another example is offered by the Cartesian product of two hierarchies, Fichet (1998). By definition, the Cartesian product $\mathcal{H}$= $\mathcal{H}_1\times \mathcal{H}_2$ of two systems of clusters $\mathcal{H}_1$ and $\mathcal{H}_2$ on $I_1$ and $I_2$ respectively, is the system on $I=I_1\times I_2$ of clusters of the type $H=H_1\times H_2,H_1\in \mathcal{H}_1,H_2\in \mathcal{H}%% _2.$ We here extend the above-mentioned property, by showing that given a $%% \lambda _k-$quasi-hierarchy $\mathcal{H}_k$ on $I_k,k=1,..,r,$ the product $%% \mathcal{H}$ = $\mathcal{H}_1\times ...\times \mathcal{H}_r$ is a $\lambda$-quasi-hierarchy on $I=I_1\times ...\times I_r,$ with $\lambda =\lambda _1+...+\lambda _r.$


Ernest Fokoue, Ohio State University, ``Variational Approximation for Gaussian Process Classifiers'' Abs: Gaussian process priors have been successfully used in the construction of highly accurate Bayesian classifiers. However, the quality of estimation and prediction with such classifiers always heavily depends on how well the intractable posterior is approximated. In this talk, I will describe the adaptation of a variational mean field approximation to Bayesian probit classification. The application of this method to some benchmark datasets is shown to produce very good results.


María Teresa Gallegos and Gunter Ritter, Universität Passau, ``A Breakpoint Analysis for Clustering'' Abs: In order to subdivide a Euclidean data set $x_1,\cdots,x_n$ in $g$ homogeneous groups, the (nowadays classical) determinant criterion of cluster analysis (Friedman and Rubin (1967), Scott and Symons (1971) postulates as estimator the partition which minimizes the determinant of the pooled SSP matrix ${\bf W}$. The estimators of the mean vectors and common covariance matrix of the $g$ underlying normal populations are the sample means and the pooled scatter matrix ${\bf W}/n$, respectively, defined by the estimated partition. To robustify the clustering procedure, Rocke and Woodruff (1999) introduced a trimmed version: given a trimming level $\alpha\in [0,1[$, find the subset of size $\lfloor (1-\alpha)n\rfloor$ of the data which is optimal w.r.t. the determinant criterion. A measure of robustness of an estimator is its breakdown value, Hodges (1967). We compute the breakdown values of the mean vectors and of the SSP matrix of the trimmed determinant criterion. It turns out that the latter is positive under very general conditions, a fact that pleads for the robustness of the trimmed determinant criterion.


Sugnet Gardner and Niel le Roux, University of Stellanbosch, ``Modified Biplots for Enhancing Two-Class Discriminant Analysis'' Abs: When applied to discriminant analysis (DA) biplot methodology leads to useful graphical displays for describing and quantifying multidimensional separation and overlap among classes. The principles of ordinary scatterplots are extended in these plots by adding information of all variables on the plot. However, we show that there are fundamental differences between two-class DA problems and the case $J > 2$: describing overlap in the two-class situation is relatively straightforward using density estimates but adding information by way of multiple axes to the plot can be ambiguous unless care is taken. Contrary to this, describing overlap for $J > 2$ classes is relatively more complicated but the fitting of multiple calibrated axes to biplots is well defined. We propose modifications to existing biplot methodology leading to useful biplots for use in the important case of two-class DA problems.


Wolfgang Gaul, University of Karlsruhe, ``Web Mining and Its Interrelations to Classification Data Mining and Market Research'' Abs: Web mining is still a challenge to data analysts as well as researchers in related fields, for whom, depending on the target audience, different starting points can be presented. From an application oriented point of view examples concerning online visibility (How to attract web visitors?), visualization of recommender system results (How to visualize the searching, viewing, and buying behavior of online shoppers?), and web robot detection (How to distinguish between robots and human web visitors?) will be used as introduction where in each case algorithmic aspects are just sketched. From a mathematical perspective it is shown how so-called ``clickstreams'' or navigation paths of web users can be analyzed. Path fragments as sequences of subpaths connected by wildcards describe interesting substructures for the analysis of frequent generalized navigational patterns. In this context the label ``substructures'' is used as basis for a more general framework in which frequent substructures are detected by modifications of the a priori algorithm where sets, sequences, and generalized sequences (of nodes of the site graph visited while browsing the web) are just special cases. The methodology is explained and examples are presented to show how web mining can enhance customer relationship management and help to tackle web controlling issues.


F. Giannandrea, Catholic University of Sacred Hearth, and D. F. Iezzi, University ``La Sapienza'', ``A Method to Classify Hospital Workers with Lower Back Pain'' Abs: Low back pain is almost universal experience among adults, and the prevalence of disability back pain has increased greatly during the past 20 years. Epidemiological studies have provided ample evidence that physical work factors like high physical load, manual material handling and patient handling are associated with the occurrence of low back pain (3). Hospital workers, particularly ward nurses, are known to be at high risk for back pain, with patient-handling tasks being implicated in most cases (6). In several studies perceived disability associated with low back pain has been collected by different questionnaires and a variety of scales (2, 5). The most popular questionnaire is Oswestry Disability Index (ODI) (1, 2). The aim of this paper is to classify hospital workers with lumbar disability by cluster analysis of their responses to the ODI (4). A classification tool was developed to categorize different lumbar disability classes (7).


E. Graubins and David Grossman, Illinois Institute of Technology, ``Applying Hybrid Modeling to Predict the Stock Market'' Abs: Many voting algorithms exist for classification problems. These algorithms typically use the results of numerous classifiers for an entire data set. We identify good classifiers for a particular training set and then apply separate classifiers for given portions of the dataset based on their performance. We have some initial results on a stock market data set that shows the potential for this approach. Our initial work has exhibited an accuracy level of over 90%.


