Machine Learning has been regarded as the empirical science for a long time. There is no the theoretical foundation for the following problems concerned by machine learning: generalization error, computational cost, nonlinear, description length of learning model and so on. Fortunately, many researchers have been devoted to establishing the theory on machine learning. Generalization of machine learning is based on statistical learning theory. Based on this theory, PAC theory is established to guide the research on computational complexity of machine learning. Kernel method is a new way to solve nonlinear problems in machine learning. The above facts show that machine learning is becoming a really science step by step. This thesis includes two parts. Statistical properties of machine learning are introduced in the first part. My research is focused on the second part "Geometry foundation of machine learning" including theoretical analysis of universal kernel functions, geometrical algorithm for SVM. Insides, boosting will be introduced in this part.
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