Structural Classification Analysis of Three-Way Dissimilarity Data

The paper presents a methodology for classifying three-way dissimilarity data, which are reconstructed by a small number of consensus classifications of the objects each defined by a sum of two order constrained distance matrices, so as to identify both a partition and an indexed hierarchy. Specific...

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Bibliographic Details
Published in:Journal of classification Vol. 26; no. 2; pp. 121 - 154
Main Authors: Vicari, Donatella, Vichi, Maurizio
Format: Journal Article
Language:English
Published: New York Springer-Verlag 01.08.2009
Springer
Springer Nature B.V
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Automatic classification
Automatic text analysis
Bioinformatics
Classification
Computer science; control theory; systems
Exact sciences and technology
Hierarchies
Logic and foundations
Marketing
Mathematical analysis
Mathematical logic, foundations, set theory
Mathematics
Mathematics and Statistics
Matrices
Methods of scientific computing (including symbolic computation, algebraic computation)
Multivariate analysis
Numerical analysis. Scientific computation
Partition
Pattern Recognition
Probability and statistics
Psychometrics
Recursion theory
Sciences and techniques of general use
Signal,Image and Speech Processing
Simulation
Statistical Theory and Methods
Statistics
Studies
Theoretical computing
Hierarchy
Partition
Dissimilarity
Three-Way data
Classification
Discriminant analysis
Data analysis
Multivariate analysis
Algorithm
Integer
Algorithm performance
Simulation
Least squares method
Three way analysis of variance
Mixed problem
Structural analysis
ISSN:0176-4268, 1432-1343
Online Access:Get full text
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Description
Summary:The paper presents a methodology for classifying three-way dissimilarity data, which are reconstructed by a small number of consensus classifications of the objects each defined by a sum of two order constrained distance matrices, so as to identify both a partition and an indexed hierarchy. Specifically, the dissimilarity matrices are partitioned in homogeneous classes and, within each class, a partition and an indexed hierarchy are simultaneously fitted. The model proposed is mathematically formalized as a constrained mixed-integer quadratic problem to be fitted in the least-squares sense and an alternating least-squares algorithm is proposed which is computationally efficient. Two applications of the methodology are also described together with an extensive simulation to investigate the performance of the algorithm.
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ISSN:0176-4268
1432-1343
DOI:10.1007/s00357-009-9033-0