A flexible EM-like clustering algorithm for noisy data

Though very popular, it is well known that the EM for GMM 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 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 accommodate for heavier tails distributions and outliers without significantly loosing efficiency in various classical scenarios. We first derive and analyze the proposed algorithm in the context of elliptical distributions, showing in particular important insensitivity properties to the underlying data distributions. We then 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 for Gaussian mixture models and its recent modifications or spectral clustering when applied to real data sets as MNIST, NORB, and 20newsgroups.