Vahan Grigoryan, Donald Chiarulli, and Milos Hauskrecht, University of Pittsburgh, ``Subject Filtering for Passive Biometric Monitoring'' Abs: Biometric data can provide useful information about the person's overall wellness. However, the invasiveness of the data collection process often prevents their wider exploitation. To alleviate this difficulty we are developing a biometric monitoring system that relies on nonintrusive biological traits such as speech and gait. We report on the development of the pattern recognition module of the system that is used to filter out nonsubject data. Our system builds upon a number of signal processing and statistical machine learning techniques to process and filter the data, including, Principal Component Analysis for feature reduction, the Naive Bayes classifier for the gait analysis, and the Mixture of Gaussian classifiers for the voice analysis. The system achieves high accuracy in filtering non-subject data, more specifically, 84% accuracy on the gait channel and 98% accuracy on the voice signal. These results allow us to generate sufficiently accurate data streams for health monitoring purposes.


Patrick J. F. Groenen, Erasmus University, and Michael W. Trosset, College of William & Mary, ``Fast Multidimensional Scaling of Large Data Sets'' Abs: Multidimensional scaling (MDS) algorithms tend to be slow if thenumber of objects is large, say larger than n=500 objects. In someapplications such as dimension reduction, molecular confirmation,and data mining, larger data sets are available but traditionalMDS algorithms get too slow. However, if so much data areavailable, it generally suffices to use only a fraction. Formissing data, the SMACOF algorithm (see, e.g., De Leeuw andHeiser, 1977, De Leeuw 1988, and Borg and Groenen, 1997) requiresa Moore-Penrose inverse of an n times n matrix. For large n, thecomputation of this inverse becomes prohibitive. Here we proposeto impose missing data according to a symmetric circulant designs.An advantage of this design is that a very efficientimplementation of the Moore-Penrose inverse is available (Gowerand Groenen, 1991).In this presentation, we show a working prototype programmed inMatLab. In a small simulation study, we investigate how well thetechnique is able to find true underlying representations.


Alain Guénoche, Institute de Mathématiques de Luminy-CNRS, ``Clustering By Vertex Density in a Graph'' Abs: In this paper we introduce a new principle for two classical problems in clustering: obtaining a set of partial classes and a partition on a set $X$ of $n$ elements. These structures are built from a distance $D$ and a threshold value $\sigma$ giving a threshold graph on $X$ with maximum degree $\delta$. The method is based on a density function $De : X \rightarrow \hbox{{I}\kern-.1667em\hbox{R}}$ which is computed first from $D$. Then, the number of classes, the classes, and the partitions are established using only this density function and the graph edges, with a computational complexity of ${\cal O}(n \delta)$. Monte Carlo simulations, from random Euclidian distances, validate the method.


David Hand, Imperial College, ``Academic Obsessions and Classification Realities: Ignoring Practicalities in Supervised Classification'' Abs: Supervised classification methods have been the focus of a vast amount of research in recent decades, within a variety of intellectual disciplines, including statistics, machine learning, pattern recognition, and data mining. Highly sophisticated methods have been developed, using the full power of recent advances in computation. Many of these methods would have been simply inconceivable to earlier generations. However, most of these advances have largely taken place within the context of the classical supervised classification paradigm of data analysis. That is, a classification rule is constructed based on a given `design sample' of data, with known and well-defined classes, and this rule is then used to classify future objects. This paper argues that this paradigm is often, perhaps typically, an over-idealisation of the practical realities of supervised classification problems. Furthermore, it is also argued that the sequential nature of the statistical modelling process means that the large gains in predictive accuracy are achieved early in the modelling process. Putting these two facts together leads to the suspicion that the apparent superiority of the highly sophisticated methods is often illusory: simple methods are often equally effective or even superior in classifying new data points.


André Hardy and Pascale Lallemand, University of Namur, ``The Clustering of Symbolic Objects Described by Multi-Valued and Modal Variables'' Abs: In this paper we investigate the problem of the determination of the number of clusters for symbolic objects described by multi-valued and modal variables. Three dissimilarity measures are selected in order to define distances on the set of symbolic objects. Methods for the determination of the number of clusters are applied to hierarchies of partitions produced by four hierarchical clustering methods, and to sets of partitions given by the symbolic clustering procedure SCLUST. Two real data sets are analysed.


Georges Hébrail, ENST, and Yves Lechevallier, INRIA, ``Building Small Scale Models of Multi-Entity Databases by Clustering'' Abs: A framework is proposed to build small scale models of very large databases describing several entities and their relationships. In the first part, it is shown that the use of sampling is not a good solution when several entities are stored in a database. In the second part, a model is proposed which is based on clustering all entities of the database and storing aggregates on the clusters and on the relationships between the clusters. The last part of the paper discusses the different problems which are raised by this approach. Some solutions are proposed: in particular, the link with symbolic data analysis is established.


