Constrained matrix factorization for financial data clustering

Abstract

Financial time series analysis is crucial to a successful assets allocation. Applying a matrix factorization technique can generate genuine grouping knowledge for the allocation of assets according to their association with a number of underlying bases. A constrained nonnegative matrix factorization NSMF is proposed to incorporate three penalties in order to compute a solution which can maximize between-base disjointness and volatility difference. A series of quantitative measures are designed for evaluation of bases and their volatility. Different types of real data are used in the experiments and compared regarding clustering consistency. Experimental analysis of historical prices of US blue chip stocks indicates that NSMF is superior to agglomerative clustering and independent component analysis and NSMF can extract bases with a higher discrepancy of volatility. The non-stochasticity constraint increases the dissimilarity of bases and it governs basis deviation over smoothness and sparseness. The clustering results of bases and persistent pairs, which are gained from NSMF, can consolidate our understanding of financial data properties and they provide meaningful knowledge in the construction of a well risk-balanced and diversified portfolio.