Non-Negative Matrix Factorization for Stock Market Pricing

In this paper, we use non-negative matrix factorization (NMF) to analyze the data from stock market. By using the multiplicative update rules algorithm, we decompose the data matrix V of the daily closing prices of the 40 stocks, of which the Shenzhen component index is made up, into two matrices W and H, in which the columns of W correlate to the underlying trends. In addition, the Euclidean distance between the 40 stocks and the underlying forces is constructed. By means of the K-means routine in MATLAB, the 40 stocks are classified into different clusters with the center of the underlying forces, which can be finished automatically by MATLAB. Finally, the properties of these clusters are studied.