基于范畴的数据降维方法

Data Dimension Reduction Based on Category Theory

范畴理论主要是一些特定数学的对象和映射的概括和抽象,在此利用范畴理论阐述图像分析和识别中的数据降维问题,定义高维数据降维范畴的过程,并以主成分分析范畴和等距映射范畴分别验证了范畴理论应用到图像数据降维问题中的正确性。

The research of category theory is mainly about summary and abstraction of some specific mathematical objects and mapping.The dimensionality reduction problem based on category theory was discussed,and it could solve the problems of image analysis and image recognition.Besides,the process of dimensionality reduction based on category theory was listed.There are two examples,Principal Component Analysis Category and Isomap Category,which verified the correctness of the category theory applied to the dimensionality reduction problem.