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Abstracts A-D

Rafik Abdesselam, Université de Caen Basse-Normandie, ``Sequential Multiple Discriminant Analysis'' Abs: A sequential discriminant analysis method of evolutionary data classifying aim is described. This method of decision-making is based on the research of principal axes of a configuration of points in the individual-space with a relational distance. We are in presence of a discriminant analysis problem, in which the decision must be taken as the partial knowledge evolutionary information of the observations of the statistical unit, which we want to classify. The constraint consists in imposing to the discriminant factors to be part of the subspace associated to all the observations carried out during this partial period. The sequential analysis proposed consist to make a relational multiple discriminant analysis of the global explanatory configuration of points, corresponding to all the observations carried out during the global period, projected on the partial subspace. We thus show how what the knowledge from the observation of the global testimony sample carried out during the entire period, can benefit to the classifying decision on supplementary statistical units, which we only have partial information about. This sequential discriminant analysis is a simple method which can be very useful particularly in the medical field for diagnosis-making, where it is often important to anticipate before term to be able to intervene in time if necessary. An analysis using real data is here described using this method.

Edgar Acuña and Caroline Rodriguez, University of Puerto Rico, ``The Treatment of Missing Values and Its Effect on Classifier Accuracy'' Abs: The presence of missing values in a dataset can affect the performance of a classifier constructed using that dataset as a training sample. Several methods have been proposed to treat missing data and the one used most frequently deletes instances containing at least one missing value of a feature. In this paper we carry out experiments with twelve datasets to evaluate the effect on the misclassification error rate of four methods for dealing with missing values: the case deletion method, mean imputation, median imputation, and the KNN imputation procedure. The classifiers considered were the Linear Discriminant Analysis (LDA) and the KNN classifier. The first one is a parametric classifier whereas the second one is a nonparametric classifier.

Kohei Adachi, Ritsumeikan University, ``An Oblique Procrustes Technique for Simultaneously Rotating Component and Loading Matrices'' Abs: Let F$ (n \times p)$ and A$ (m \times p)$ express the component and loading matrices, respectively, obtained with the principal component analysis of X $(n \times m)$. That is, X* = FA' = FSS$^{-1}$A', where X* is the matrix of rank $p$ approximating X best and S is an arbitrary nonsingular matrix of $p \times p$. We consider the problem of transforming F and A into FS and AS'$^{-1}$ so that they match G (containing target components) and B (target loadings), respectively, as closely as possible. This problem is formulated as minimizing $\eta = n^{-1} \Vert \mbox{{\bf FS-G}} \Vert^2 + m^{-1} \Vert
\mbox{{\bf AS'}}^{-1} - \mbox{{\bf B}} \Vert^2$ over S. Let S = K$\Lambda$L' define the singular value decomposition of S with $\Lambda = \mbox{diag}(\lambda_1, \ldots,
\lambda_p)$. Then, $\eta$ is rewritten as $ n^{-1} \Vert \mbox{{\bf FK$\Lambda$L'-G}} \Vert^2 + m^{-1} \Vert
\mbox{{\bf AK$\Lambda$L'}}^{-1} - \mbox{{\bf B}} \Vert^2$. For minimizing this, we use an algorithm in which the following three steps are iterated alternately. First, $\eta$ is minimized over K subject to K'K=KK'= I (the identity matrix). Second, $\eta$ is minimized over L under L'L=LL' = I. Third, $\eta$ is minimized over $\lambda_s$ for $s = 1, \ldots, p$, which is attained by solving an quartic equation of $\lambda_s$. The method is detailed and illustrated with numerical examples in the presentation.

F. Afonso, University of Paris-Dauphine, Lynne Billard, University of Georgia, and Edwin Diday, University of Paris-Dauphine, ``Symbolic Linear Regression with Taxonomies'' Abs: This work deals with the extension of classical linear regression to symbolic data and constitutes a continuation of previous papers from Billard and Diday on linear regression with interval and histogram-valued data. In this paper, we present a method for regression with taxonomic variables. Taxonomic variables are variables organized in a tree with several levels of generality. For example, the towns are aggregated up to their regions, the regions are aggregated up to their country.

Ulas Akkucuk and Doug Carroll, Rutgers University, ``Mapping of Nonlinear Manifolds: ISOMAP and a Version of PARAMAP'' Abs: Dimensionality reduction techniques are used for representing higher dimensional data by a more meaningful lower dimensional structure. In this paper we will study two such approaches, namely Carroll's Parametric Mapping (abbreviated PARAMAP) (Shepard & Carroll, 1966) and ISOMAP (Tenenbaum, de Silva, & Langford, 2000). The former relies on iterative minimization of a cost function while the latter applies classical MDS after a preprocessing step involving the use of a shortest path algorithm to define approximate geodesic distances. We will develop a measure of congruence based on preservation of local structure between the input data and the mapped low dimensional embedding, and compare the different approaches on various sets of data with and without error and irregular spacing of points (in the case of 62 points on the surface of a closed sphere). We will also improve PARAMAP to deal with a larger number of data points by devising a method to split the data into a landmark and a holdout sample, and then extrapolate the holdout points from the landmark configuration. The former will be accomplished by using a procedure intended to find an initial seed for the K-means procedure (DeSarbo, Carroll, Clark, & Green, 1984) and the latter by applying PARAMAP to map in the holdout points into the lower dimensional landmark configuration.

