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ICONIP
2007

Principal Component Analysis for Sparse High-Dimensional Data

10 years 1 months ago
Principal Component Analysis for Sparse High-Dimensional Data
Abstract. Principal component analysis (PCA) is a widely used technique for data analysis and dimensionality reduction. Eigenvalue decomposition is the standard algorithm for solving PCA, but a number of other algorithms have been proposed. For instance, the EM algorithm is much more efficient in case of high dimensionality and a small number of principal components. We study a case where the data are high-dimensional and a majority of the values are missing. In this case, both of these algorithms prove inadequate. We propose using a gradient descent algorithm inspired by Oja’s rule, and speeding it up by an approximate Newton’s method. The computational complexity of the proposed method is linear to the number of observed values in the data and to the number of principal components. The experiments with Netflix data confirm that the proposed algorithm is about ten times faster than any of the four comparison methods.
Tapani Raiko, Alexander Ilin, Juha Karhunen
Added 29 Oct 2010
Updated 29 Oct 2010
Type Conference
Year 2007
Where ICONIP
Authors Tapani Raiko, Alexander Ilin, Juha Karhunen
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