Random Matrix Asymptotics of Inner Product Kernel Spectral Clustering

Type
Conference Paper

Authors
Ali, Hafiz Tiomoko
Kammoun, Abla
Couillet, Romain

KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Online Publication Date
2018-09-21

Print Publication Date
2018-04

Date
2018-09-21

Abstract
We study in this article the asymptotic performance of spectral clustering with inner product kernel for Gaussian mixture models of high dimension with numerous samples. As is now classical in large dimensional spectral analysis, we establish a phase transition phenomenon by which a minimum distance between the class means and covariances is required for clustering to be possible from the dominant eigenvectors. Beyond this phase transition, we evaluate the asymptotic content of the dominant eigenvectors thus allowing for a full characterization of clustering performance. However, a surprising finding is that in some particular scenarios, the phase transition does not occur and clustering can be achieved irrespective of the class means and covariances. This is evidenced here in the case of the mixture of two Gaussian datasets having the same means and arbitrary difference between covariances.

Citation
Ali HT, Kammoun A, Couillet R (2018) Random Matrix Asymptotics of Inner Product Kernel Spectral Clustering. 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Available: http://dx.doi.org/10.1109/ICASSP.2018.8462052.

Acknowledgements
The work of R. Couillet and H. Tiomoko Ali is supported by the ANR Project RMT4GRAPH (ANR-14-CE28-0006)

Publisher
IEEE

Journal
2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

Conference/Event Name
2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018

DOI
10.1109/ICASSP.2018.8462052

Additional Links
https://ieeexplore.ieee.org/document/8462052https://hal.archives-ouvertes.fr/hal-01812005/file/article_update_version3.pdf

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