Preliminary Study on Law Dimension and Visualization of Nonlinear System
|School||Hefei University of Technology|
|Course||Computer Software and Theory|
|Keywords||Nonlinear systems Law -dimensional Visualization Chaos Theory Manifold Learning Temporal data|
With the in-depth study of the nonlinear system and the rapid development of visualization techniques, it was found that a large number of phenomena of life that exist within a complex nonlinear mechanism, relying solely on abstract thinking to discover and understand things behind the law of Vietnam and more difficult. Although visualization techniques can be overcome because of the limited capacity of human cognition, the law of things is not visible, and complexity of the inconvenience caused by the people to understand things, but the single-dimensional time series sampled data, due to its complexity and non-geometric characteristics, it is difficult to hide the law of information in such data analysis and visualization. Internal law of the nonlinear system for the study proposed law-dimensional concept of nonlinear systems, and explore a nonlinear system based on chaos theory and manifold learning algorithm, the law and its development trend visualization method used to assist people to understand and analyze the internal mechanism of nonlinear systems. This paper studies include the following aspects: 1) nonlinear systems based on manifold learning visualization method. First, according to the chaos theory, the time series data of phase space reconstruction, recovery in the high-dimensional phase space of the original non-linear system of law; Secondly, calculate the visual quality and regularity dimension, select the appropriate manifold learning low-dimensional phase trajectory in the high-dimensional phase space is mapped to a two-dimensional or three-dimensional space, visualization of nonlinear system regular. 2) based on the Isomap nonlinear system incremental visualization methods. Nonlinear systems visualization method framework based first new sample point conversion for high-dimensional phase; Secondly, the geodesic matrix by adjacency matrix updates, updating and visualization of coordinate point mapping processing, nonlinear system of law-dimensional update and map new sample point to the visualization of results. The incremental visualization algorithm not only can handle the data flow and mass data information and timely updates manifold can also assist people to understand the manifold information in the dynamics of the formation of the high-dimensional phase space. 3) design and to achieve nonlinear systems combined analysis visualization platform. Characteristics and key technologies of visualization of time series data for analysis of nonlinear systems, nonlinear system analysis visualization of the entire process. The platform can be based on the specific needs, through the combination of the different functional modules to complete the analysis and visualization of time-series data, image data, and other data types.