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Important data mining problems such as nearest-neighbor search and clustering admit theoretical guarantees when restricted to objects embedded in a metric space. Graphs are ubiquitous, and clustering and classification over graphs arise in diverse areas, including, e.g., image processing and social networks. Unfortunately, popular distance scores used in these applications, that scale over large graphs, are not metrics and thus come with no guarantees. Classic graph distances such as, e.g., the chemical and the CKS distance are arguably natural and intuitive, and are indeed also metrics, but they are intractable: as such, their computation does not scale to large graphs. We define a broad family of graph distances, that includes both the chemical and the CKS distance, and prove that these are all metrics. Crucially, we show that our family includes metrics that are tractable. Moreover, we extend these distances by incorporating auxiliary node attributes, which is important in practice, while maintaining both the metric property and tractability.
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DiSCoVeR: a materials discovery screening tool for high performance, unique chemical compositions
We present Descending from Stochastic Clustering Variance Regression (DiSCoVeR) (https://www.github.com/sparks-baird/mat_discover), a Python tool for identifying and assessing high-performing, chemically unique compositions relative to existing compounds using a combination of a chemical distance metric, density-aware dimensionality reduction, clustering, and a regression model. In this work, we create pairwise distance matrices between compounds via Element Mover's Distance (ElMD) and use these to create 2D density-aware embeddings for chemical compositions via Density-preserving Uniform Manifold Approximation and Projection (DensMAP). Because ElMD assigns distances between compounds that are more chemically intuitive than Euclidean-based distances, the compounds can then be clustered into chemically homogeneous clusters via Hierarchical Density-based Spatial Clustering of Applications with Noise (HDBSCAN*). In combination with performance predictions via Compositionally-Restricted Attention-Based Network (CrabNet), we introduce several new metrics for materials discovery and validate DiSCoVeR on Materials Project bulk moduli using compound-wise and cluster-wise validation methods. We visualize these via multi-objective Pareto front plots and assign a weighted score to each composition that encompasses the trade-off between performance and density-based chemical uniqueness. In addition to density-based metrics, we explore an additional uniqueness proxy related to property gradients in DensMAP space. As a validation study, we use DiSCoVeR to screen materials for both performance and uniqueness to extrapolate to new chemical spaces. Top-10 rankings are provided for the compound-wise density and property gradient uniqueness proxies. Top-ranked compounds can be further curated via literature searches, physics-based simulations, and/or experimental synthesis. Finally, we compare DiSCoVeR against the naive baseline of random search for several parameter combinations in an adaptive design scheme. To our knowledge, this is the first time automated screening has been performed with explicit emphasis on discovering high-performing, novel materials.
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- PAR ID:
- 10319410
- Date Published:
- Journal Name:
- Digital Discovery
- ISSN:
- 2635-098X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/D1DD00028D
