Understanding Complex Datasets: Data Mining with Matrix Decompositions
David B. Skillicorn · 2007
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 Issues CONCLUSION APPENDIX: MATLAB SCRIPTS BIBLIOGRAPHY INDEX