Yasumasa Baba and $\,$ Noboru Ohsumi, Institute of Statistical Mathematics, ``Chikio Hayashi and Data Science in Japan'' Chikio Hayashi was one of the leading researchers in the field of statistics and data analysis in Japan and also the pioneer of data science. Covering a wide range of statistics subjects for half a century, Hayashi continued to drive the development of data science in this country, particularly in the area of survey research and data analysis. Talking about his research achievements is talking about the progress of data science in Japan. Thus, this paper attempts to trace the footsteps of his research activities, focusing on his two important study themes: quantification methods (or named formally as quantification theory) for qualitative data and survey research. Hayashi always based his studies on observation of real phenomena maintaining his distinctive research style of ``from designing the experiments to analyzing data collected originally.'' A series of methods for analyzing qualitative data, named by social psychologist Hiroshi Akuto as Hayashi's quantification method type I, II and so on, were born out of a need for data analysis in the course of the professor's pursuit for individual research goals. The first method of the series was conceived in 1950 when Hayashi was groping for the procedures to evaluate criminal convicts for their post-release recidivism possibilities and divide them into two groups in accordance with resulting risk factors. Hayashi began his study on this subject in 1947, and in 1950 formulated a method of discriminant analysis based on multivariate categorical data which was to be named later as quantification method type II. This was followed by quantification method type IV (1951) which is now regarded as a kind of MDS (multidimensional scaling methods), quantification method type I (1952) which is a kind of multiple regression analysis of qualitative data, quantification method type III (1956) which is comparable to correspondence analysis proposed by Benzécri in 1960s, and so on. Placing a particular emphasis on sample survey, Hayashi conducted researches in a wide range of fields. His broad interest included such areas of marketing research, social survey research, and animal population assessment. In the late 1940s, Hayashi studied sample survey theory with his colleagues, and applied it to social survey. In 1953, the Institute of Statistical Mathematics (ISM) initiated a five-year interval sample survey project to study the Japanese national character. Hayashi, who played a leader in the initial project designing, has remained one of the project leaders until 1998. This project is now regarded that was contributing to the establishment of sample survey methods in Japan, and hence Hayashi is admired as the key person who enabled it to happen. Advancing his survey methodologies with interests extended to the field of international comparative survey, Hayashi was lately working on analysis of the national character of a nation by extracting its features from the findings of social surveys carried out there. One fruit born out his efforts was CLA (cultural link analysis), the cross-national studies to alternatively cast a distinctive light on the relationship among the Americans, the Japanese and Japanese-American people who embody culture of the both countries. Hayashi was proposing that this approach is applied to compare among other counties in Asia and Europe as the means to interpret complicated interrelations among many nations. After his death, his successors are continuing to advance his achievements in these studies. In advocating data science, Hayashi of late years was intending to break through traditional statistics and make an effort to find a new dimension with much broader perspective.

Kaddour Bachar, Ecole Supérieure des Sciences Commerciales d'Angers, and Israël Lerman, University of Rennes 1, ``Fixing Parameters in the Constrained Hierarchical Classification Method: Application to Digital Image Segmentation'' Abs: We analyse the parameter influence of the likelihood of the maximal link criteria family (LLA hierarchical classification method) in the context of the CAHCVR algorithm (Classification Ascendante Hiérarchique sous Contrainte de contiguïté et par agrégation des Voisins Réciproques). The results are compared to those obtained with the inertia criterion (Ward) in the context of digital image segmentation. New strategies concerning multiple aggregation in the class formation and contiguity notion are positively evaluated in terms of algorithmic complexity.

Daniel Baier, Brandenburg University of Technology Cottbus, ``Pharmaceutical eDetailing and Market Sementation'' Abs: More and more pharmaceutical companies consider internet based technologies for explaining and promoting products as a possible means to stimulate physicians' prescribing without increasing salesforce costs (see, e.g., Cap Gemini Ernst & Young (2002), Lerer et al. (2002)). Various so-called eDetailing technologies such as one-to-one-conferencing, interactive websites, co-browsing, virtual detailing or online communities have been proposed, implemented and tested for this purpose (see, e.g., Baier et al. (2004), Bates et al. (2002)). The talk gives an overview on these technologies and discusses findings on how to use these technologies for which market segments and for which purposes. Furthermore, am own survey on physicians' usage of the internet and their accessibility as well as the design and analysis of a larger virtual detailing campaign in corporation with a pharmaceutical company are discussed.

Simona Balbi and Emilo Di Meglio, University of Naples, ``Contributions of Textual Data Analysis to Text Retrieval'' Abs: The aim of this paper is to show how Textual Data Analysis techniques, developed in Europe under the influence of the Analyse Multidimensionelle des Données School, can improve performance of the LSI retrieval method. A first improvement can be obtained by properly considering the data contained in a lexical table. LSI is based on Euclidean distance, which is not adequate for frequency data. By using the chi-squared metric, on which Correspondence Analysis is based, significant improvements can be achieved. Further improvements can be obtained by considering external information such as keywords, authors, etc. Here an approach to text retrieval with external information based on PLS regression is shown. The suggested strategies are applied in text retrieval experiments on medical journal abstracts.

