Regression Learning For Vector-valued Reproducing Kernel Hilbert Space

Modern information technology is mainly based on data analysis and data mining. Machine learning and learning theory are playing an important role in data analysis. Due to the close connection between the research of regularization learning algorithms and the dimension reduction, data mining, image processing, regularization learning algorithms has important theoretical significance and application value to its theoretical research and breakthrough. This thesis focuses on the regression learning algorithm for vector-valued reproducing kernel Hilbert space.In this paper, the regression learning algorithm with vector-valued reproducing kernel Hilbert space(RKHS) is studied. We motivate the need for extending learning theory of scalar-valued functions and analze the learning performance. In this setting, the output data are from a Hilbert space Y, the associated RKHS consists of functions from a probability space X to Y. By providing mathematical aspects of vector-valued integral operator KL, the capacity independent error bounds and learning rates are derived by means of the integral operator technique.In the consistency analysis for vector-valued regression learning algorithm, there are two major innovation points: firstly, we prove the properties of integral operator based on vector-valued kernel; secondly, we study the error analysis and learning rate of vector-valued based regularized regression learning algorithm by integral operator techniques. On the basis of the above work, we prove the consistency of the regularization algorithm based on vector-valued reproducing kernel Hilbert space.