David I Holmes and Daniel W Crofts, The College of New Jersey, ``The Diary of a Public Man: A Case Study in Traditional and Non-Traditional Authorship Attribution'' Abs: In 1879 the North American Review published in four separate monthly installments excerpts from ``The Diary of a Public Man'' in which the name of the diarist was withheld. It was, or purported to be, a diary kept during the ``secession winter'' of 1860-61. It appeared to offer verbatim accounts of behind-the-scenes discussions at the very highest levels during the greatest crisis the US had ever faced. Interest in this real or purported diary was considerable. The diarist had access to a wide spectrum of key officials, from the South as well as the North, gave a number of striking anecdotes about Abraham Lincoln, and provided an important account of events at Washington during the critical days just before the Civil War. This paper argues that the diarist was not Samuel Ward as has been suggested; it was, instead, William Hurlbert. The preponderance of the evidence also suggests that the Diary may well be a legitimate historical document. For testing and validating the stylometric techniques involved in this study, preliminary textual samples were taken from prominent diarists of that era, i.e., George Templeton Strong, Gideon Welles, and Salmon Chase. Analysis of the frequently occurring function words involving principal components analysis show clear discrimination between writers and internal consistency within writers. The Diary itself also shows remarkable internal consistency and strongly appears to have been written by a single person. A pioneering use of the new Delta method, proposed recently by Burrows, was then employed on a wide cast of contenders. This technique, based on the 100 most frequently occurring words in the pooled corpus, shows that the closest ``match'' to the Diary is indeed Hurlbert, followed by Ward. Attention then focuses on these two contenders only. For the attributional stage of the analysis, discriminant analysis was employed. All 12 Diary samples are placed into the Hurlbert group. The non-traditional stylometric analysis has supplied objective evidence that supports traditional scholarship regarding the problem of the authorship of the Diary. The likelihood that the entire document was written by one person is very strong. William Hurlbert has been pinpointed, to the exclusion of all others, as the Diarys author. Much of the Diary could never have been concocted after the fact; the chances are that the entire document is authentic.


Leanna House and D. Banks, Duke University, ``Cherry-Picking as a Robustness Tool'' Abs: When there are problems with data quality, it often happens that a reasonably large fraction is good data, and expresses a clear statistical signal, while a smaller fraction is bad data that shows little signal. If it were possible to identify the subset of the data that collectively expresses a strong signal, then one would have a robust tool for uncovering structure in problematic datasets. This paper describes a search strategy for finding large subsets of data with strong signals. The methodology is illustrated for problems in regression. This work is part of a year-long program in statistical data mining that has been organized by SAMSI, the new National Science Foundation center for research at the interface of statistics and applied mathematics.


J. Hughes-Oliver, North Carolina State University, ``Twins and High Dimensional Data: Can Leave-one-out Cross Validation Survive?'' Abs: High-dimensional low-sample-size problems cause many difficulties for analysis and interpretation. Leave-one-out cross validation is routinely recommended as a technique for assessing a model's predictive power without overfitting. Unfortunately, when the dataset contains virtually identical cases (which we call twins), leave-one-out cross validation may give an overly optimistic assessment of a model's predictive power. Using a recently published study for investigating whether in vitro gene expression profiles of drug efficacy can predict therapeutic classes of compounds, we demonstrate the existence of twins and their impact on several cross-validation studies.


Myung-Hoe Huh, Korea University, ``Enhancing Self-Organizing Maps for Statistical Use'' Abs: Self-organizing map (SOM) is an unsupervised learning neural network method developed by Teubo Kohonen of Finland and his colleagues since 1980's (Kohonen, 1995). SOM is known to be very useful in pattern recognition and text information retrieval areas, as demonstrated by numerous studies (cf. www.cis.hut.fi/research/som-bibl/ and www.soe.ucsc.edu/NCS). The main virtue of SOM is the topological ordering property, which enables visualization and abstraction of data sets at the same time (Kohonen, 1998). SOM has been neglected in statistical community, because of its engineering orientation. Only a few years ago, applied statisticians began to use Kohonen's mapping method in exploratory analyses of large data sets or data mining. Readable writings are available now in several statistical text books such as Ripley (1996) and Hastie, Tibshirani and Friedman (2001). Statisticians face several problems in applying SOM, as I experienced in several mining occasions: 1) How to select the size and the shape of SOM appropriate for the given data set? For instance, which is a better map between 12$\times$4 SOM and 7$\times$7 SOM? [These two have nearly same number of nodes, but different shapes.] If 12$\times$4 is the choice, is there better one of the same shape? 2) SOM yields the visual plot of discrete form, which is not natural to statisticians who expect a visual plot of continuous type. How to get one without much effort? 3) SOM displays observation units, but the map is not guided by variables. Consequently, it is not easy to catch the meaning of SOM intuitively.


Myung-Hoe Huh, Korea University, and Yong-Goo Lee, Chung Ang University, ``Reproducibility Evaluation of k-Means Clustering'' Abs: On the K-means clustering, the number of clusters(K) have to be decided at first. But there are no objective ways to decide the appropriate number of clusters, and we usually decide it by ad hoc trial. We propose a reproducibility assessment procedure of K-means cluster analysis by randomly partitioning the data set into three parts, of which two subsets are used for developing clustering rules and one subset for testing consistency of the rules. Based on the results of the consistency measure between two clustering rules, we can determine the number of clusters in K-means clustering. For measuring the consistency between two clustering rules, we propose an entropy-based method as an alternative to Rand Index and corrected Rand Index that have been widely used for measuring the consistency.


Krzysztof Jajuga, ``Data Analysis and Financial Risk Management: Overview of Modern Approaches'' Abs: Financial risk management is one of the areas, which gained considerable importance in last decade. Here the application of data analysis methods has the significant influence. In this paper we give very synthetic and systematic survey of the main approaches used in financial risk analysis. We concentrate on two main types of risk, namely market risk and credit risk. The methods developed for risk analysis emerged independently in two fields: econometrics, where the main notion applied is stochastic process; and statistics, where the main notion applied is statistical distribution. In the paper we make attempt to integrate these two fields, by putting most approaches in the framework of multivariate statistical distribution derived under the data structure consisting of multivariate time series. We use this framework to integrate the methods derived in financial econometrics, like GARCH models, and modern statistics, like Extreme Value Theory and copula analysis. It will be shown that this unified framework encompasses most risk analysis methods proposed by theoreticians and financial practitioners. We also discuss some other approaches derived in the theory of finance, where the calibration of the models is done by data analysis methods.