Xinli Bao and Hamparsum Bozdogan, University of Tennessee at Knoxville, ``Subsetting Kernel Regression Models Using Genetic Algorithm and the Information Measure of Complexity'' Abs: In this paper we introduce and develop a computationally feasible subset selection of best predictor variables with kernel partial least squares regression (K-PLSR) model in reproducing kernal Hilbert space (RKHS), using genetic algorithm (GA) and the information-theoretic measure of complexity (ICOMP) criterion of the estimated inverse-Fisher information matrix (IFIM) developed by Bozdogan (1988, 1990, 1994, 2000, and 2004).

Jean-Pierre Barthélemy, GET-ENST Bretagne, ``Binary Clustering and Boolean Dissimilarities'' Abs: In many clustering systems (hierarchies, pyramids, weak hierarchies) clusters are generated by two elements only. This talk is devoted to such clustering systems. It includes three parts. In the first one the notion of binary clustering is presented and discussed. In the second relationships between binary clustering and weak hierarchies is discussed. Finally we introduce a variant of Melter's boolean metric space, under the name of boolean dissimilarities, and we establish purely qualitative bijection theorems between classes of boolean clustering systems and classes of boolean dissimilarities.

Vladimir Batagelj and Matjaz Zaversnik, University of Ljubljana, ``Islands, an Approach to Clustering in Large Networks'' Abs: In large network analysis we are often interested in important parts of a given network. There are several ways how to determine them. In the paper we present a very efficient approach based on the notion of islands. Assume that in a given network each vertex has a value measuring its importance. Let $t$ be any real number. If we delete all vertices (and corresponding edges) with the value less than $t$, we get the subnetwork called vertex-cut at level $t$. The number and sizes of its components depend on $t$. Often we consider only components of size at least $k$ and not exceeding $K$. The components of size smaller than $k$ are discarded as noninteresting while the components of size larger than $K$ are cut again at some higher level. A vertex-island is a connected subnetwork whose vertices have greater values than the vertices in its neighborhood. It is easy to see that the components of vertex-cuts are all vertex-islands. We developed an algorithm that identifies all maximal vertex-islands of sizes in the interval $k..K$ in a given network. Each island is identified with its port - its lowest vertex. The main problem are the vertices at the same level - flat regions. The set of all maximal vertex-islands determines a hierarchy. For networks with weighted edges we can similarly define edge-islands. The edge-islands algorithm is based on edge-cuts. Both algorithms and some applications of islands in analysis of large networks will be presented. We shall also describe several ways how to determine values of vertices or weights of edges.

François Bavaud, University of Lausanne, ``Generalized Factor Analysis for Contingency Tables'' Abs: Quotient dissimilarities constitute a broad aggregation-invariant family; among them, $f$-dissimilarities are Euclidean embeddable (cf. Bavaud, 2002). We present a non-linear principal components analysis (NPA) applicable to any quotient dissimilarity, based upon the spectral decomposition of the central inertia. For $f$-dissimilarities, the same decomposition yields a non-linear correspondence analysis (NCA), permitting us to modulate as finely as wished the contributions of positive or negative deviations from independence. The resulting coordinates exactly reproduce the original dissimilarities between rows or between columns; however, Huygens's weak principle is generally violated, as measured by a quantity we call `eccentricity'.

Mónica Bécue, Universitat Politècnica de Catalunya, J. Pagès, Institut Nationales Supérieur, and Campo-Elías Pardo, Universidad Nacional de Colombia, ``Analysis of Cross-Language Open-Ended Questions Through MFACT'' Abs: International surveys lead to multilingual open-ended responses. By grouping the answers for the same categories from different countries, sets of comparable category-documents are obtained. The methodology here presented, called multiple factor analysis of contingency tables (MFACT), provides a representation of all of the documents in a common reference space, on the one hand, and of all of the words in a common reference space, on the other hand; these both spaces are related by transition formulae. This methodology allows a direct generalized canonical analysis approach to analyzing multiple contingency tables as well as for keeping correspondence analysis-like features. It works from the raw data, without any previous translation. An example, extracted from a large international survey in four countries, illustrates the potential of this approach.

Halima Bensmail and Hamparsum Bozdogan, University of Tennessee, ``Bayesian Unsupervised Clustering for Mixed Data with Missing Observations'' Abs: Here we try to develop and broaden the application areas of a new statistical modeling technology which will cover a research study on unsupervised classification with mixed data using multidimensional scaling and Bayesian approach. We attempt to make a bridge and apply Bayesian multidimensional scaling for unsupervised clustering. This new methodology is formulated in the multivariate non-Gaussian settings. We propose a new way of clustering observations described by a mixed collection of variables (nominal, ordinal and numerical). We, then use a non-parametric clustering procedure based on optimally scaling the large data and estimate the distribution of the object scores obtained. We propose a multivariate kernel distribution as non-parametric distribution for the variables, this distribution is characterized by a variety of window widths that controls the degree of smoothness of the estimate and a variety of robust covariance matrices. This gives a variety of flexible models to choose from. The prior choice here is challenging especially when dealing with the window width distribution for that we use some conjugate and Entropy based prior to overcome this difficulties. Another challenging part of cluster analysis is to propose a criteria that help us choosing the number of clusters. We use here a Bayesian information complexity ICOMP criterion (Bozdogan 1988) for choosing the best window width, the right robust matrix and the optimal number of clusters k.

