Self-Organizing Maps with Optimized Latent Positions
Graduate School of Informatics（信息科学研究生院）；Osaka Metropolitan University（大阪 metropolitan 大学）
Seiki Ubukata, Akira Notsu, Katsuhiro Honda
备注：
9 pages, 4 figures. Author's accepted manuscript of the paper published in the 2026 International Joint Conference on Neural Networks (IJCNN 2026), part of the 2026 IEEE World Congress on Computational Intelligence (WCCI 2026). v2: Added the IEEE copyright notice and full publication information
发表信息：
2026 International Joint Conference on Neural Networks (IJCNN), pp. 1-8, 2026
Self-Organizing Maps (SOM) are a classical method for unsupervised learning, vector quantization, and topographic mapping of high-dimensional data. However, existing SOM formulations often involve a trade-off between computational efficiency and a clearly defined optimization objective. Objective-based variants such as Soft Topographic Vector Quantization (STVQ) provide a principled formulation, but their neighborhood-coupled computations become expensive as the number of latent nodes increases. In this paper, we propose Self-Organizing Maps with Optimized Latent Positions (SOM-OLP), an objective-based topographic mapping method that introduces a continuous latent position for each data point. Starting from the neighborhood distortion of STVQ, we construct a separable surrogate local cost based on its local quadratic structure and formulate an entropy-regularized objective based on it. This yields a simple block coordinate descent scheme with closed-form updates for assignment probabilities, latent positions, and reference vectors, while guaranteeing monotonic non-increase of the objective and retaining linear per-iteration complexity in the numbers of data points and latent nodes. Experiments on a synthetic saddle manifold, scalability studies on the Digits and MNIST datasets, and 16 benchmark datasets show that SOM-OLP achieves competitive neighborhood preservation and quantization performance, favorable scalability for large numbers of latent nodes and large datasets, and the best average rank among the compared methods on the benchmark datasets.
aweSOM: a CPU/GPU-accelerated Self-organizing Map and Statistically Combined Ensemble Framework for Machine-learning Clustering Analysis
University of Massachusetts-Amherst（马萨诸塞大学阿默斯特分校）；Flatiron Institute（弗拉蒂伦研究所）；University of Helsinki（赫尔辛基大学）；Columbia University（哥伦比亚大学）；Princeton University（普林斯顿大学）
Entropy optimized semi-supervised decomposed vector-quantized variational autoencoder model based on transfer learning for multiclass text classification and generation
Thapar Institute of Engineering and Technology（塔帕尔工程技术学院）
