This paper proposes a novel variable learning rate to address two main challenges of the conventional Self-Organizing Maps (SOM) termed VLRSOM: high accuracy with fast convergence and low topological error. We empirically showed that the proposed method exhibits faster convergence behavior. It is also more robust in topology preservation as it maintains an optimal topology until the end of the maximum iterations. Since the learning rate adaption and the misadjustment parameter depends on the calculated error, the VLRSOM will avoid the undesired results by exploiting the error response during the weight updation. Then the learning rate is updated adaptively after the random initialization at the beginning of the training process. Experimental results show that it eliminates the tradeoff between the rate of convergence and accuracy and maintains the data's topological relationship. Extensive experiments were conducted on different types of datasets to evaluate the performance of the proposed method. First, we experimented with synthetic data and handwritten digits. For each data set, two experiments with a different number of iterations (200 and 500) were performed to test the stability of the network. The proposed method was further evaluated using four benchmark data sets. These datasets include Balance, Wisconsin Breast, Dermatology, and Ionosphere. In addition, a comprehensive comparative analysis was performed between the proposed method and three other SOM techniques: conventional SOM, parameter-less self-organizing map (PLSOM2), and RA-SOM in terms of accuracy, quantization error (QE), and topology error (TE). The results indicated the proposed approach produced superior results to the other three methods.

本文提出了一种新的可变学习率来解决称为 VLRSOM 的传统自组织映射 (SOM) 的两个主要挑战：高精度、快速收敛和低拓扑误差。我们凭经验表明，所提出的方法表现出更快的收敛行为。它在拓扑保存方面也更加健壮，因为它保持最佳拓扑直到最大迭代结束。由于学习率适应和失调参数取决于计算的误差，VLRSOM 将通过在权重更新期间利用误差响应来避免不希望的结果。然后在训练过程开始时的随机初始化之后自适应地更新学习率。实验结果表明，它消除了收敛速度和准确率之间的权衡，保持了数据的拓扑关系。对不同类型的数据集进行了广泛的实验，以评估所提出方法的性能。首先，我们尝试了合成数据和手写数字。对于每个数据集，进行了两个具有不同迭代次数（200 和 500）的实验来测试网络的稳定性。使用四个基准数据集进一步评估了所提出的方法。这些数据集包括 Balance、Wisconsin Breast、Dermatology 和 Ionosphere。此外，对所提出的方法与其他三种 SOM 技术进行了全面的比较分析：常规 SOM、无参数自组织图 (PLSOM2) 和 RA-SOM 在准确性方面，量化误差 (QE) 和拓扑误差 (TE)。结果表明，所提出的方法比其他三种方法产生了更好的结果。