Batch and median neural gas
Batch and median neural gas
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DOI：
10.1016/j.neunet.2006.05.018
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发表时间：
2006-07-01
期刊：
影响因子：
7.8
通讯作者：
Villmann, Thomas
中科院分区：
文献类型：
--
作者：
Cottrell, Marie;Hammer, Barbara;Villmann, Thomas
神经气体（NG）在给定欧几里德数据的情况下构成了一种非常鲁棒的聚类算法，它不会遇到简单矢量量化等局部最小值问题，也不会遇到自组织映射等拓扑限制问题。基于 NG 的成本函数，我们引入了 NG 的批量变体，它表现出更快的收敛速度，并且可以解释为通过牛顿法对成本函数的优化。该公式还有一个额外的好处，即基于与中值 SOM 类似的广义中值概念，可以引入非矢量邻近数据的变体。我们证明了 NG、SOM 和 k 均值的批量版本和中值版本在统一公式中的收敛性，并在多个实验中研究了算法的行为。 (c) 2006 Elsevier Ltd. 保留所有权利。
Neural Gas (NG) constitutes a very robust clustering algorithm given Euclidean data which does not suffer from the problem of local minima like simple vector quantization, or topological restrictions like the self-organizing map. Based on the cost function of NG, we introduce a batch variant of NG which shows much faster convergence and which can be interpreted as an optimization of the cost function by the Newton method. This formulation has the additional benefit that, based on the notion of the generalized median in analogy to Median SOM, a variant for non-vectorial proximity data can be introduced. We prove convergence of batch and median versions of NG, SOM, and k-means in a unified formulation, and we investigate the behavior of the algorithms in several experiments. (c) 2006 Elsevier Ltd. All rights reserved.