Issue with Eigenvalues

[Vijay Chakilam]

Hi,

I am trying to implement a spectral clustering algorithm in java. I am using jblas (as a maven dependency) for matrix algebra. The problem I am running into is I am getting negative eigenvalues for the Laplacian, which shouldn't be possible theoretically. In case of very small matrices (up to 5x5), the values are fine, but once the matrices start getting bigger (for even as small as 15x15), I am seeing negative eigenvalues (for example, in the attachments, the first eigenvalue is -0.05515). Anyone with experience of seeing dubious eigenvalues with Eigen.symmetricEigenValues method before? 

Attached is my Laplacian and the eigenvalues I got from Eigen.symmetricEigenValues method. 

Any suggestion/help is greatly appreciated.

Thanks,

Vijay

[Mikio Braun]

Hi Vijay,

those are the exact same eigenvalues I get when I put the matrix in a program like octave. Maybe something wrong with the matrix setup? Are you sure it is positive definite?

Best,

Mikio

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[Vijay Chakilam]

Thanks much for your reply Mikio. It indeed is a bug in my program. My laplacian was not PSD. I now see valid eigenvalues. Thanks for the great library and apologies for the inconvenience.

Thanks again,

Vijay

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[Mikio Braun]

No problem, you're welcome!

-M