Bilateral random projections
Bilateral random projections
Low-rank structure have been profoundly studied in data mining and machine learning. In this paper, we show a dense matrix $X$'s low-rank approximation can be rapidly built from its left and right random projections $Y_1=XA_1$ and $Y_2=X^TA_2$, or bilateral random projection (BRP). We then show power scheme can further improve the precision. The deterministic, average and deviation bounds of the proposed method and its power scheme modification are proved theoretically. The effectiveness and the efficiency of BRP based low-rank approximation is empirically verified on both artificial and real datasets.
17 pages, 3 figures, technical report
- University of Technology Sydney Australia
- University of Technology Russian Federation
FOS: Computer and information sciences, Statistics - Machine Learning, Computer Science - Data Structures and Algorithms, Machine Learning (stat.ML), Data Structures and Algorithms (cs.DS)
FOS: Computer and information sciences, Statistics - Machine Learning, Computer Science - Data Structures and Algorithms, Machine Learning (stat.ML), Data Structures and Algorithms (cs.DS)
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