Patrice Bertrand, GET-ENST Bretagne, and Ghazi Bel Mufti, ESSEC, ``Loevinger's Measures of Rule Quantity for Assessing Cluster Stability'' Abs: We present a method for measuring clustering stability under the removal of a few objects from a set of objects to be partitioned. Measures of stability of an individual cluster are defined as Loevinger's measures of rule quality. The stability of an individual cluster can be interpreted as a weighted mean of the inherent stabilities in the isolation and cohesion of the examined cluster respectively. The design of the method enables us to measure also the stability of a partition, that can be viewed as a weighted mean of the stability measures of all clusters in the partition. As a consequence, an approach is derived for determining the optimal number of clusters of a partition. Furthermore, using a Monte Carlo test, a probability significance is computed in order to assess how likely any stability measure is, under a null model that specifies the absence of cluster stability. In order to illustrate the potential of the method, we present stability measures that were obtained by using the batch K-Means algorithm on artificial data sets and on Iris data.

Lynne Billard, University of Georgia, ``Symbolic Data Analysis: An Overview of Principles and Some Descriptive Statistics'' Abs: This paper looks at measures of dependence for symbolic interval-valued data. A method is given to calculate an empirical copula for a bivariate interval-valued variable. This copula is then used to determine an empirical formula for calculating Spearman's rho for such data. The methodology is illustrated from a set of hematocrit-hemoglobin data and the results compared with Pearson's product-moment correlation coefficient.

David Birnbaum, University of Pittsburgh, and David Dubin, University of Illinois at Urbana-Champaign, ``Measuring Similarity in the Contents of Medieval Miscellany Manuscripts'' Abs: Edit distance for strings is measured in terms of the smallest number of specific stepwise modifications (insertions, deletions, transpositions, or replacements of characters) required to make a transition from one state to another. We describe our experiments with an analogous measure for larger units of analysis, namely texts copied in medieval miscellany manuscripts. The goal of the project is to describe the likely process employed by medieval scribes in compiling these manuscripts, and the data consists of the manuscripts' (virtual) tables of contents. The process of compiling a miscellany manuscript is different from the process of copying prose text, and one inserts, deletes, transposes, or replaces constituent texts in a miscellany manuscript differently than one inserts, deletes, transposes, or replaces words in continuous prose. We present an algorithm for measuring similarity that is informed by those differences, and hierarchical cluster analyses on the contents of approximately one hundred manuscripts.

Hans-Hermann Bock, University of Aachen, ``Classification in the Life Span of Chikio Hayashi'' Abs: This talk reviews the origin and development of cluster analysis and classfication theory during the life span of Chikio Hayashi, one of the founders of the Japanese Classification Society (JCS) and of the International Federation of Classification Societies (IFCS). It presents a survey of important streams of research in the last 40 years, intermingled with personal reminiscences of Hayashi's activities.

Nicholas I. Bohnen, Marius Buliga, and Gregory M. Constantine, University of Pittsburgh, ``Classifying the State of Parkinsonism by Using Electronic Force Platform Measures of Balance'' Abs: Several measures of balance obtained from quiet stance on an electronic force platform are described. These measures were found to discriminate patients with Parkinson's disease (PD) from normal control subjects. First-degree relatives of patients with PD show greater variability on these measures. A primary goal is to develop sensitive measures that would be capable of identifying impaired balance in early stages of non-clinical PD. We developed a trinomial logistic model that classifies a subject as either normal, pre-parkinsonian, or parkinsonian taking as input the measures developed from the platform data.

Kathy Bogie, Jiayang Sun, and Xiaofeng Wang, Case Western University, ``Mining Huge-p-Small-n Data and New Image Registration Procedures'' Abs: This paper is concerned with developing effective procedures for analyzing sequences of image data from neuromuscular electrical stimulation (NMES) experiments. The data are large in its dimension and small in its subject sample size. In addition, images taken at different sessions from one subject may not align spatially; and artifacts can arise from on-off moments if images are not aligned temporally. We develop a spatial and a temporal registration schemes; they are applicable to image data beyond the NMES experiments. We study a statistical mapping method for analyzing large image data, simultaneously; it leads to an efficient procedure for computing ``FDR map'' to determine whether a change is clinically relevant or spurious.

Stefan Born, Liebig University, and Lars Schmidt-Thieme, University of Freiburg ``Optimal Discretization of Quantitative Attributes for Association Rules'' Abs: Association rules for objects with quantitative attributes require the discretization of these attributes to limit the size of the search space. As each such discretization might collapse attribute levels that need to be distinguished for finding association rules, optimal discretization strategies are of interest. In 1996 Srikant and Agrawal formulated an information loss measure called measure of partial completeness and claimed that equidepth partitioning (i.e. discretization based on base intervals of equal support) minimizes this measure. We prove that in many cases equidepth partitioning is not an optimal solution of the corresponding optimization problem. In simple cases an exact solution can be calculated, but in general optimization techniques have to be applied to find good solutions.

Helena Brás Silva, Paula Brito, and Joaquim Costa, University of Porto, ``Clustering and Validation Using Graph Theory: Application to Data Sets with Numerical and Categorical Values'' Abs: Applying graph theory to clustering, we propose a partitional clustering method and a clustering tendency index, which may be applied to data sets with numerical and categorical values. No initial assumptions about the data set are requested by the method. The partitional algorithm is based on graph colouring and uses an extended greedy algorithm. The number of clusters and the partition that best fits the data set are selected according to the optimal clustering tendency index value. The key idea of this index is that there are k well-separated and compact clusters, if a complete k-partite graph can be defined in the data set, after clustering. The clustering tendency index can also identify data sets with no clustering structure. We propose a partition quality evaluation index and some evaluation indexes of clusters' density and isolation, which select the best partitions between the candidates resulting from the clustering method. We have applied our methodology on simulated and real data sets, so as to evaluate its reliability. This study has showed that the method is efficient; in particular, for detecting non spherical clusters and is robust as concerns outliers. Our methodology has been compared with some classical clustering methods, namely k-means and hierarchical, and using some validation indexes present in the literature.