Maojin Jiang, Eric Jensen, Steve Beitzel, and Shlomo Argamon, Illinois Institute of Technology, ``Choosing the Right Bigrams for Information Retrieval'' Abs: After more than 30 years of research in information retrieval, the dominant paradigm remains the ``bag-of-words,'' in which query terms are considered independent of their coocurrences with each other. Although there has been some work on incorporating phrases or other syntactic information into IR, such attempts have given modest and inconsistent improvements, at best. This paper is a first step at investigating more deeply the question of using bigrams for information retrieval. Our results indicate that only certain kinds of bigrams are likely to aid retrieval. We used linear regression methods on data from TREC 6, 7, and 8 to identify which bigrams are able to help retrieval at all. Our characterization was then tested through retrieval experiments using our information retrieval engine, AIRE, which implements many standard ranking functions and retrieval utilities.


David Johannsen and Jeff Solka, Naval Surface Warfare Center, ``Modern Geometric Methods for Dimensionality Reduction'' Abs: This talk will discuss some of our recent work in the discovery of 2-manifolds within 3-dimensional data sets. Our approach is predicated on first extracting a simplicial complex representation of the data using the method of Dey. Given this simplicial complex representation of the data one can then compute the genus of the underlying manifold via Euler's equation. The genus, together with the classification of closed and orientable 2-manifolds, allows us to endow the simplicial complex with a homogeneous and isotropic metric. The original observations can then be projected into this space and this more appropriate metric can be used for subsequent cluster or discriminant analysis.


Karen Kafadar, University of Colorado at Denver, and $\,$ Cliff Speigelman, Texas A&M University, ``Forensic Analyis of Bullet Data'' Abs: Since the 1960s, FBI has performed Compositional Analysis of Bullet Lead (CABL), a forensic technique that compares the elemental composition of bullets found at a crime scene to that of bullets found in a suspect's possession. CABL has been used when no gun is recovered, or when bullets are too small or fragmented to compare striations on the casings with those on the gun barrel. The National Academy of Sciences formed a Committee charged with the assessment of CABL's scientific validity. The report, ``Forensic Analysis: Weighing Bullet Lead Evidence'' (National Research Council, 2004), included discussions on the effects of the manufacturing process on the validity of the comparisons, the precision and accuracy of the chemical measurement technique, and the statistical methodology used to compare two bullets and test for a ``match''. This talk will focus on the statistical analysis: the FBI's methods of testing for a ``match'', the apparent false positive and false negative rates, the FBI's clustering algorithm (``chaining''), and the Committee's recommendations. Finally, additional analyses on data made available for future studies will be discussed.


Tony Kearsley and Luis Melara, National Institute of Standards and Technology, ``Nonlinear Programming and Multi-Dimensional Scaling'' Abs: In this presentation, a numerical method for approximating the solution of specific multidimensional scaling problems is presented. These problems arise in the analysis of data such as those produced by nuclear magnetic resonance (NMR) machinery. The procedure seeks to find a set of n points in a p-dimensional Euclidean space which minimizes the proximity of a distance matrix and a predistance matrix. The presented approach constructs an embedding of the problem into a higher dimensional space and follows a homotopy path to the lower p-dimensional space. The optimization can be performed using less expensive quasi-Newton methods or more expensive Newton methods. The presentation will conclude with numerical results of a computationally efficient Gauss-Newton procedure which is matrix free.


Balaji Krishnapuram, Duke University, ``Autonomous Learning of Multi-Sensor Classifiers'' Abs: We present an adaptive classifier-learning algorithm that fuses information (features) from multiple types of sensors. The proposed methods are adaptive in the sense that they automatically decide what additional information should be collected in order to optimally improve the accuracy of the classifier, under the constraints of a limited data-acquisition budget. Experimental results on measured radar and hyper-spectral image data attest to the efficacy of the proposed methods in improving the accuracy of the learned classifier.


Koji Kurihara, Okayama University, ``Classification of Geospatial Lattice Data and Their Graphical Representation'' Abs: Statistical analyses for spatial data are important problems in various types of fields. Lattice data are synoptic observations covering an entire spatial region, like cancer rates broken out by each county in a state. There are few approaches for cluster analysis of spatial data. But echelons are useful techniques to study the topological structure of such spatial data. In this paper, we explore cluster analysis for geospatial lattice data based on echelon analysis. We also provide new definitions of the neighbors and families of spatial data in order to support the clustering procedure. In addition, the spatial cluster structure is demonstrated by hierarchical graphical representation with several examples. Regional features are also shown in this dendrogram.


Katarzyna Kuziak, Wroclaw University of Economics, ``Evaluation of Risk in the Index Option Pricing Model'' Abs: In the finance theory many mathematical models are used to value securities or to manage risk. These models are not perfect and they are subject to many errors, for example these coming from: incorrect model of price dynamics, using of indirect input parameters in the estimation, improper implementation of theoretical models, misunderstanding of relationship between assets in multi-asset derivatives. Most financial models are derived under the assumption of the existence of perfect and efficient capital market, but in practice markets are not perfect and not efficient. This causes the additional risk, a so called model risk. To avoid this type of risk in some cases, appropriate data analysis methods can be used (e.g. robust estimation procedures, distribution analysis, forecasting techniques). The purpose of this paper is to evaluate existence of risk in index option pricing model. Some different models of asset price dynamics will be considered. Using different models to value the same option, would yield different option prices. The paper will present how sensitive option pricing model is to the assumption about price dynamics. Empirical evidence for index option listed on Warsaw Stock Exchange will be given.


Vicki Laidler, Computer Sciences Corporation, Space Telescope Science Institute, ``A Tale of Two Probabilities: Assessing Accuracy on Classified Astronomical Data'' Abs: I will explore the use of conditional probabilities, together with a priori domain knowledge, to understand the reliability of classified data sets such as astronomical catalogs that label objects as stars or galaxies. Complications that affect the general problem (such as minority populations and contamination) will be considered, as well as those more specific to astronomical observations (such as incompleteness and blending).


