On the Concentration of Spectral Properties

Part of Advances in Neural Information Processing Systems 14 (NIPS 2001)

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John Shawe-Taylor, Nello Cristianini, Jaz Kandola


We consider the problem of measuring the eigenvalues of a ran(cid:173) domly drawn sample of points. We show that these values can be reliably estimated as can the sum of the tail of eigenvalues. Fur(cid:173) thermore, the residuals when data is projected into a subspace is shown to be reliably estimated on a random sample. Experiments are presented that confirm the theoretical results.