Random matrix-improved kernels for large dimensional spectral clustering

Abstract : Leveraging on recent random matrix advances in the performance analysis of kernel methods for classification and clustering, this article proposes a new family of kernel functions theoretically largely outperforming standard kernels in the context of asymp-totically large and numerous datasets. These kernels are designed to discriminate statistical means and covariances across data classes at a theoretically minimal rate (with respect to data size). Applied to spectral clustering, we demonstrate the validity of our theoretical findings both on synthetic and real-world datasets (here, the popular MNIST database as well as EEG recordings on epileptic patients). Index Terms— Spectral clustering, inner product kernels, random matrix theory.
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Hafiz Tiomoko Ali, Abla Kammoun, Romain Couillet. Random matrix-improved kernels for large dimensional spectral clustering. 2018 IEEE Statistical Signal Processing Workshop (SSP), Jun 2018, Freiburg, Germany. ⟨10.1109/ssp.2018.8450705 ⟩. ⟨hal-01812009⟩

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