This research aims to develop kernel GNG, a kernelized version of the growing neural gas (GNG) algorithm, and to investigate the features of the networks generated by the kernel GNG. The GNG is an unsupervised artificial neural network that can transform a dataset into an undirected graph, thereby extracting the features of the dataset as a graph. The GNG is widely used in vector quantization, clustering, and 3D graphics. Kernel methods are often used to map a dataset to feature space, with support vector machines being the most prominent application. This paper introduces the kernel GNG approach and explores the characteristics of the networks generated by kernel GNG. Five kernels, including Gaussian, Laplacian, Cauchy, inverse multiquadric, and log kernels, are used in this study.

翻译：本研究旨在开发核生长神经气（kernel GNG）算法——生长神经气（GNG）算法的核化版本，并探究该算法生成网络的特性。GNG是一种无监督人工神经网络，可将数据集转换为无向图，从而以图的形式提取数据集特征，广泛应用于向量量化、聚类及三维图形学领域。核方法常被用于将数据集映射至特征空间，其中支持向量机是最具代表性的应用。本文介绍了核GNG方法，并深入分析了其生成网络的特性，研究中采用了高斯核、拉普拉斯核、柯西核、反多二次核及对数核共五种核函数。