Matrices that can be factored into a product of two simpler matricescan serve as a useful and often natural model in the analysis oftabulated or high-dimensional data. Models based on matrixfactorization (Factor Analysis, PCA) have been extensively used instatistical analysis and machine learning for over a century, withmany new formulations and models suggested in recent years (LatentSemantic Indexing, Aspect Models, Probabilistic PCA, Exponential PCA,Non-Negative Matrix Factorization and others). In this thesis weaddress several issues related to learning with matrix factorizations:we study the asymptotic behavior and generalization ability ofexisting methods, suggest new optimization methods, and present anovel maximum-margin high-dimensional matrix factorizationformulation.
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/30507 |
| Date | 22 November 2004 |
| Creators | Srebro, Nathan |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Format | 132 p., 96239481 bytes, 5561927 bytes, application/postscript, application/pdf |
| Relation | Massachusetts Institute of Technology Computer Science and Artificial Intelligence Laboratory |
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