Michael D. Larsen, Iowa State University, ``Issues in Record Linkage'' Abs: Record linkage is the process of combining information about individuals or entities across databases. In order to conduct a statistical analysis, one often has to combine information on people or units from various sources. Considering the possibility of terrorist threats, record linkage takes on additional significance - it might be possible to link databases to determine if the collective behavior of individuals or entities suggests suspicious or threatening activities. The use of record linkage in counterterrorism efforts will involve linking together certain administrative records and possibly commercial files on the population and interpreting the results in an effort to identify potentially dangerous or suspicious occurrences. In the United States, the Department of Homeland Security (DHS), the Defense Advanced Research Projects Agency (DARPA), and other agencies are interested in record linkage as part of their counterterrorism efforts. This talk will review probabilistic record linkage methods, discuss new advances, and comment on difficulties and dangers that will be encountered when using these and other methods for purposes of counterterrorism.


Nicole Lazar, Carnegie Mellon University, ``Are All fMRI Subjects Created Equal?'' Abs: Group maps created from individual functional neuroimaging maps provide useful summaries of patterns of brain activation. Different methods for combining information have been proposed over the years in the statistical literature; we have recently applied some of these methods to functional MRI data. The resultant group maps are statistics, hence it is natural to ask how sensitive they are to the effects of unusual subjects. "Unusual" here might be in terms of extent, location or strength of activation. In this talk, I consider a jackknife approach to assessing the influence of individual subjects on group inferences from an fMRI study. This approach not only helps users to understand the different effects that subjects have on the combined data, but also to evaluate the sensitivity of the different combining methods themselves.


Ludovic Lebart, ENST, ``Validation Techniques for Correspondence Analysis'' Abs: Correspondence Analysis (CA) techniques play a major role in the computerized exploration of categorical data. It provides useful visualizations (e.g. in socio-economic surveys, in marketing) highlighting associations and patterns between two or more categorical variables. Chikio Hayashi is recognized as one of the main discoverer of CA, which is known also as Hayashi quantification method number 3 ever since his seminal paper of 1956. Another pioneering work of Professor Hayashi concerns the early applications of multidimensional methods, including CA, to a wide range of national and multinational sample surveys (see: Hayashi, 1987). Several decades ago, his general conception of applied multivariate statistics, coined later by himself ``Data Science'', was almost identical to the modern fields of Data Mining and Visualization Techniques. However, most of the outputs of these ``unsupervised procedures'' (parameters, graphical displays) still remain difficult to assess. We will then focus on the two following complementary issues: - External validation, involving external data or meta-data (generally considered as supplementary or illustrative elements) and allowing for classical statistical tests, often involving multiple comparisons problems. - Internal validation, based on re-sampling techniques such as bootstrap and its variants, allowing for systematically enriching the scattering diagrams on the principal axes with confidence areas. Validation techniques are particularly complex in the case of eigenvalues and eigenvectors problem, and the bootstrap appears to be the only method that provides feasible and efficient procedures. The data set serving as an example is the British section of a multinational survey conducted in seven countries (Japan, France, Germany, Italy, Nederland, United Kingdom, USA) in the late nineteen eighties (Hayashi et al., 1992). Re-sampling techniques (mainly bootstrap in the case of unsupervised approaches) possess all the required properties to provide the user with the versatile tools that transform appealing visualizations into scientific documents.


Bruno Leclerc, EHESS, ``The Consensus of Classification Systems, with Adams' Results Revisited'' Abs: The problem of aggregating a profile of closure systems into a consensus closure system has interesting applications in classification. We first present an overview of the results obtained by a lattice approach. Then, we develop a more refined approach based on overhangings and implications that appears to be a generalization of Adams' consensus tree algorithm. Adams' uniqueness result is explained and generalized.


Herbert K. H. Lee, University of Santa Cruz, ``Priors for Neural Networks'' Abs: Neural networks are commonly used for classification and regression. The Bayesian approach may be employed, but choosing a prior for the parameters presents challenges. This paper reviews several priors in the literature and introduces Jeffreys priors for neural network models. The effect on the posterior is demonstrated through an example.


Seong Keon Lee, Chuo University, ``On Classification and Regression Trees with Multiple Responses'' Abs: The tree method can be extended to multivariate responses, such as repeated measures and longitudinal data, by modifying the split function so as to accommodate multiple responses. Recently, some decision trees for multiple responses have been constructed by other researchers. However, their methods have limitations on the type of response, that is, they allow only continuous or only binary responses. Also, there is no tree method to analyze polytomous and ordinal responses. In this paper, we will modify the tree for the univariate response procedure and suggest a new tree-based method that can analyze any type of multiple response by using Generalized Estimating Equations (GEE) techniques.


Sun-Soon Lee, Seoul National University, Hong-Seok Lee, Sung Kyun Kwan University, Joong-Hwan Lee, Needs I Co. Ltd., and Sung-Soo Kim, Korea National Open University, ``Customer Segmentation using gCRM'' Abs: gCRM(geographical Customer Relationship Management) is an integrated solution of GIS(Geographic Information System) and CRM(Customer Relationship Management). It is Territory Market Customer Relation Management that includes database system of GIS and CRM. gCRM uses GIS technique to show one or multi dimensional analytical result of customer information. gCRM technique is being improved by using the space data mining, a satellite location confirmation system (Global Positioning System), the PDA and mobile phone techniques. In this research, we introduce gCRM combined with Life Style Information. This system can be efficiently used for customer segmentation graphically. Especially the interactive visualization of clustered customer groups using gCRM can be powerfully used for customer segmentation in marketing.