Matevz Bren, University of Maribor, and Vladimir Batagelj, University of Ljubljana, ``Compositional Data Analysis with R'' Abs: R (at is `GNU S'--a language and environment for statistical computing and graphics. R is similar to the award-winning S system, which was developed at Bell Laboratories by John Chambers et al. It provides a wide variety of statistical and graphical techniques (linear and nonlinear modelling, statistical tests, time series analysis, classification, clustering, and others). Further extensions can be provided as packages. We started to develop the R package MixeR for the compositional data analysis that provides support for: We illustrate the use of MixeR with some real data.

François Brucker, GET-ENST Bretagne, ``Bijection Between Dissimilarities and Binary Realizations'' Abs: One of the aim of numerical taxonomy is to associate a preindexed clustering system to a dissimilarity. Bertrand (2000) has shown that if the clusters of a dissimilarity are exactly the maximal cliques of its threshold graphs, there is a bijection between the set of all dissimilarities and a class of preindexed clustering systems. Since a graph can have an exponential number of maximal cliques, finding all the clusters of a given dissimilarity is practically impossible. Thus, classically, a given dissimilarity is approximated by a dissimilarity of a given type whose clusters are easily computable like ultrametrics, robinsonian dissimilarities or quasi-ultrametrics. The computability of those particular models comes from the fact that their maximal cliques are generated by pairs of elements. We show that this idea can be generalized to any dissimilarity by changing the definition of a cluster. Defining a cluster by the intersection of all the maximal cliques containing a pair of elements (called binary realization), we show that there is a bijection between the set of dissimilarities and a class of preindexed clustering systems. Moreover the computation of all the binary realizations can be performed in polynomial time for any dissimilarity.

Gilles Celeux, INRIA, ``Choosing a Model for Purposes of Classification'' Abs: We advocate the usefulness of taking into account the modeling purpose when selecting a model. Two situations are considered to support this idea: Choosing the number of components in a mixture model in a cluster analysis perspective, and choosing a probabilistic model in a supervised classification context. For this last situation we propose a new criterion, the Bayesian Entropy Criterion, and illustrate its behavior wtih numerical experiments. Those numerical experiments show that this new criterion compares favorably with the classical BIC criterion to choose a model minimizing the prediction error rate.

Seong-San Chae, Daejeon University, Chansoo Kim, and William D. Warde, Oklahoma State University, ``Cluster Analysis Using Robust Estimators'' Abs: Partitioning objects into closely related groups that have dierent states allows to understand the underlying structure in the data set treated. Several clustering algorithms with different kinds of similarity measure are commonly used to find an optimal clustering or close to original clustering. The retrieval ability of six chosen clustering algorithms of using different correlation coeffcients is evaluated using Rand's (1971) C values, presenting how the resultant clustering is close to the original clustering. In the procedure, the concept of informative variables is examined. The retrieval ability is robust using the correlation coefficient with the weighted likelihood estimators (WLE) in simulation study. Using the data set from Spellman et al. (1998), the recovery levels of clusters by the six clustering algorithms with different correlation coe±cients, shrinkage-based correlation(Cherepinsky et al., 2003) and rank-based correlation (Bickel, 2003), are also obtained and compared.

Anil Chaturvedi, Capital One Services, J. Douglas Carroll, Rutgers University, and Vicki Caxsrtwright, Capital One Services, ``A Three-Way, Three-Mode Hybrid Factor/Components Analysis Model'' Abs: This paper presents an approach to enhancing the traditional CANDECOMP/PARAFAC factor or components analysis model for three-way, three-mode data. It enables the extraction of a combination of continuous (a la the CANDECOMP/PARAFAC model of Carroll and Chang, 1970 and Harshman; see Harshman and Lundy, 1984) as well as discrete factor scores and factor loadings for three-way, three-mode data, thus enabling a richer exploration of the data at hand. It precludes the assumption that there is only continuous structure in typical three-way, three-mode data. Users can try to examine the true structure present in the data - be it discrete or continuous. This model is also a special case of a very general class of models and methods called CANDCLUS presented by Carroll and Chaturvedi (1994). We present various results from this three-way, three-mode factor/components analysis model applied to data gathered from a marketing research study.

Marie Chavent, University of Bordeaux, ``A Hausdorff Distance Between Hyper-Rectangles for Clustering Interval Data'' Abs: The Hausdorff distance between two sets is used in this paper to compare hyper-rectangles. An explicit formula for the optimum class prototype is found in the particular case of the Hausdorff distance for the $L_\infty$ norm. When used for dynamical clustering of interval data, this prototype will ensure that the clustering criterion decreases at each iteration.

