A flexible EM-like clustering algorithm for noisy data

Though very popular, it is well known that the EM algorithm suffers from non-Gaussian distribution shapes, outliers and high-dimensionality. In this paper, we design a new robust clustering algorithm that can efficiently deal with high-dimensionality, noise and outliers in diverse data sets. As an EM-like algorithm, it is based on both estimations of clusters centers and covariances. In addition, using a semi-parametric paradigm, the method estimates an unknown scale parameter per data-point. This allows the algorithm to leverage high-dimensionality and to accommodate for heavier tails distributions and outliers without significantly loosing efficiency in various classical scenarios. After deriving and analyzing the proposed algorithm, we study the convergence and accuracy of the algorithm by considering first synthetic data. Then, we show that the proposed algorithm outperforms other classical unsupervised methods of the literature such as $k$-means, the EM algorithm and its recent modifications or spectral clustering when applied to real data sets as MNIST, NORB and $20newsgroups$.