Generating Information-Rich High-Throughput Experimental Materials Genomes using Functional Clustering via Multitree Genetic Programming and Information Theory

Abstract

In this article, we propose a new Cauchy-Schwarz divergence function that is invariant to number of clusters. To illustrate the applicability of our approach, we assign random memberships for various number of clusters (2 to 8) to 486 compositions distributed at a 3.33 at.% interval in a ternary library; and plot the cross cluster information potential, self-information potential and their ratio using the Cauchy-Schwarz divergence function proposed by Boric et al. 1 (Eq. 1) and the Cauchy-Schwarz divergence function proposed in our article (Eq. 2) in Fig.1 and 2 respectively. From Fig. 1 we see that the self-information potential increases as a power of number of clusters (c); whereas the cross information potential increases very slowly as a function of c. Thus, the selfinformation potential dominates the Cauchy-Schwarz divergence function as the number of clusters increases.In Fig. 2; we show that the Cauchy-Schwarz divergence function proposed in our approach results in cross-information and self-information potentials that are invariant to number of clusters (c). Further, the ratio of cross-information potential to self-information potential is approximately 1 resulting in approximately zero Cauchy-Schwarz divergence; as expected for compositions with random memberships.

Band Gap Prediction for Large Organic Crystal Structures with Machine Learning

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