Multiplicative Updates for Nonnegative Quadratic Programming
Many problems in neural computation and statistical learning involve optimizations with nonnegativity constraints. In this article, we study convex problems in quadratic programming where the optimization is confined to an axis-aligned region in the nonnegative orthant. For these problems, we derive...
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| Veröffentlicht in: | Neural computation 2007-08, Vol.19 (8), p.2004-2031 |
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| container_title | Neural computation |
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| creator | Sha, Fei Lin, Yuanqing Saul, Lawrence K. Lee, Daniel D. |
| description | Many problems in neural computation and statistical learning involve optimizations with nonnegativity constraints. In this article, we study convex problems in quadratic programming where the optimization is confined to an axis-aligned region in the nonnegative orthant. For these problems, we derive multiplicative updates that improve the value of the objective function at each iteration and converge monotonically to the global minimum. The updates have a simple closed form and do not involve any heuristics or free parameters that must be tuned to ensure convergence. Despite their simplicity, they differ strikingly in form from other multiplicative updates used in machine learning. We provide complete proofs of convergence for these updates and describe their application to problems in signal processing and pattern recognition. |
| doi_str_mv | 10.1162/neco.2007.19.8.2004 |
| format | Article |
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In this article, we study convex problems in quadratic programming where the optimization is confined to an axis-aligned region in the nonnegative orthant. For these problems, we derive multiplicative updates that improve the value of the objective function at each iteration and converge monotonically to the global minimum. The updates have a simple closed form and do not involve any heuristics or free parameters that must be tuned to ensure convergence. Despite their simplicity, they differ strikingly in form from other multiplicative updates used in machine learning. 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| subjects | Algorithms Animals Applied sciences Artificial intelligence Biological and medical sciences Calculus of variations and optimal control Computer programming Computer science control theory systems Exact sciences and technology Fundamental and applied biological sciences. Psychology General aspects Heuristic Humans Information Storage and Retrieval - methods Learning and adaptive systems Mathematical analysis Mathematics Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects) Miscellaneous Neural Networks (Computer) Optimization Programming, Linear Sciences and techniques of general use Signal Processing, Computer-Assisted |
| title | Multiplicative Updates for Nonnegative Quadratic Programming |
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