Linear KernelPCA and K-Means Clustering Using New Estimated Eigenvectors of the Sample Covariance Matrix

Nassara Elhadji Ille Gado (1) , Edith Grall-Maës (1) , Malika Kharouf (1)

1 LM2S - Laboratoire Modélisation et Sûreté des Systèmes

In this article, random matrix theory is used to propose a new K-means clustering algorithm via linear PCA. Our approach is devoted to linear PCA estimation when the number of the features d and the number of samples n go to infinity at the same rate. More precisely, we deal with the problem of building a consistent estimator of the eigenvectors of the covariance data matrix. Numerical results, based on the normalized mutual information (NMI) and the final error rate (ER), are provided and support our algorithm, even for a small number of features/samples. We also compare our approach to spectral clustering, K-means and traditional PCA methods.

Domains: Machine Learning [cs.LG]

Nassara Elhadji Ille Gado, Edith Grall-Maës, Malika Kharouf. Linear KernelPCA and K-Means Clustering Using New Estimated Eigenvectors of the Sample Covariance Matrix. 2015 IEEE 14th International Conference on Machine Learning and Applications (ICMLA), Dec 2015, Miami, United States. pp.386-389, ⟨10.1109/ICMLA.2015.207⟩. ⟨hal-02330752⟩