Manifold Learning for Financial Market Visualization

Financial market is a nonlinear complex system. It is notably hard to construct an integral mathematical model to characterize the financial system. The aim of this paper is to present financial market states by visualization approach, to explore the essential information hidden in the financial data sets to provide objective decision support. Manifold learning is a data-driven feature extraction method, which can successfully capture the intrinsic geometry of the data set. In this paper, manifold learning algorithm, Laplacian Eigenmaps (LE), would be employed to extract the intrinsic manifold structure embedding in the financial system, which is the intrinsic "skeleton" of financial system. Based on the "skeleton", we will further derive the structural and dynamical characteristics of financial markets, and to obtain more essential discoveries.