Random matrix-improved kernels for large dimensional spectral clustering

Hafiz Tiomoko Ali (1) , Abla Kammoun (2) , Romain Couillet (3)

1 L2S - Laboratoire des signaux et systèmes
2 KAUST - King Abdullah University of Science and Technology [Saudi Arabia]
3 NXP Semiconductors

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.

Domaines: Intelligence artificielle [cs.AI]; Apprentissage [cs.LG]; Statistiques [math.ST]

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⟩