(2) Construction of a low-dimensional map of the materials and properties. The rows of a fully observed version of A, which lie in a P -dimensional vector space, can be viewed as feature vectors of the materials. In this view, each material is represented by a list of its properties. The set of latent vector representations of the materials, in the rows of M , are embeddings/ compressions of the rows of A into a lower (k < P ) dimensional vector space. Within this latent space, materials, represented by {m m }, that tend to have similar (dissimilar) properties congregate (separate). Using low-dimensional embedding techniques , we can visualize the scatter of the materials in the lowdimensional space to draw a "map" of materials. The latent representations of the materials, {m m }, and the map that visualizes them are useful for: (i) grouping together/organizing materials with similar properties, (ii) lead-optimization, where we search the map for materials nearby a "lead" material with good but still suboptimal performance, (iii) selecting diverse materials to efficiently explore material space in an experimental design strategy, and (iv) training supervised machine learning models for other prediction tasks, as m m is a feature vector for material m.