Data-Driven Cluster Reinforcement and Visualization in Sparsely-Matched Self-Organizing Maps

Abstract

A self-organizing map (SOM) is a self-organized projection of high-dimensional data onto a typically 2-dimensional (2-D) feature map, wherein vector similarity is implicitly translated into topological closeness in the 2-D projection. However, when there are more neurons than input patterns, it can be challenging to interpret the results, due to diffuse cluster boundaries and limitations of current methods for displaying interneuron distances. In this brief, we introduce a new cluster reinforcement (CR) phase for sparsely-matched SOMs. The CR phase amplifies within-cluster similarity in an unsupervised, data-driven manner. Discontinuities in the resulting map correspond to between-cluster distances and are stored in a boundary (B) matrix. We describe a new hierarchical visualization of cluster boundaries displayed directly on feature maps, which requires no further clustering beyond what was implicitly accomplished during self-organization in SOM training. We use a synthetic benchmark problem and previously published microbial community profile data to demonstrate the benefits of the proposed methods.

Function Approximation Using Combined Unsupervised and Supervised Learning

“…Here we propose to use a combination of unsupervised and supervised learning to improve function approximation performance in the case of functions defined on data that can be expected to reside on a low dimensional manifold embedded into a high dimensional space. To deal with the lack of information about the analytical form of the manifold, we use an over-complete self-organizing map (SOM) [19][20][21][22][23][24] to learn the topographic structure of the unknown manifold. Then we learn the approximation of a function defined over the node space of the SOM.…”

Fast unsupervised learning for visual pattern recognition using spike timing dependent plasticity

“…Such rule yields a unimodal weight distribution where the height of the plasticity window associated with STDP is modulated causing stability after a period of training. Other papers [41], [42], [43], [44] combines the self-organizing map (SOM)…”

Enhanced radial basis function neural networks for ozone level estimation

“…Substantial results from the existing works illustrate that using metamodels to locate an optimum solution is often sufficiently accurate in many applications requiring prediction, optimisation and validation. Datadriven methods such as kriging [17], splines [18], support vector regression [19], self-organising maps [20], cluster reinforcement [21], and neural networks [22] are usual methods for metamodelling in complex system identification and pattern recognition. In this paper, the RBFNN is adopted, making use of such advantages [23] as good accuracy, simplicity, high robustness and efficiency, sample sizes, and capability of dealing with different problem types.…”

“…Accordingly, the selection of the network centres can be made by taking the iteration number with different vectors ϕ k corresponding to the maximum value of M k defined in (21). To avoid the iteration process, this set can be assessed by the Gram matrix, P, as suggested in [38], where P is a symmetrical and orthogonal matrix of all the possible radial basis outputs for given training data used in the case of exact interpolation.…”