Skillicorn D. Understanding complex datasets: data mining with matrix decompositions

Chapman & Hall/CRC – 2007, 257 p.
ISBN: 1584888326, 9781584888321Making obscure knowledge about matrix decompositions widely available, Understanding Complex Datasets: Data Mining with Matrix Decompositions discusses the most common matrix decompositions and shows how they can be used to analyze large datasets in a broad range of application areas. Without having to understand every mathematical detail, the book helps you determine which matrix is appropriate for your dataset and what the results mean.
Explaining the effectiveness of matrices as data analysis tools, the book illustrates the ability of matrix decompositions to provide more powerful analyses and to produce cleaner data than more mainstream techniques. The author explores the deep connections between matrix decompositions and structures within graphs, relating the PageRank algorithm of Google's search engine to singular value decomposition. He also covers dimensionality reduction, collaborative filtering, clustering, and spectral analysis. With numerous figures and examples, the book shows how matrix decompositions can be used to find documents on the Internet, look for deeply buried mineral deposits without drilling, explore the structure of proteins, detect suspicious emails or cell phone calls, and more.
Concentrating on data mining mechanics and applications, this resource helps you model large, complex datasets and investigate connections between standard data mining techniques and matrix decompositions.Data Mining
What Is Data Like?
Data Mining Techniques
Why Use Matrix Decompositions?
Matrix Decompositions
Definition
Interpreting Decompositions
Applying Decompositions
Algorithm Issues
Singular Value Decomposition (SVD)
Definition
Interpreting an SVD
Applying SVD
Algorithm Issues
Applications of SVD
Extensions
Graph Analysis
Graphs versus Datasets
Adjacency Matrix
Eigenvalues and Eigenvectors
Connections to SVD
Google's PageRank
Overview of the Embedding Process
Datasets versus Graphs
Eigendecompositions
Clustering
Edge Prediction
Graph Substructures
The ATHENS System for Novel Knowledge Discovery
Bipartite Graphs
Semidiscrete Decomposition (SDD)
Definition
Interpreting an SDD
Applying an SDD
Algorithm Issues
Extensions
Using SVD and SDD Together
SVD Then SDD
Applications of SVD and SDD Together
Independent Component Analysis (ICA)
Definition
Interpreting an ICA
Applying an ICA
Algorithm Issues
Applications of ICA
Non-Negative Matrix Factorization (NNMF)
Definition
Interpreting an NNMF
Applying an NNMF
Algorithm Issues
Applications of NNMF
Tensors
The Tucker3 Tensor Decomposition
The CP Decomposition
Applications of Tensor Decompositions
Algorithmic IssuesAppendix: MatLAB Scripts