Taerim Lee, Korea National Open University, ``A Tree-Structured Survival Model for AIDS in Korea'' Abs: TBA


Mohamed Mehdi Limam and Edwin Diday, University of Paris IX-Dauphine, and Suzanne Winsberg, Institut de Recherche et Coordination Acoustique/Musique, ``Probabilistic Allocation of Aggregated Statistical Units in Classification Trees for Symbolic Class Description'' Abs: Consider a class of statistical units, in which each unit may be an aggregate of individual statistical units. Each unit is decribed by an interval of values for each variable. Our aim is to develop a partition of this class of aggregated statistical units in which each part of the partition is described by a conjunction of characteristic properties. We use a stepwise top-down binary tree method and we introduce a probabilistic approach to assign units to the nodes of the tree. At each step we select the best variable and its best split to optimize simultaneously a discrimination criterion given by a prior partition and a homogeneity criterion. Finally, we present an example of real data.


Xiaodong Lin, SAMSI, and Yu Zhu, Purdue University, ``Degenerate Expectation-Maximization Algorithm for Local Dimension Reduction'' Abs: Dimension reduction techniques based on principal component analysis (PCA) and factor analysis are commonly used in statistical data analysis. The effectiveness of these methods is limited by their global nature. Recent efforts have focused on relaxing global restrictions in order to identify subsets of data that are concentrated on lower dimensional subspaces. In this paper, we propose an adaptive local dimension reduction method, called the Degenerate Expectation-Maximization Algorithm (DEM). This method is based on the finite mixture model. We demonstrate that the DEM yields significantly better results than the local PCA (LPCA) and other related methods in a variety of synthetic and real datasets. The DEM algorithm can be used in various applications ranging from clustering to information retrieval.


Regina Liu, Rutgers University, ``Mining Massive Text Data and Developing Tracking Statistics'' Abs: This paper outlines a systematic data mining procedure for exploring large free-style text datasets to discover useful features and develop tracking statistics, generally referred to as performance measures or risk indicators. The procedure includes text mining, risk analysis, classification for error measurements and nonparametric multivariate analysis. Two aviation safety report repositories PTRS from the FAA and AAS from the NTSB will be used to illustrate applications of our research to aviation risk management and general decision-support systems. Some specific text analysis methodologies and tracking statistics will be discussed. Approaches to incorporating misclassified data or error measurements into tracking statistics will be discussed as well.


Hermann Locarek-Junge, Dresden University of Technology, ``Estimation of Tail Coefficients and Extreme Correlations for Market and Credit Risk: Problems, Pitfalls, and Possible Solutions'' Abs: Value-at-Risk (VaR) is a well known risk measurement concept. It has its special problems, however. A new concept for market risk measurement is conditional VaR (CVaR), which has its own problems. To estimate probabilities from historical data, it is necessary to address the problem of extreme correlation and for credit risk - correlated defaults. First estimators are discussed in the framework of a Bernoulli-mixture model, and second for the single-factor model known from Basel II, the maximum-likelihood estimators are given. Analogously to rating classes homogeneous groups of obligors are considered.


Vincent Loonis, ENSAE, ``The Simultaneous Row and Column Partitioning of Several Contingency Tables'' Abs: This paper focuses on the simultaneous aggregation of modalities for more than two categorical variables. I propose to maximize an objective function closely similar to the criteria used in multivariate analysis. The algorithm I suggest is a greedy process which, at each step, merges the two most criterion-improving items in the nomenclature. As the solution is only quasi-optimal, I present a consolidation algorithm to improve on this solution, for a given number of clusters.


Carlos Lourenço and Margarida Cardoso, ISCTE, ``Market Segmentation: A Comparison Between Mixture Models and Data Mining Techniques'' Abs: While many of both marketing research scientists and marketers are still segmenting markets by means of nonoverlapping and overlapping methods, two distinct approaches are competing for a place in the segmentation methods podium: probabilistic methods and data mining techniques. With the clear advantage of allowing for statistical inference, probabilistic methods provide some of the most powerful algorithms for market segmentation. However, data mining techniques are increasingly applied to market segmentation and trying to overcome the accusation of lack of statistical properties. Using recent computational developments and the same data, we compare the estimation of mixture models with two data mining techniques: the TwoStep method (based on the BIRCH clustering method) and Kohonen neural networks to build up a SOM. We extensively explore different (and appropriate) parameterizations on the referred methods and analyse their performance. We suggest some methodologies of evaluation and characterization of segments' structures for the methods used.


Guanzhong Luo and David Andrich, Murdoch University, ``The Weighted Likelihood Estimation of Person Locations in an Unfolding Model for Polytomous Responses'' Abs: It is well known that there are no meaningful sufficient statistics for the person locations in a single peaked unfolding response model. The bias in the estimates of person locations of the general unfolding model for polytomous responses (Luo 2001) with conventional Maximum Likelihood Estimation (MLE) is likely to accumulate with various algorithms proposed in the literature. With the main aim of preventing the bias in the estimates of person locations in the equi-distant unfolding model when the values of item parameters are given, this paper derives the Weighted Likelihood Estimation (WLE) equations, following the approach of Warm (1989). A preliminary simulation study is also included.


Vladimir Makarenkov, Alix Boc, and Abdoulaye Baniré Diallo, University of Quebec, ``Determining Horizontal Gene Transfers in Species Classification: Unique Scenario'' Abs: The problem of species classification, taking into account the mechanisms of reticulate evolution such as horizontal gene transfer (HGT), species hybridization,or gene duplication, is very delicate. In this paper, we describe a new algorithm for determining a unique scenario of HGT events in a given additive tree (i.e., a phylogenetic tree) representing the evolution of a group of species. The algorithm first establishes differences between topologies of species and gene-additive trees. Then it uses a least-squares optimization procedure to test for the possibility of horizontal gene transfers between any pair of edges of the species in the tree, considering all previously added HGTs in order to determine the next one. We show how the proposed algorithm can be used to represent possible ways in which the rubisco $rbcL$ gene has spread in a species classification that includes plastids, cyanobacteria, and proteobacteria.


