An optimized probabilistic neural network with unit hyperspherical crown mapping and adaptive kernel coverage.

It is important to improve the classification accuracy and reduce the storage space when probabilistic neural networks are used for pattern classification tasks. Based on a unit hyperspherical crown mapping and adaptive kernel coverage strategy, this paper presents an optimized hyperspherical crown probabilistic neural network(HCPNN). To overcome the separability problem caused by the fusion of heterogeneous samples, we adopt an unconventional unit hyperspherical crown mapping model in the sample space. Theoretical analysis indicates that nonlinear mapping can improve the separability of the original sample set under certain conditions. In addition, to optimize the pattern layer structure of probabilistic neural networks, we adopt an adaptive kernel coverage method for the training sample space to generate initial pattern nodes. The accumulation potential of the sample in each training subclass is used to measure the distribution density of different classes, and an adaptive update mechanism of potential values is established. In each iteration, nodes with high accumulation potential values are searched as pattern nodes from the dense to sparse regions. The precise position of each pattern node and the corresponding kernel width are adjusted by the Expected Maximum algorithm. Experiments show that HCPNN outperforms other algorithms with respect to the classification performance.