Research On Mapping Mechnism Of Learning Expression

The research on Machine Learning has made much progress. In recend years, more and more researchers are inclined to use the mathematical methods in machine learning, this have been created new methods for the research of machine learning. In this thesis we try to apply category theory to the representation of machine learning. Lots of results have been obtained after three years'hard work, and it can be concluded as follows:1. The category description of machine learning systems and the related concepts are proposed. And its correctness and feasibility are verified by some experiments.2. The mapping mechanism of learning expression is represented.3. Suggest how to represent the dimensionality reduction and classifiers by using category theory. Also some illustration examples are provided to validate its feasibility.Overall, this thesis has made some achievements. But compared with other learning algorithms, we still have a long way to go. And there is still a lot of work to be studied,such as the deep semantic analysis based on Expression, multi-layer structure based on expression and so on.