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Sparse Methods

The volume of the digitized data generated by modern analytical instruments is increasing, and handling this huge amount of data requires advanced statistical methods for processing and interpretation. Extraction of valuable information from the raw data dump is a very challenging problem in data science. To address this problem, statisticians developed data-analysis tools with Lp-norm penalty terms for reducing the complexity of models and making them more simple and interpretable. These models, which mainly include L0- and L1-penalty terms in their building designs, are usually called as “sparse methods.” This chapter provides an overview about the meaning of the term sparsity and describes different sparse methods in data science. The implementation of sparsity constraint in PCA, PLS, DA, NMF, MCR, and PARAFAC methods is discussed. Different ways for imposing this constraint in an MCR-ALS algorithm are given, and the effects of this constraint on the ranges of feasible solutions in MCR methods are explored. The application of sparsity constraint in MCR helped chemometricians to better analyze the GC/LC-MS data, the resolution of microscopic fluorescent images, and the hyperspectral imaging datasets. Finally, it is desired that this chapter will help chemometricians to understand sparsity constraint and to learn how to use sparse methods for interpretation of very complicated datasets with chemical applications.

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