Harnessing nonnegative matrix factorization for computational materials modeling

Interpretable representation learning is becoming an essential requirement for materials modeling and discovery, where accurate predictions alone are often insufficient for guiding scientific understanding or experimental design. Nonnegative Matrix Factorization (NMF) offers a natural framework for this purpose because many materials descriptors, including elemental compositions, spectral intensities, structural counts, and engineered feature groups, are nonnegative and can be meaningfully decomposed into additive latent factors. In this work, we develop and evaluate \texttt{nimd}, a computational framework for Nonnegative Interpretable Matrix Decomposition in materials informatics. The framework brings together standard NMF, Frobenius- and beta-divergence formulations, hierarchical and multilayer NMF, deep NMF, min-volume regularized deep NMF, and semi-supervised NMF variants within a unified workflow for prediction, comparison, and interpretation. Using a high-dimensional Heuslerene monolayer dataset as a representative materials discovery test case, we compare NMF-based representations with PCA across regression and classification tasks. The results show that NMF models can achieve predictive performance comparable to PCA while providing substantially more interpretable latent factors through nonnegative, parts-based decompositions. Deep and multilayer NMF further expose hierarchical structure in the descriptor space, while semi-supervised NMF provides a route for aligning latent representations with target properties. Beyond this demonstration, the framework is designed to support broader materials datasets where interpretability, factor stability, and chemically or physically meaningful feature attribution are central to model usefulness. These results establish NMF-based representation learning as a transparent and scientifically grounded alternative to conventional dimensionality reduction for materials modeling and discovery. The code and data are available through \href{https://github.com/thaksheel/nimd}{\texttt{https://github.com/thaksheel/nimd}}