Chih-Chou Chiu, $\,$ National Taipei University of Technology, and Tian-Shyug Lee, Fu-Jen Catholic University, ``Integrating Classification and Regression Trees with Multivariate Adaptive Regression Splines in Mining Customer Credit Data'' Abs: Credit scoring has become a very important task as the credit industry has been experiencing tough competition during the past few years. The artificial neural network is becoming a very popular alternative in credit scoring models due to its associated memory characteristic and generalization capability. However, the relative importance of potential input variables and the long training process have often long been criticized and hence limited its application in handling credit scoring problems. The objective of the proposed study is to explore the performance of credit scoring using two commonly discussed data mining techniques-classification and regression tree (CART) and multivariate adaptive regression splines (MARS). To demonstrate the effectiveness of credit scoring using CART and MARS, credit scoring tasks are performed on one bank credit card data set. As the results reveal, CART and MARS outperform traditional discriminant analysis, logistic regression, neural networks, and support vector machine (SVM) approaches in terms of credit scoring accuracy and hence provide efficient alternatives in implementing credit scoring tasks.

C. Cifaelli and L. Nieddu, University of Rome, ``An Iterative k-Means-Like Algorithm for Statistical Face Recognition'' Abs: A face recognition algorithm based on a iterated k-mean classifiation technique (1) will be presented in this paper. The proposed algorithm, when compared with popular PCA algorithms for face recognition has an improved recognition rate on various benchmark datasets (2). The algorithm considered in this paper, unlike PCA, is not a dimensional reduction algorithm, nonetheless it yields barycentric-faces which can be used to determine different types of face expressions, light conditions and pose. The technique presented consists in iteratively computing centroyds faces until some conditions are met on the training set. The accuracy PCA and k-mean methods have been evaluated under varying expression, illumination and pose using standard face databases.

Gilles Clermont, Carson Chow, Greg Constantine, et al., University of Pittsburgh, ``Mathematical Modeling of Acute Inflammation'' Abs: A mathematical model involving a system of ordinary differential equations has been developed with the goal of assisting the design of therapies directed against the inflammatory consequences of infection and trauma. Though the aim is to build a model of greater complexity, which would eventually overcome some existing limitations (such as a reduced subset of inflammatory interactions, the use of mass action kinetics, and calibration to circulating but not local levels of cytokines), the model can at this time simulate certain disease scenarios qualitatively as well as predicting the time course of cytokine levels in distinct paradigms of inflammation in mice. A parameter search algorithm is developed that aids in the identification of different regimes of behaviour of the model and helps with its calibration to data. Extending this mathematical model, with validation in humans, may lead to the in silico development of novel therapeutic approaches and real-time diagnostics.

Kevin Coakley, National Institute of Standards and Technology, ``A Classification Problem in Neutrino Physics'' Abs: In CLEAN (Cryogenic Low Energy Astrophysics with Noble gases), a proposed neutrino and dark matter detector, low energy neutrinos would be detected based on scintillation light produced by neutrino-electron and neutrino-nucleus scattering in a spherical detection volume filled with liquid neon. On average, the number of scintillation photons produced by a neutrino event would be proportional to the energy deposited by the neutrino. The scintillation photons Rayleigh scatter as they propagate in the neon. Thus, the scintillation photons do not travel in straight line trajectories. Further, each scintillation photon is shifted to lower wavelength and diffusely re-emitted by the detectors before ultimate detection. Due to the radioactive decay of materials at the outer spherical wall of the detection region, unwanted gamma rays are produced. As these gamma rays propagate inward, they would be attenuated. However, due to energy deposited by either Compton scattering or photoelectric absorption, gamma rays would produce scintillation light. Since background events are orders of magnitude more numerous than events of interest, statistical methods for background discrimination are essential for enabling this measurement system. We define an inner spherical fiducial volume that occupies a fraction $p$ of the total spherical detection volume. By design, the probability that a background event occurs within the fiducial volume is low. In contrast, events of interest occur uniformly throughout the entire detection volume. We assign events into one of two classes. The first class consists of events which occur within the fiducial volume. The second class consists of events which occur outside the fiducial volume. The rate at which we assign background events to the first class is the background rate. We develop classification rules based on the estimated radial location of an event computed from the spatial pattern of detected scintillation photons. One rule is based on the approximate maximum likelihood estimate of event location. The other is based on the centroid of the detected scintillation photons. We calibrate the classification rules so that the probability of assigning an event of interest to the first class is $p$. We quantify the relative performance of the two rules by estimating their associated background rates. (This talk is based on collaborative work with D. N. McKinsey of Yale University.)

Brieuc Connan-Guez, INRIA-Rocquencourt, and Frabrice Rossi, University of Paris IX-Dauphine, ``Phoneme Discrimination with Functional Multi-Layer Perceptrons'' Abs: In many situations, high dimensional data can be considered as sampled functions. We recall in this paper how to implement a Multi-Layer Perceptron (MLP) on such data by approximating a theoretical MLP on functions thanks to basis expansion. We illustrate the proposed method on a phoneme discrimination problem.

Gregory Constantine, University of Pittsburgh, ``A Multidimensional Parameter Estimation Algorithm Based on Optimal Linear Codes'' Abs: Systems of Ordinary Differential Equations (ODE) yield qualitatively different behaviour of the response function as the input parameters change. In medical applications, such as attempting to describe the reaction of the immune system to accute illness, understanding the different regimes of a response as a function of the parameter space underlying the ODE system is of central concern. An optimization search algorithm based on optimal linear codes is developed to explore and partition a multi-dimensional parameter space into classes that yield essentially different regimes of the response function. The algorithm searches disjoint regions of the parameter space in accordance with the words of a code and certain select cosets associated to these regions. Depth searches are conducted in appropriately small subregions near bifurcation points, by iteratively calling the same algorithm within such subregions.