David Marchette, Naval Surface Warfare Center, ``Iterative Denoising for Cross-Corpus Discovery'' Abs: Given two disparate corpora we wish to identify meaningful cross-corpus associations; e.g., observations in different corpora satisfying, perhaps, a dictionary definition of serendipity: a meaningful discovery not explicitly sought. Toward this end, we introduce an iterative denoising methodology for cross-corpus discovery. This is a method for dimensionality reduction and search that utilizes corpus-dependent projections. We take a (perhaps overly) broad definition of corpus; we will illustrate the methodology on hyperspectral data analysis, text document processing, and analyzing user login sessions.


M. Markatou, H. Tian, S. Biswas, and G. Hripsack, Columbia University, ``Analysis of the Effect of Correlation on the Cross-Validation Estimates of the Performance of Learning Algorithms'' Abs: We address the problem of estimating the variance of cross-validation estimates of the generalization error. For cross-validation based on random sampling of training and test sets, we show that the variability induced by different training and test sets can be quantified by the expectation of two random variables. One is the random variable that expresses the cardinality between the intersection of two different training sets, the other denotes the cardinality of the intersection between the corresponding test sets. We provide moment approximations of the cross-validation statistic that estimates the generlization error. The moment approximations are then used to analyze the variance of the CV-estimator. The case of non-overlapping test sets is obtained as a special case of the derived results.


Paul Marriott, University of Waterloo, ``On the Geometry of Mixtures'' Abs: The class of statistical models known as mixtures have wide applicability in applied problems due to their flexibility, naturalness and interpretability. However despite their apparent simplicity the inference problem associated with them remains hard, both from a theoretical and a practical standpoint. This talk gives an overview of some methods which use geometric techniques to understand the problem of inference under mixture models. The recently introduced class of local mixtures is shown to have many applications, managing to retain a great deal of flexibility and interpretability while having excellent inference properties. Throughout this talk technical issues will be kept to a minimum and a visual and graphical approach will be taken when explaining both statistical and geometric ideas.


Chérif Mballo, ESIEA, and Edwin Diday, University of Paris-Dauphine IX, ``Kolmogorov-Smirnov for Decision Trees on Interval and Histogram Variables'' Abs: With advances in technology, data sets often contain a very large number of observations. Symbolic data analysis treats new units that are underlying concepts of the given data base or that are found by clustering. In this way, it is possible to reduce the size of the data to be treated by transforming the initial classical variables into variables called symbolic variables. In symbolic data analysis, we consider, among other types, interval and histogram variables. The algebraic structure of these variables leads us to adapt dissimilarity measures to be able to study them. The Kolmogorov-Smirnov criterion is used as a test selection metric for decision tree induction. Our contribution in this paper is to adapt this criterion of Kolmogorov-Smirnov to these types of variables. We present an example to illustrate this approach. Masahiro Mizuta, Hokkaido University, ``Relative Projection Pursuit and Its Applications'' Abs: In this paper, we propose a new method of projection pursuit, relative projection pursuit (RPP), which finds `interesting' low dimensional spaces different from reference data sets predefined by the user. In addition, as an application of the method, we develop a new dimension reduction method: sliced inverse regression with relative projection pursuit. Recently, high dimensional datasets such as microarray gene data and point-of-sale data have become important. It is generally difficult to see the structure of data when the dimension of data is high. Therefore, many studies have invented methods that reduce high dimensional data to lower dimensional data. Among these methods, projection pursuit was developed by Friedman and Tukey (1974) in order to search for an `interesting' linear projection of multidimensional data. They defined the degree of `interestingness' as the difference between the distribution of the projected data and the normal distribution. We call this measure a projection index. However, projection indices that measure the difference from the normal distribution do not always reveal interesting structure because interesting structure depends on the purpose of the analysis. According to the scientific situation that motivates the data analysis, `uninteresting' structure is not always the normal distribution. Relative projection pursuit allows the user to predefine a reference data set that represents `uninteresting' structure. The projection index for relative projection pursuit measures the distance between the distribution of the projected target data set and that of the projected reference data set. We show the effectiveness of RPP with numerical examples and actual data.


Takashi Murakami, Nagoya University, ``The Direct Procrustes Method and Perfect Congruence'' Abs: The direct procrustes method is a procedure to obtain a set of orthonormal composites of variables whose pattern is closest to a specified target matrix in the least-squares sense (Murakami, 2000). Derivation of a set of oblique composites whose pattern is perfectly congruent to any target is always possible as was proven by Ten Berge (1986). One may also define a set of composites by the use of elements of the target as weights. Sets of composites obtained from a real data by these methods were compared empirically in terms of the amount of explained variance, the congruence of the pattern to the target, and the similarity between the pattern and the matrix of weights. Extensions of direct procrustes method to the oblique case were examined as well. Principal components and their (orthogonal and oblique) procrustes rotation were used as reference points for the comparisons. The results shows that the group centroid method and its minimally orthonormalized (Johnson, 1966) version based on the simple sums of specified sets of variables generally produced most desirable solution as long as the target has the form of very simple structure.


Fionn Murtagh, Queen's University Belfast, ``Thinking Ultrametrically'' Abs: The triangular inequality is a defining property of a metric space, while the stronger ultrametric inequality is a defining property of an ultrametric space. Ultrametric distance is defined from p-adic valuation. It is known that ultrametricity is a natural property of spaces that are sparse. Here we look at the quantification of ultrametricity. We also look at data compression based on a new ultrametric wavelet transform. We conclude with computational implications of prevalent and perhaps ubiquitous ultrametricity.


