Data Dimensionality Reduction in Materials Science

Materials science research has witnessed an increasing use of data-mining techniques in establishing structure-process-property relationships. Significant advances in high-throughput experiments and computational capability have resulted in the generation of huge amounts of data. Various statistical methods are currently employed to reduce the noise, redundancy, and dimensionality of the data to make analysis more tractable. Popular methods for reduction (such as principal component analysis) assume a linear relationship between the input and output variables. Recent developments in nonlinear reduction (neural networks, self-organizing maps), though successful, have computational issues associated with convergence and scalability. This chapter reviews various spectral-based techniques that efficiently unravel linear and nonlinear structures in the data, which can subsequently be used to tractably investigate structure-property-process relationships. We compare and contrast the advantages and disadvantages of these techniques and discuss the mathematical and algorithmic underpinning of these methods. In addition, we describe techniques (based on graph-theoretic analysis) to estimate the optimal dimensionality of the low-dimensional parametric representation. We show how these techniques can be packaged into a modular, computationally scalable software framework with a graphical user interface - Scalable Extensible Toolkit for Dimensionality Reduction (SETDiR). This interface helps to separate out the mathematics and computational aspects from the material science applications, thus significantly enhancing utility to the materials science community. The applicability of the framework in constructing reduced order models of complicated materials data sets is illustrated.