Raphaël Couturier, LIFC-IUT Belfort-Montbéliard, Régis Gras, and F. Guillet, École Polytechnique de l'Université de Nantes, ``Reducing the Number of Variables Using Implicative Analysis'' Abs: The interpretation of complex data with data mining techniques is often a difficult task. Nevertheless, this task may be simplified by reducing the variables which could be considered as equivalent. The aim of this paper is to describe a new method for reducing the number of variables in a large set of data. Implicative analysis, which builds association rules with a measure more powerful than conditional probability, is used to detect quasi-equivalent variables. This technique has some advantages over traditional similarity analysis.

Di Cook, Iowa State University, ``Visualizing Class and Cluster Structure beyond 3D'' Abs: This talk will describe methods to look at cluster structure in high-dimensional data relative to class labels. We will examine plots of the data in relation to results from numerical classifiers such as random forests, support vector machines and neural networks. The reason to use graphics, in the spirit of exploratory data analysis, seeks to develop a conceptual image and understanding of the process generating our data. Much of the research being done on methods for supervised classification dwells on predictive accuracy, which although good and worthwhile is just a small part of a data analysis. Ideally we come away from a data analysis with a story about a real problem, and answers to pertinent questions, with a little more understanding for our physical world. This is what this talk addresses.

Marc Csernel, INRIA, Francisco de A. T. Carvalho, Universidade Federal de Pernambuco, and Yves Lechevallier, INRIA, ``Partitioning of Constrained Symbolic Data'' Abs: Instead of containing a single value, each cell of a Symbolic table can contain a set of values. Each row of this table contains a symbolic description. Such a table can be constrained by domain knowledge, expressed by rules, in a way similar to integrity constraints in a database. We present a method to obtain a partition of the set of symbolic description described in a table, into a fixed number of homogenous classes, on the bases of a dissimilarity table. The partitioning algorithm minimizes a criterion, which is based on the sum of dissimilarities between the description belonging to the same cluster. As comparison of couples of constrained symbolic descriptions induces usually an exponential growing of computation times, a pre-processing step, where symbolic descriptions are put on the Normal Symbolic Form, is necessary in order to keep computation time polynomial. The Normal Symbolic Form (NSF) is a decomposition of symbolic description in such a way that only coherent descriptions (i.e., which do not contradict the rules) are represented. An example derived from biology is presented.

Guy Cucumel, Université du Québec à Montréal, ``Average Consensus and $L_{\infty}$-consensus: Comparison of Two Consensus Methods for Ultrametric Trees'' Abs: Consensus methods are widely used to combine hierarchies defined on a common set of n objects (Leclerc, 1998). Given a profile P = (T1, , Ti, , Tk) of k ultrametric trees, the average consensus (Lapointe and Cucumel, 1997) allows to obtain a consensus solution that is representative of the entire profile P by minimizing the sum of squared distances between the initial profile and the consensus (L2-consensus). As this problem is NP-complete, when the data set is large, one has to use heuristics to resolve it. As a result, the uniqueness and optimality of the solution is not certain. Moreover, the convergence toward a solution is sometimes difficult. Chepoi and Fichet (2000) have developed an algorithm that yields to a universal L8-consensus in a maximum of n2 steps. The two methods will be presented and compared on some numerical examples.

Ana Lorga da Silva, Universidade Lusofona de Humanidades e Tecnologias, G. Saporta, CNAM, and H. Bacelar-Nicolau, University of Lisbon, ``Missing Data and Imputation Methods in Partition of Variables'' Abs: We deal with the effect of missing data under a ``Missing at Random Model'' on classification of variables with non-hierarchical methods. The partitions are compared by the Rand index.

Francisco de A. T. Carvalho, Universidade Federal de Pernambuco, Yves Lechevallier, INRIA-Rocquencourt, Renata M. C. R. de Souza, Cidade Universitaria-Brazil, ``A Dynamic Clustering Algorithm Based on $L_r$-Distances for Quantitative Data'' Abs: Dynamic clustering methods aim to obtain both a single partition of the input data into a fixed number of clusters and the identification of a suitable representation of each cluster simultaneously. In its adaptive version, at each iteration of these algorithms there is a different distance for the comparison of each cluster with its representation. In this paper, we present a dynamic cluster method based on $L_r$ distances for quantitative data.

Stefano De Cantis and Antonino Oliveri, University of Palermo, ``An Overview of Collapsibility'' Abs: Collapsing over variables is a necessary procedure in much empirical research. Consequences are yet not always properly evaluated. In this paper, different definitions of collapsibility (simple, strict, strong, etc.) and corresponding necessary and sufficient conditions are reviewed and evaluated. We point out the relevance and limitations of the main contributions within a unifying interpretative framework. We deem such work to be useful since the debate on the topic has often developed in terms that are neither focused nor clear.

Sérgio R. de M. Queiroz and Francisco A. T. de Carvalho, Universidade Federal de Pernambuco, ``A Symbolic Model-Based Approach for Making Collaborative Group Recommendations'' Abs: In recent years, recommender systems have achieved great success. Popular sites give thousands of recommendations every day. However, despite the fact that many activities are carried out in groups, like going to the theater with friends, these systems are focused on recommending items for sole users. This brings out the need for systems capable of performing recommendations for groups of people, a domain that has received little attention in the literature. In this article we introduce a novel method of making collaborative recommendations for groups, based on models built using techniques from symbolic data analysis. Finally, we empirically evaluate the proposed method to see its behaviour for groups of different sizes and degrees of homogeneity, and compare the achieved results with a baseline methodology.

