With the advent of computers, very large datasets have become
routine. Standard statistical methods don’t have the power or
flexibility to analyse these efficiently, and extract the required
knowledge. An alternative approach is to summarize a large dataset
in such a way that the resulting summary dataset is of a manageable
size and yet retains as much of the knowledge in the original
dataset as possible. One consequence of this is that the data may
no longer be formatted as single values, but be represented by
lists, intervals, distributions, etc. The summarized data have
their own internal structure, which must be taken into account in
any analysis.
This text presents a unified account of symbolic data, how they
arise, and how they are structured. The reader is introduced to
symbolic analytic methods described in the consistent statistical
framework required to carry out such a summary and subsequent
analysis.
* Presents a detailed overview of the methods and applications of
symbolic data analysis.
* Includes numerous real examples, taken from a variety of
application areas, ranging from health and social sciences, to
economics and computing.
* Features exercises at the end of each chapter, enabling the
reader to develop their understanding of the theory.
* Provides a supplementary website featuring links to download
the SODAS software developed exclusively for symbolic data
analysis, data sets, and further material.
Primarily aimed at statisticians and data analysts, Symbolic
Data Analysis is also ideal for scientists working on problems
involving large volumes of data from a range of disciplines,
including computer science, health and the social sciences. There
is also much of use to graduate students of statistical data
analysis courses.
Table des matières
1. Introduction.
References.
2. Symbolic Data.
2.1 Symbolic and Classical Data.
2.2 Categories, Concepts and Symbolic Objects.
2.3 Comparison of Symbolic and Classical Analysis.
3. Basic Descriptive Statistics: One Variate.
3.1 Some Preliminaries.
3.2 Multi-valued Variables.
3.3 Interval-valued Variables.
3.4 Multi-valued Modal variables.
3.5 Interval-valued Modal Variables.
4. Descriptive Statistics: Two or More Variates.
4.1 Multi-valued Variables.
4.2 Interval-valued Variables.
4.3 Modal Multi-valued Variables.
4.4 Modal Interval-valued Variables.
4.5 Baseball Interval-valued Dataset.
4.6 Measures of Dependence.
5. Principal Component Analysis.
5.1 Vertices Method.
5.2 Centers Method.
5.3 Comparison of the Methods.
6. Regression Analysis.
6.1 Classical Multiple Regression Model.
6.2 Multi-valued Variables.
6.3 Interval-valued Variables.
6.4 Histogram-valued Variables.
6.5 Taxonomy Variables.
6.6 Hierarchical Variables.
7. Cluster Analysis.
7.1 Dissimilarity and Distance Measures.
7.2 Clustering Structures.
7.3 Partitions.
7.4 Hierarchy-Divisive Clustering.
7.5 Hierarchy-Pyramid Clusters.
Data Index.
Author Index.
Subject Index.
A propos de l’auteur
Lynne Billard is a multi award winning University Professor of Statistics at the University of Georgia, USA. Her areas of interest include epidemic theory, AIDS, time series, sequential analysis, and symbolic data. A former President of the American Statistical Association as well as the ENAR Regional President and International President of the International Biometric Society, Professor Billard has co-edited 6 books, published over150 papers and been actively involved in many statistical societies and national committees.
Edwin Diday is a Professor in Computer Science and Mathematics, at the Université Paris Dauphine, France. He is the author or editor of 14 previous books. He is also the founder of the symbolic data analysis field, and has led numerous international research teams in the area.
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