Frame-based Matrix Factorizations

Aktivität: ForschungKonferenzvorträge

Sebastian Mair - Sprecher*in

Ahcène Boubekki - Sprecher*in

Ulf Brefeld - Sprecher*in

Archetypal Analysis is the method of choice to compute interpretable matrix factorizations. Every data point is represented as a convex combination of factors, i.e., points on the boundary of the convex hull of the data. This renders computation inefficient. In this paper, we make two contributions. First, we show that the set of vertices of a convex hull, the so-called frame, can be efficiently computed by a quadratic program. We provide theoretical and empirical results for our proposed approach and provide further strategies for scaling up the computation.
Second, we make use of the frame to accelerate Archetypal Analysis. This is done by restricting Archetypal Analysis to the frame and just to the frame. Empirical results show, that the novel method often yields similar reconstruction errors as baseline competitors in practice but is much faster to compute. This is especially beneficial when several
executions are needed for determining the amount of latent factors. Considering the cumulative runtime in such a scenario outperforms all baselines. In addition, we demonstrate the application of an autoencoder by comparing the quality of the embedding to a neural network.