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- W2079234446 abstract "We present an extension of Principal Component Analysis (PCA) and a new algorithm for clustering points in $R^n$ based on it. The key property of the algorithm is that it is affine-invariant. When the input is a sample from a mixture of two arbitrary Gaussians, the algorithm correctly classifies the sample assuming only that the two components are separable by a hyperplane, i.e., there exists a halfspace that contains most of one Gaussian and almost none of the other in probability mass. This is nearly the best possible, improving known results substantially. For k≫2 components, the algorithm requires only that there be some (k-1)-dimensional subspace in which the ``overlap'' in every direction is small. Our main tools are isotropic transformation, spectral projection and a simple reweighting technique. We call this combination isotropic PCA." @default.
- W2079234446 created "2016-06-24" @default.
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- W2079234446 date "2008-10-01" @default.
- W2079234446 modified "2023-10-18" @default.
- W2079234446 title "Isotropic PCA and Affine-Invariant Clustering" @default.
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- W2079234446 doi "https://doi.org/10.1109/focs.2008.48" @default.
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