Parameter Estimation Of Large-scale Dynamical Gauss Markov Process

Data analysis based on graph structure is one of the most popular technologies in the process of large data sets, which can describe the inter relationships among the time series, and their intra relationships across the time series. However, in practical applications, graph structure is often unknown for us, for example, in the stock market, stocks between in the same sector have a strong correlation and mutual influence. Dealing with these large-scale price data, there is no ready-made available graph for prediction. So it is very necessary to study the topology of the graph from the limited samples.This thesis focuses on the research of modeling large-scale spatial-temporal signal as dynamic Gauss Markov process and parameter estimation. The main contributions of this paper are as follows:1. To estimate joint graph structure parameters based on first-order Gauss Markov process, this thesis explored the data with joint graph structure and analyzed the construction of joint graph structure with noise.In detail this thesis determined the range of weighting parameters; then to obtain sparse graph structure it embedded the mechanism of threshold screening joint graph structure into the process of alternating gradient, also it proved the convergence of threshold q estimator algorithm (GTQ) and verify the convergence by simulation.2. To estimate joint graph structure parameters of first-order Gauss Markov process based on clustering, this thesis started from the spectral clustering algorithm, and embedded clustering into dynamic linear system and puts forward the algorithm to determine the number of clusters K. Then we study how the influence of different network scale on clustering performance and how the influence of threshold value q on clustering performance?clustering number K and we learn the model of complex analysis. At the same time, it compared accuracy of model estimation and topology recognition compared with GTG, CDG, MRCE, JGSE models.Finally, it is applied the algorithm into the real world stock market data.3. To estimate graph structure parameters of iterative least square method based on adaptive sparse hypothesis, this thesis started from patch-least squares method(B-LSM) and proposed iterative least squares estimation algorithm(ILSM), which making use of a priori estimation graph structure and new information to estimate graph structure online. At the same time, using the common sparse of signal structure in the range within controlled error, it proposed sparse adaptive iterative least squares algorithm(ASP-LSM), which improve the ability of topology identification.Finally, it validated the performance of ASP-LSM algorithm by simulation,and applied the algorithm into the real world stock market data.