Physical Sciences and Mathematics Commons^™

A New Algorithm For Robust Affine-Invariant Clustering, Andrews Tawiah Anum

Open Access Theses & Dissertations

Cluster analysis is an unsupervised machine learning technique commonly employed to partition a dataset into distinct categories referred to as clusters. The k-means algorithm is a prominent distance-based clustering method. Despite its overwhelming popularity, the algorithm is not invariant under non-singular linear transformations and is not robust, i.e., can be unduly influenced by outliers. To address these deficiencies, we propose an alternative clustering procedure based on minimizing a “trimmed” variant of the negative log-likelihood function. We develop a “concentration step”, vaguely reminiscent of the classical Lloyd’s algorithm, that can iteratively reduce the objective function. Multiple real and synthetic datasets are …