Random Matrix Asymptotics of Inner Product Kernel Spectral Clustering
Type
Conference PaperDate
2018-09-21Online Publication Date
2018-09-21Print Publication Date
2018-04Permanent link to this record
http://hdl.handle.net/10754/631603
Metadata
Show full item recordAbstract
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.Sponsors
The work of R. Couillet and H. Tiomoko Ali is supported by the ANR Project RMT4GRAPH (ANR-14-CE28-0006)Conference/Event name
2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018Additional Links
https://ieeexplore.ieee.org/document/8462052ae974a485f413a2113503eed53cd6c53
10.1109/ICASSP.2018.8462052