Mark de Rooij, Leiden University, ``Scaling the Odds'' Abs: The odds ratio is the main measure of association for contingency tables. In the present paper a scaling of a basic set of odds ratios is proposed through the singular value decomposition. Properties valid for the relation between a basic set of odds ratios and all odds ratios translate nicely into properties of the singular vectors. Some simple structures are discussed that might be used for diagnostic plotting. Estimates for the standard errors and the bias are obtained using a jackknife procedure. Key words: (log) odds ratio; inner product; singular value decomposition.

Renata M. C. R. de Souza, Cidade Universitaria-Brazil, Francisco A. T. de Carvalho, Universidade Federal de Pernambuco, Camilo P. Tenório, and Yves Lechevallier, INRIA-Rocquencourt, ``Dynamic Clustering Methods for Interval Data Based on Mahalanobis Distances'' Abs: Dynamic cluster methods for interval data are presented. Two methods are considered: the first method furnishes a partition of the input data and a corresponding prototype (a vector of intervals) for each class by optimizing an adequacy criterion which is based on Mahalanobis distances between vectors of intervals. The second is an adaptive version of the first method. Experimental results with artificial interval-valued data sets show the usefulness of these methods. In general, the adaptive method outperforms the non-adaptive one in terms of the quality of the clusters which are produced by the algorithms.

Reinhold Decker, University of Bielefeld ``Self-Controlled Growing Neural Networks and Their Application to Pattern Representation in Data Analysis'' Abs: This presentation introduces a new growing neural network approach for data analysis. The algorithm is similar to the one suggested by Marsland et al. (2002) and Decker, Monien (2003) concerning its structural design and it bears certain analogies with the growing neural gas network introduced by Fritzke (1995). However, the algorithm on hand is more parsimonious regarding the number of parameters to be specified a priori, which increases its autonomy with respect to the insertion of new units or rather weight vectors during the adaptation process. To demonstrate its performance and flexibility the new algorithm will be applied to synthetical 2D data with a distinct heterogeneity with regard to the arrangement of the individual data points as well as to real point of sale scanner data provided by a German supermarket chain.

Markus Demleitner, $\,$ University of Heidelberg, Michael Kurtz, Harvard University, et al., ``Automated Resolution of Noisy Bibliographic References'' Abs: We describe a system used by the NASA Astrophysics Data System to identify bibliographic references obtained from scanned article pages by OCR methods with records in a bibliographic database. We analyze the process generating the noisy references and conclude that the three-step procedure of correcting the OCR results, parsing the corrected string and matching it against the database provides unsatisfactory results. Instead, we propose a method that allows a controlled merging of correction, parsing and matching, inspired by dependency grammars. We also report on the effectiveness of various heuristics that we have employed to improve recall.

José G. Dias, Instituto Superior de Ciências do Trabalho e da Empresa, ``Controlling the Level of Separation of Components in Monte Carlo Studies of Latent Class Models'' Abs: The paper proposes a new method to control the level of separation of components using a single parameter. An illustration for the latent class model (mixture of conditionally independent multinomial distributions) is provided. Further extensions to other finite mixture models are discussed.

Edwin Diday, University of Paris IX-Dauphine, ``Introduction to Spatial Classification'' Abs: Indexed hierarchies and indexed clustering pyramids are based on an underlying order for which each cluster is connected. In this paper our aim is to extend standard pyramids and their underlying one-to-one correspondence with Robinsonian dissimilarities to spatial pyramids where each cluster is ``compatible'' with a spatial network given by a kind of tessellation called ``m/k-network''. We focus on convex spatial pyramids and we show that they are in one-to-one correspondence with a new kind of dissimilarities. We give a building algorithm for convex spatial pyramids illustrated by an example. We show that spatial pyramids can converge towards geometrical pyramids. We indicate finally that spatial pyramids can give better results than Kohonen mappings and can produce a geometrical representation of conceptual lattices.

Arta Doci and Peter Bryant, University of Colorado at Denver, ``An MDL Criterion for k-Means Clustering'' Abs: In this presentation, we examine the use of a criterion based on the Minimum Description Length (MDL) Principle to evaluate the results of a k-means clustering procedure, in particular to select the appropriate number of clusters. We present the criterion and give results from the analysis of a number of data sets, and suggest some possible further avenues for future development.

Pedro Domingos, University of Washington, ``A General Framework for Mining Massive Data Streams'' Abs: In many domains, data now arrives faster than we are able to mine it. To avoid wasting this data, we must switch from the traditional "one-shot" data mining approach to systems that are able to mine continuous, high-volume, open-ended data streams as they arrive. In this talk I will identify some desiderata for such systems, and outline our framework for realizing them. A key property of our approach is that it minimizes the time required to build a model on a stream, while guaranteeing (as long as the data is i.i.d.) that the model learned is effectively indistinguishable from the one that would be obtained using infinite data. Using this framework, we have successfully adapted several learning algorithms to massive data streams, including decision tree induction, Bayesian network learning, k-means clustering, and the EM algorithm for mixtures of Gaussians. These algorithms are able to process on the order of billions of examples per day using off-the-shelf hardware. Building on this, we are currently developing software primitives for scaling arbitrary learning algorithms to massive data streams with minimal effort.

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