A Geometric Approach to Archetypal Analysis via Sparse Projections

Archetypal analysis (AA) aims to extract patterns using self-expressive decomposition of data as convex combinations of extremal points (on the convex hull) of the data. This work presents a computationally efficient greedy AA (GAA) algorithm. GAA leverages the underlying geometry and sparseness property of AA, is scalable to larger datasets, and has significantly faster convergence to existing methods. To achieve this, archetypes are learned via sparse projection of data in linearly transformed space. GAA employs an iterative subset selection approach to identify archetypes based on the sparsity of convex representations. The work further presents the use of GAA algorithm for extended AA models such as robust and kernel AA. Experimental results show that GAA is significantly faster while performing comparable to existing methods for tasks such as classification, data visualization/categorization.