Generation and Frame Characteristics of Predefined Evenly-Distributed Class Centroids for Pattern Classification

Abstract

Predefined evenly-distributed class centroids (PEDCC) can be widely used in models and algorithms of pattern classification, such as CNN classifiers, classification autoencoders, clustering, and semi-supervised learning, etc. Its basic idea is to predefine the class centers, which are evenly-distributed on the unit hypersphere in feature space, to maximize the inter-class distance. The previous method of generating PEDCC uses an iterative algorithm based on a charge model. The generated class centers will have some errors with the theoretically evenly-distributed points, and the generation time is long. This paper takes advantage of regular polyhedron in high-dimensional space and the evenly distributed points on the $n$ dimensional hypersphere to generate PEDCC mathematically. Then, we discussed the basic and extended characteristics of the frames formed by PEDCC, and some meaningful conclusions are obtained. Finally, the effectiveness of the new algorithm and related conclusions are proved by experiments. The mathematical analysis and experimental results of this paper can provide a theoretical tool for using PEDCC to solve the key problems in the field of pattern recognition, such as interpretable supervised/unsupervised learning, incremental learning, uncertainty analysis and so on.

Keywords

• Predefined evenly-distributed class centroids
• polyhedron in high-dimensional space
• pattern classification
• CNN classifiers
• frame theory