  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, that is, the initial values of various centers (charge positions)
are randomly set from the normal distribution, and the charge positions are
updated iteratively with the help of the repulsive force between charges of the
same polarity. The class centers generated by the algorithm will produce some
errors with the theoretically evenly-distributed points, and the generation
time will be longer. This paper takes advantage of regular polyhedron in
high-dimensional space and the evenly distribution of points on the n
dimensional hypersphere to generate PEDCC mathematically. Then, we discussed
the basic and extensive characteristics of the frames formed by PEDCC. Finally,
experiments show that new algorithm is not only faster than the iterative
method, but also more accurate in position. 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.
