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Seminario
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DOTTORATO DI RICERCA IN STATISTICA COMPUTAZIONALE
DIPARTIMENTO DI MATEMATICA E STATISTICA
UNIVERSITA' di NAPOLI - FEDERICO II
AVVISO DI SEMINARIO
LUOGO Dipartimento di Matematica e Statistica, via Cinhia Monte S.Angelo
DATA Venerdì 29 settembre ore 10
RELATORE Jacqueline J. Meulman, University of Leiden
TITOLO Some new approaches in multivariate categorical data analysis
ABSTRACT:
In this seminar we will discuss various approaches to the analysis of
multivariate categorical data. The first is a form of principal components
analysis combined with multiple correspondence analysis: in addition to the
fitting of points for individual subjects, additional points may be fitted
for groups among the subjects. There is a large emphasis on graphical
display of the results in biplots (with variables and subjects) and
triplots (with variables, subjects, and groups). The information contained
in the biplots and triplots is used to draw special graphs that identify
particular groups in the data that standout on selected variables. The
approach can also be used for data mining, and will be applied to a data
set for a large number of European countries with respect to a variety of
nonmetric variables.
The second is an extension of correspondence analysis to include the
representation of three-way data through an individual differences model,
adapted from multidimensional scaling. A particular application will be the
analysis of a longitudinal series of contingency matrices pertaining to
various infections occurring during different seasons, with infection rates
measured over a nine-year period.
Finally, we will discuss a new approach to unidimensional scaling in
multivariate data. Here we have to deal with a combinatorial optimization
problem. The result is an optimal ordering of objects while the original
data have been transformed by monotonic spline functions. A real life data
example will demonstrate the technique to a consensus ordering of birth
control methods according to four different groups of reviewers scoring the
methods on four different criteria.
Keywords: Optimal Scaling, Correspondence Analysis, Principal Components,
Biplot, Triplot, Categorical Data, Ordinal Data, Longitudinal Data,
Multidimensional Scaling, Three-way Models, Unidimensional Scaling.
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LUOGO Dipartimento di Matematica e Statistica, via Cinhia Monte S.Angelo
DATA Venerdì 29 settembre ore 12
RELATORE Jean-Jacques Denimal, Université de Lille
TITOLO A New Method Combining Factor Analysis and Classification
for Easier Interpretations in Table Analysis
ABSTRACT:
The analysis of a data table is usually performed through a four-step
procedure:
1)Factor Analysis of the table,
2)Hierarchical Classifications of both rows and columns,
3)Interpretation of classifications,
4)Study of the relations between factorial axes and hierarchies nodes.
Even if the dimensions of the table are not too large, both study and
synthesis of the results given by the four stages generally represent
long-lasting work for the user. In order to ease it, a new method is
proposed, combining steps one and two, and making easier the interpretation
of both factorial axes and clusters. The method may be presented as a new
hierarchical classification of variables, whose nodes are obtained and
interpreted from particular Principal Component Analyses. By construction,
each analysis provides only two factorial axes, the first describing what
is common to the two clusters, merging at the considered node, and the
second one showing what is different among them. Therefore, the
interpretation of each node can be easily done from the inspection of his
associated factorial plane.
As this method belongs to the set of techniques dealing with factorial
representations associated to hierarchies, comparisons will be proposed
with usual techniques. Finally, as the method can be used with both
ordinary tables, crossing objects and variables, and contingency tables
(with some adjustments), some applications to tables of both types will be
given.
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LUOGO Dipartimento di Matematica e Statistica, via Cinhia Monte S.Angelo
DATA Lunedì 10 ottobre ore 11
RELATORE Javier Trejos, University of Costarica
TITOLO: Clustering Binary Data Using Combinatorial Optimitation Techniques
Abstract:
We study theoretical and practical Properties of seven generalised
criterion indexes especially designed for clustering binary data:
Single linkage; Complete linkage; Sum of dissimilarities;
Average of the dissimilarities; Variance of dissimilarities;
Weighted sum of dissimilarities and the L1 aggregation index.
Among theoretical properties, we study monotonicity, the empty classes,
Huygens-like decomposition and updating and downdating formulas after
transformation objects.
We implement these aggregation indexes using global combinatorial
optimisation techniques, such as simulated annealing and tabosearch,
achieving excellent results on well known and fictions binary data sets,
compared to the results obtained by traditional cluster analysis
methods of partitioning.
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Prof. Carlo Lauro
Dipartimento di Matematica e Statistica
Universita' degli Studi di Napoli "Federico II"
Via Cintia - Complesso Monte Sant'Angelo
I-80126 Napoli
tel.: +39 081 675189 fax: +39 081 675113
e-mail: carlo.lauro@unina.it
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