Externally indexed torrent

If you are the original uploader, contact staff to have it moved to your account

Textbook in PDF format

This monograph offers an original broad and very diverse exploration of the seriation domain in data analysis, together with building a specific relation to clustering.
Relative to a data table crossing a set of objects and a set of descriptive attributes, the search for orders which correspond respectively to these two sets is formalized mathematically and statistically.
State-of-the-art methods are created and compared with classical methods and a thorough understanding of the mutual relationships between these methods is clearly expressed. The authors distinguish two families of methods:
Geometric representation methodsAlgorithmic and Combinatorial methods
Original and accurate methods are provided in the framework for both families. Their basis and comparison is made on both theoretical and experimental levels. The experimental analysis is very varied and very comprehensive. Seriation in Combinatorial and Statistical Data Analysis has a unique character in the literature falling within the fields of Data Analysis, Data Mining and Knowledge Discovery. It will be a valuable resource for students and researchers in the latter fields.
Acknowledgements
General Introduction: Methods and History
Seriation from Proximity Variance Analysis
Definition of a Seriation Its Unicity
Definition of a σ Form
Unicity
Association Coefficient Between Columns of a σ Seriation Form
Preamble
The Association Coefficient
Equation of the Association Coefficient in the Case of a σ Form
Representation on a Directed Unit Line Segment
Simultaneous Mean and Variance Analysis of Pairwise Proximities
Preamble
Optimal Properties of an Extreme Point of Rectilinear Cloud
Discovering from an Optimal Property, a σ Form
Block Seriation from Simultaneous Mean and Variance Analysis of Pairwise Proximities The ``Attraction Poles'' Method
Proximity Variance Analysis Equation
Geometrical Representation by the Attraction Poles Method
Main Approaches in Seriation: The Attraction Pole Case
Visual and Combinatorial Methods
Graphical Methods of J Bertin
Block Seriation Method of F Marchotorchino
Methodological Developments
Elisséeff Heuristic
The Deutsch and Martin Algorithm
The Niermann Algorithm
Seriation Defined as a Combinatorial Optimization Problem
Preamble
General Facets
A Criterion for Evaluating the Seriation
Usual Criteria for Evaluating a Seriation
Spectral Approaches
Some Methodological Points and Extensions
Methods Using a Planar Geometrical Representation
Introduction: The Most Classical Methods
The Horse-Shoe Method of Kendall
Combinatorial and Algorithmic Approaches of the Pole Attraction Method
Comparing Geometrical and Ordinal Seriation Methods in Formal and Real Cases
Methods
Similarities and Distances
Multidimensional Data Analysis
Techniques and Algorithms
Results in Processing Data
Preamble
Simulated Data According to σ Forms Models
Real Data
Some Concluding Remarks
A New Family of Combinatorial Algorithms in Seriation
Introduction: The Fundamental Principles
Row Data Table Ranking Associated with a Column Ordering in Seriation
The Combinatorial Algorithm
The Statistical Algorithm
Seriation Algorithms
The Seriation Search Space Is Associated with the First Element
The Seriation Search Space Is Associated with Sized Sequences of Elements
Applying on σ Forms and Real Data
Preamble
Simulated σ Forms
Real Data
Clustering Methods from Proximity Variance Analysis
Introduction and General Presentation
The Method Family of Attraction Poles by Successive Reallocations (APMSR)
Data, Similarities and Distances
Determination of a System of Attraction Poles
Cluster Formation Around the Attraction Poles
Assignment Criteria
Criteria and Algorithmic of the Attraction Pole Methods by Successive Aggregations (APMSA)
Criteria for APMSA
On the Number of Poles to Extract and on the Quality of the Clusterings Obtained
The Fitting Criterion
Inertia or Ward Criterion
Interesting Partitions from APMSR and from APMSA
Developments
Applying Clustering Attraction Pole Methods in Real Data
Ruspini Data
Fisher Data
Merovingian Belt Buckles-Plates Data
Some Words to Conclude
Conclusion and Developments
The Algorithms and Their Respective Logics
Geometric Representations of the Descriptive Attributes and the Objects Described
Row Seriation from Column Seriation
Algorithms by Successive Chaining
Attraction Pole Clustering Algorithms
Structures and Algorithms in Asymmetrical Hierarchical Clustering
Directed Ascendant Hierarchical Clustering
Oriented Hierarchical Clustering
Hierarchical Clustering of Successive Intervals
Some Additional Interactions Between Seriation and Hierarchical Clustering
Appendix A Index