Identification of intrinsic characteristics and structure of high-dimensional data is an important task for financial analysis. This paper presents a kernel entropy manifold learning algorithm, which employs the information metric to measure the relationships between two financial data points and yields a reasonable low-dimensional representation of high-dimensional financial data. The proposed algorithm can also be used to describe the characteristics of a financial system by deriving the dynamical properties of the original data space. The experiment shows that the proposed algorithm cannot only improve the accuracy of financial early warning, but also provide objective criteria for explaining and predicting the stock market volatility. 
A kernel entropy manifold learning approach for financial data analysis