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[edit] Data Spectroscopy: Learning Mixture Models using Eigenspaces of Convolution Operators

warning: the following is a confused summary

presented by Mikhail Belkin

• compute the kernel matrix, for a Gaussian kernel. Since this matrix is symmetric, all its eigenvalues are real.
• look at the eigenvalues: most eigenvalues will be small negative numbers. But for each mode of the distribution, there will be a large positive eigenvalue.
• eigenvectors' indices correspond to data points
• we can find the maximum index (i.e. data point most amplified by the kernel matrix). That will be the mean?

slogan:

• we can hear the shape of a drum from its spectrum; can we hear the shape of a Gaussian?