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Techniques of matrix completion aim to impute a large portion of missing entries in a data matrix through a small portion of observed ones. In practice, prior information and special structures are usually employed in order to improve the accuracy of matrix completion. In this paper, we propose a unified nonconvex optimization framework for matrix completion with linearly parameterized factors. In particular, by introducing a condition referred to as Correlated Parametric Factorization, we conduct a unified geometric analysis for the nonconvex objective by establishing uniform upper bounds for low-rank estimation resulting from any local minimizer. Perhaps surprisingly, the condition of Correlated Parametric Factorization holds for important examples including subspace-constrained matrix completion and skew-symmetric matrix completion. The effectiveness of our unified nonconvex optimization method is also empirically illustrated by extensive numerical simulations.
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Data-Driven Imputation of Miscibility of Aqueous Solutions via Graph-Regularized Logistic Matrix Factorization
Aqueous, two-phase systems (ATPSs) may form upon mixing two solutions of independently water-soluble compounds. Many separation, purification, and extraction processes rely on ATPSs. Predicting the miscibility of solutions can accelerate and reduce the cost of the discovery of new ATPSs for these applications. Whereas previous machine learning approaches to ATPS prediction used physicochemical properties of each solute as a descriptor, in this work, we show how to impute missing miscibility outcomes directly from an incomplete collection of pairwise miscibility experiments. We use graph-regularized logistic matrix factorization (GR-LMF) to learn a latent vector of each solution from (i) the observed entries in the pairwise miscibility matrix and (ii) a graph where each node is a solution and edges are relationships indicating the general category of the solute (i.e., polymer, surfactant, salt, protein). For an experimental data set of the pairwise miscibility of 68 solutions from Peacock et al. [ACS Appl. Mater. Interfaces 2021, 13, 11449–11460], we find that GR-LMF more accurately predicts missing (im)miscibility outcomes of pairs of solutions than ordinary logistic matrix factorization and random forest classifiers that use physicochemical features of the solutes. GR-LMF obviates the need for features of the solutions and solutions to impute missing miscibility outcomes, but it cannot predict the miscibility of a new solution without some observations of its miscibility with other solutions in the training data set.
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- PAR ID:
- 10462522
- Date Published:
- Journal Name:
- The Journal of Physical Chemistry B
- ISSN:
- 1520-6106
- 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/10.1021/acs.jpcb.3c03789
