High dimensional data are rapidly growing in many different disciplines, particularly in natural language processing. The analysis of natural language processing requires working with high dimensional matrices of word embeddings obtained from text data. Those matrices are often sparse in the sense that they contain many zero elements. Sparse principal component analysis is an advanced mathematical tool for the analysis of high dimensional data. In this paper, we study and apply the sparse principal component analysis for natural language processing, which can effectively handle large sparse matrices. We study several formulations for sparse principal component analysis, together with algorithms for implementing those formulations. Our work is motivated and illustrated by a real text dataset. We find that the sparse principal component analysis performs as good as the ordinary principal component analysis in terms of accuracy and precision, while it shows two major advantages: faster calculations and easier interpretation of the principal components. These advantages are very helpful especially in big data situations.

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