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Activity Number:
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445
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Type:
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Contributed
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Date/Time:
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Wednesday, August 6, 2008 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Statistical Computing
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| Abstract - #301818 |
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Title:
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Principal Component Analysis and Subspace Detection Under Random Projection
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Author(s):
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Qi Ding*+ and Eric Kolaczyk+
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Companies:
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Boston University and Boston University
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Address:
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111 Cummington Street, Boston, MA, 02215, Department of Mathematics and Statistics, Boston, MA, ,
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Keywords:
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Random matrix theory ; Principal component analysis ; Eigenvalue distribution ; Spiked covariance model ; Johnson-Lindenstrauss Theorem
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Abstract:
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Random projection is widely used as a method of dimension reduction. In recent years, its combination with standard techniques of regression and classification has been explored. Here we examine its use with principal component analysis (PCA) and subspace detection methods. Specifically, we show that, under appropriate conditions, with high probability the magnitude of the residuals of a PCA analysis of randomly projected data behaves nearly the same as that of the residuals of a similar PCA analysis of the original data. Our results indicate the feasibility of applying subspace-based anomaly detection algorithms to randomly projected data, when the data have a covariance of an appropriately compressed nature. We illustrate in the context of computer network traffic anomaly detection.
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- The address information is for the authors that have a + after their name.
- Authors who are presenting talks have a * after their name.
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