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    Random Matrix Asymptotics of Inner Product Kernel Spectral Clustering

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    Type
    Conference Paper
    Authors
    Ali, Hafiz Tiomoko
    Kammoun, Abla cc
    Couillet, Romain
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2018-09-21
    Online Publication Date
    2018-09-21
    Print Publication Date
    2018-04
    Permanent link to this record
    http://hdl.handle.net/10754/631603
    
    Metadata
    Show full item record
    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.
    Sponsors
    The work of R. Couillet and H. Tiomoko Ali is supported by the ANR Project RMT4GRAPH (ANR-14-CE28-0006)
    Publisher
    Institute of Electrical and Electronics Engineers (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/8462052
    ae974a485f413a2113503eed53cd6c53
    10.1109/ICASSP.2018.8462052
    Scopus Count
    Collections
    Conference Papers; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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