Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan,
Cogn Neurodyn. 2009 Mar;3(1):9-15. doi: 10.1007/s11571-008-9060-2. Epub 2008 Sep 24.
The Self-organizing map (SOM) is an unsupervised learning method based on the neural computation, which has found wide applications. However, the learning process sometime takes multi-stable states, within which the map is trapped to an undesirable disordered state including topological defects on the map. These topological defects critically aggravate the performance of the SOM. In order to overcome this problem, we propose to introduce an asymmetric neighborhood function for the SOM algorithm. Compared with the conventional symmetric one, the asymmetric neighborhood function accelerates the ordering process even in the presence of the defect. However, this asymmetry tends to generate a distorted map. This can be suppressed by an improved method of the asymmetric neighborhood function. In the case of one-dimensional SOM, it is found that the required steps for perfect ordering is numerically shown to be reduced from O(N (3)) to O(N (2)). We also discuss the ordering process of a twisted state in two-dimensional SOM, which can not be rectified by the ordinary symmetric neighborhood function.
自组织映射（SOM）是一种基于神经计算的无监督学习方法，已经得到了广泛的应用。然而，学习过程有时会进入多稳定状态，在这种状态下，地图会被困在一个不理想的无序状态，包括地图上的拓扑缺陷。这些拓扑缺陷极大地影响了 SOM 的性能。为了克服这个问题，我们提出了在 SOM 算法中引入非对称邻域函数。与传统的对称邻域函数相比，即使存在缺陷，非对称邻域函数也能加速排序过程。然而，这种不对称性往往会导致地图扭曲。通过改进非对称邻域函数的方法可以抑制这种扭曲。在一维 SOM 的情况下，从数值上可以看出，完全排序所需的步骤从 O（N^3）减少到 O（N^2）。我们还讨论了二维 SOM 中扭曲状态的排序过程，普通的对称邻域函数无法纠正这种扭曲。
