International Mathematical Forum

Abstract

We apply Non-negative Matrix Factorization (NMF) to the prob-lem of identifying underlying trends in stock market data. NMF is arecent and very successful tool for data analysis including image andaudio processing; we use it here to decompose a mixture a data, thedaily closing prices of the 30 stocks which make up the Dow Jones In-dustrial Average, into its constitute parts, the underlying trends which govern the financial marketplace. We demonstrate how to impose ap-propriate sparsity and smoothness constraints on the components of thedecomposition. Also, we describe how the method clusters stocks to-gether in performance-based groupings which can be used for portfoliodiversification.

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