Abstract
Self-Organizing Maps (SOM) are unsupervised neural networks that map an underlying regular neighbourhood structure onto a codebook that is learned to perform vector quantization onto an input space. They are used in a wide range of applications, where an increase in the number of neurons in the SOM often leads to better results or new emerging properties. Therefore highly efficient algorithms for learning and evaluation are key to improve the performance of such models. The most time-greedy component of the SOM learning algorithm is the computation of the best matching unit (BMU) that is usually performed by means of a standard Winner Takes All algorithm. In a previous paper, we have proposed FastBMU, an algorithm to compute the BMU that scales better with a large number of neurons. Our algorithm has shown a significant improvement in computing time with a minimal degradation of performance in the context of a sequential implementation. In the perspective of hardware implementations, we propose here a parallel version of FastBMU, and we analyse its behavior and its performance. Based on the performed analysis, we finally derive principles of a parallel hardware structure that maximize resource utilization.
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Notes
- 1.
\(\sigma (t)\) influences the neighbourhood function. The higher it is, the more the BMU influences other neurons. Here, it starts at 0.5 and linearly decreases to 0.001, so that at the beginning of the training, neurons are significantly influenced by the BMU (unfolding the SOM), and at the end, nearly none except the BMU are (optimizing the quantization). \(\epsilon (t)\) is the learning parameter, it starts at 0.6 and linearly decreases to 0.05. We ran the SOM for 10 epochs.
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Bernard, Y., Girau, B. (2022). Fast Parallel Search of Best Matching Units in Self-organizing Maps. In: Faigl, J., Olteanu, M., Drchal, J. (eds) Advances in Self-Organizing Maps, Learning Vector Quantization, Clustering and Data Visualization. WSOM+ 2022. Lecture Notes in Networks and Systems, vol 533. Springer, Cham. https://doi.org/10.1007/978-3-031-15444-7_2
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