The singular value decomposition (SVD) is fundamental to many data modeling/mining algorithms, but SVD algorithms typically have quadratic complexity and require random access to complete data sets. This is problematic in most data mining settings. We detail a family of sequential update rules for adding data to a "thin" SVD data model, revising or removing data already incorporated into the model, and adjusting the model when the data-generating process exhibits nonstationarity. We also leverage the SVD to estimate the most probable completion of incomplete data. We use these methods to model data streams describing tables of consumer/product ratings, where fragments of rows and columns arrive in random order and individual table entries are arbitrarily added, revised, or retracted at any time. These purely online rules have very low time complexity and require a data stream cache no larger than a single user's ratings. We demonstrate this scheme in an interactive graphical movie recommender that predicts and displays ratings/rankings of thousands of movie titles in real-time as a user adjusts ratings of a small arbitrary set of probe movies. The system "learns" as it is used by revising the SVD in response to user ratings. Users can asynchronously join, add ratings, add movies, revise ratings, get recommendations, and delete themselves from the model. This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Information Technology Center America; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Information Technology Center America. All rights reserved.  Matthew Brand * The singular value decomposition (SVD) is fundamental to many data modeling/mining algorithms, but SVD algorithms typically have quadratic complexity and require random access to complete data sets. This is problematic in most data mining settings. We detail a family of sequential update rules for adding data to a "thin" SVD data model, revising or removing data already incorporated into the model, and adjusting the model when the data-generating process exhibits nonstationarity. We also leverage the SVD to estimate the most probable completion of incomplete data. We use these methods to model data streams describing tables of consumer×product ratings, where fragments of rows and columns arrive in random order and individual table entries are arbitrarily added, revised, or retracted at any time. These purely online rules have very low time complexity and require a data stream cache no larger than a single user's ratings. We demonstrate this scheme in an interactive graphical movie recommender that predicts and displays ratings/rankings of thousands of movie titles in real-time as a user adjusts ratings of a small arbitrary set of probe movies. The system "learns" as it is used by revising the SVD in response to user ratings. Users can asynchronously join, add ratings, add movies, revise ratings, get recommendations, and delete themselves from the model.
In REF , Brand proposed update rules for adding data to a "thin" SVD data model, which is used to update new data into the lightweight recommender systems.
Fast Online SVD Revisions for Lightweight Recommender Systems
SDM
Computer Science