Manifold Learning Based Analysis Method Research For Financial Data

As the unpredictable and turbulent financial markets, it is an urgent need to find the characteristics reflecting the nature and regularity of the market from the financial data ocean, which make the economic ship successfully bypass the financial crisis of the reef, and avoid market unpredictable. In recent years, Manifold learning has become a promising method of extracting nonlinear data features. It aims to extract the essential features and inherent laws of the data from the high dimensional data, which has become a hot research topic in data mining, pattern recognition and machine learning.In this paper, we put forward a manifold learning algorithm based on the financial data set for the structural features of the financial data set. In the empirical analysis of financial data, we have achieved good results. This study generally includes the following sections:(1) We tried to discover the intrinsic manifold(or lowdimensional representation) in high-dimensional financial data by proposing a manifold learning algorithm for financial data. Different from traditional manifold learning methods, our KEML employs the informationmetric tomeasure the relationships between financial data points and yields reasonable and accurate low-dimensional embedding of the original financial data set. The results of the experiment indicate that the KEML algorithm outperforms other six dimensionality reduction algorithms in terms of accuracy of low-dimensional embedding. In the subsequent financial early warning experiment, the error rates of the clustering results generated by KEML were lower than the six other algorithms. Our manifold learning methods based on information metric would further be deduced the properties reflecting the dynamics properties of the financial market, so as to provide objective and quantitative analysis supports for the analysis of stock market volatility.(2) We presented a new denoising approach for financial time series based on manifold learning, namely Mutual Information-based ISOMAP. The proposed method extracted the intrinsic features of the reconstructed phase space obtained by the traditional method,and thus reduced the noise interference. Experimental study showed our method decreased the reconstruction error of phase space than the traditional method, and provided more accurate data support for the subsequent studies about financial system.(3) This paper presents to detect the warning high probability points for critical transition in the financial system, and porpose the thoughts about early warning interval in which the warning points are intensive. Firstly, by using the phase space reconstruction technique, the one-dimensional financial time series are reconstructed to high dimensional financial dynamic system. Second, we propose the manifold learning method for financial data, to extract the dynamic attractor manifold. Third, according to the extracted attractor manifold, we detect detect the warning high probability points for critical transition in the financial system. Further, we discover the instric geometric properties embedded in a higher dimensional financial system, to provide the objective analysis evidence for the financial markets early warning.(4) According to the intrinsic geometric properties of manifolds, the Lyapunov exponent based on the curvature of the financial dynamics system are calculated, thus, the intrinsic relationships are obtained between the financial data manifolds. In the empirical research, through the derived Lyapunov index, the dynamical relationship between the industry subsystem and the financial market is further found to provide a new quantitative analysis basis for financial decision making.