Mohamed Nadif, Université de Metz, and Gérard Govaert, Université de Technologie de Compiègne, ``Another Version of the Block EM Algorithm'' Abs: While most clustering procedures aim to construct an optimal partition of objects or, sometimes, of variables, there are other methods, called block clustering methods, which consider simultaneously the two sets and organize the data into homogeneous blocks. Recently, we have proposed a new mixture model called a block mixture model that addresses this situation. Our model allows one to embed simultaneous clustering of objects and variables through a mixture approach. We use maximum likelihood (ML) to implement the method, and have developed a new EM algorithm to estimate the parameters of this model. This requires an approximation of the likelihood and we propose an alternating-optimization algorithm, which is compared to another version of EM based on an interpretation given by Neal and Hinton. The comparison is performed through numerical experiments on simulated binary data.


Jeremy Nadolski and Kert Viele, University of Kentucky, ``The Role of Latent Variables in Model Selection Accuracy'' Abs: Mixture models are often formulated in terms of latent variables Z which determine the component membership of the observations. While these latent variables are often used solely as a computational tool, we will discuss how the latent variable formulation provides insight into model selection procedures. We will demonstrate conditions on the latent variables that cause BIC (and other model selection procedures) to fail, and suggest alternative methods for model selection more suited for those conditions.


Seungmin Nam, Kiwoong Kim, and Sinsup Cho, Seoul National University, and Inkwon Yeo, Chonbuk National University, ``A Bayesian Analysis Based on Beta-Mixtures for Software Reliability Models'' Abs: Nonhomogeneous Poisson Process is often used to model failure times occurred in software reliability and hardware reliability models. It can be characterized by its intensity functions or mean value functions. Many parametric intensity models have been proposed to account for the failure mechanism in real situation. In this paper, we propose a Bayesian semiparametric approach based on beta-mixtures. Two real datasets are analyzed. Tom Nichols, University of Michigan, ``Detecting a Conjunction of Alternatives: Finding Consistent Activations in Functional Neuroimaging Data using FDR'' Abs: Detecting a Conjunction of Alternatives: Finding Consistent Activations in Functional Neuroimaging Data using FDR Psychologists studying memory use Functional Magnetic Resonance Imaging (fMRI) to understand how information is encoded, stored and retrieved in the brain. Short term, or working memory, can be 'probed' in a number of ways, say by asking a subject to remember a list of words, or a list of digits, or even even a collection of shapes (triangles, squares, etc). The goal is to identify regions of the brain that support working memory generically, but which are not specialized to words or numbers or shapes. This requires testing a union of nulls (no effect in one or more of the three tasks) versus an intersection of alternatives (effects in all three tasks). Worsley and Friston proposed using the maximum P-value to test for a intersection of effects, but their inference is based on the intersection of nulls. This is problematic, as a rejection of the intersection null is just the union of alternatives, and not the psychologist's desired "conjunction". We show that a simple approach does allow 'Conjunction Inference' using the minimum statistic. Further, we propose using Storey's Positive False Discovery Rate (pFDR) to make inference on the union of nulls. Storey shows that pFDR can be interpreted as the posterior probability of the null given that a statistic lies in a rejection region. Our method can approximately be seen as making inference on the sum of q-values. We demonstrate the method on simulated and real data.


Ole Nordhoff, Institut für Statistik und Wirtschaftsmathematik, ``Expectation of Random Sets and the `Mean Values' of Interval Data'' Abs: Clustering methods often use class representatives or prototypes to describe data clusters. Prototypes are involved in many clustering criteria, where the dissimilarity between a data point and a cluster representative is considered. Moreover, the properties of a cluster are often characterized briefly by one single data point, e.g., the class centroid. When one clusters $p$-dimensional interval data $x_1, \ldots, x_n \subset {\cal{B}}^p$ (rectangles in $\hbox{{I}\kern-.1667em\hbox{R}}^p$) with a certain clustering method one is searching for `mean value of intervals' in ${\cal{B}}^p$ as a prototype of data in a class. This paper deals with the question how the mean of some $p$-dimensional intervals can be defined. We will introduce two different ways for defining the mean of ($p$-dimensional) intervals. The first approach is to reduce an interval to its 'lower left' and 'upper right vertex' and shift the problem to the case of real-valued data points, where the definition of expectation and mean is well known. In the second approach we consider an interval as a special form of a closed (convex) set and utilise the theory of Random Closed Sets (RCSs) to define the mean via definitions of expectation. This approach is influenced by papers of Molchanov and Stoyan. There are a couple of different definitions, each of them with special properties. We pick out three definitions, illustrate them by examples and check for an extract of axiomatic properties, if they are fulfilled or not. Finally, we will discover that in some cases different definitions of `expectation' are equal, if the considered sets are intervals.


Hodaka Numasaki, Hajime Harauchi, Yuko Ohno, Osaka University, Kiyonari Inamura, Kansi University of International Studies, Satoko Kasahara, Morito Monden, and Masato Sakon, Osaka University, ``Application of Spectrum Analysis and Sequence Relational Analysis for the Medical Staff's Job Classification: Use of Time Factor and Behavior Factors for Job Workflow'' Abs: Object: To investigate the efficient job workflow, the occurrence order and frequency of the job elements and the relation between the job elements are the important information. In this research, new methodology of job classification was proposed from the viewpoint of periodicity and relationship among job elements. Method: The periodicity and the incident condition of job elements were analyzed by the discrete Fourier transformation on the time-series occurrence information of the time-motion study data. The strength of the relation among the job-sequence was investigated by the sequence relational analysis. Data: A series of 24 hr time-motion studies for the medical staff at a surgical ward was carried out from 1998 to 2001, and a total of 23 days of job was observed and recorded. Results: All job elements of the ward were classified into five incident patterns based on the periodicity of each element [emergent, routine, time-dependent, arbitrary-provided and mixed] and into three patterns based on the association with other jobs [independent, interdependent with other jobs and random]. Using this classification framework, a total of 250 job elements were clearly categorized and the job-workflow patterns of medical staff were clarified.