Abstract: For a long time, it is thought that the representation is one of the bottleneck problems in the field of machine learning. The performance of machine learning methods is heavily dependent on the choice of data representation. The rapidly developing field of representation learning is concerned with questions surrounding how we can best learn meaningful and useful representations of data. We take a broad view of the field and include topics such as deep learning, feature learning, metric learning, compositional modeling, structured prediction, reinforcement learning, etc. The range of domains to which these techniques apply is also very broad, from vision to speech recognition, text understanding, etc. Thus, the research on new representation methods for machine learning is a piece of work which is long-term, explorative and meaningful. Based on this, we propose several basic concepts of category representation of machine learning methods via the category theory. We analyze the decision tree, support vector machine, principal component analysis and deep neural network with category representation and give the corresponding category representation for each algorithms: the category representation of decision tree, slice category representation of support vector machine, and functor representation of the neural network. We also give the corresponding theoretical proof and feasibility analysis. According to further reach of category representation of machine learning algorithms, we find the essential relationship between support vector machine and principal component analysis. Finally, we confirm the feasibility of the category representation method using the simulation experiments.