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Self-Organizing Maps
Published in Bogdan M. Wilamowski, J. David Irwin, Intelligent Systems, 2018
One category of the visualization techniques is to visualize the SOM topology through distance matrices. The most widely used method in this category is the unified distance matrix (U-matrix) [22], which enables visualization of the topological relations between the neurons in a trained SOM. The idea is to show the underlying data structure by graphically displaying the inter-neuron distances between neighboring units in the network. The distances of the prototype vector of each map unit to its immediate neighbors are calculated and form a matrix. The same metric is used to compute the distances between map units, as is used during the SOM training to find the BMU. By displaying the values in the matrix as a three-dimensional (3D) landscape or a gray-level image, the relative distances between adjacent units on the whole map becomes visible. The U-matrix is calculated in the prototype space and displayed using the map space.
Dimensionality Reduction — Nonlinear Methods
Published in Wendy L. Martinez, Angel R. Martinez, Jeffrey L. Solka, Exploratory Data Analysis with MATLAB®, 2017
Wendy L. Martinez, Angel R. Martinez, Jeffrey L. Solka
Several methods exist for visualizing the resulting map and prototype vectors. These methods can have any of the following goals. The first is to get an idea of the overall shape of the data and whether clusters are present. The second goal is to analyze the prototype vectors for characteristics of the clusters and correlations among components or variables. The third task is to see how new observations fit with the map or to discover anomalies. We will focus on one visualization method called the U-matrix that is often used to locate clusters in the data [Ultsch and Siemon, 1990].
Mapping fractional landscape soils and vegetation components from Hyperion satellite imagery using an unsupervised machine-learning workflow
Published in International Journal of Digital Earth, 2018
Michael J. Friedel, Massimo Buscema, Luiz Eduardo Vicente, Fabio Iwashita, Andréa Koga-Vicente
Several visualization techniques have been developed to provide insight into quality of the trained SOM. One method used to define cluster boundaries in a SOM is the unified distance matrix, also called the U-matrix (Ultsch 2003). The U-matrix represents the relative closeness (in terms of Euclidean distance) between adjacent neurons on the SOM. This gives rise to a topographic analogy (valleys and ridges) in which the color differences represent class-boundaries, or samples belonging to different groups. Valleys, associated with low U values (cool colors), contain neurons whose weight vectors are close together, whereas high U values (warm colors) contain neurons whose weight vectors are distant from the weight vectors of its neighbors. One drawback of the U-matrix is that the average distance only is based on the final weight vectors; therefore, it does not take into account if the neuron represents one or more input vectors, or if it is far from most of the input vectors.
Modelling of household electricity consumption with the aid of computational intelligence methods
Published in Advances in Building Energy Research, 2018
Kostas Karatzas, Nikos Katsifarakis
The SOM method is based on neural networks composed of a two-dimensional array of randomly weighted neurons (Kohonen, 1997). As data points are passed through the neural network, they are matched with a winning neuron, causing the network topology to adjust and eventually form clusters of similar attributes. The unified distance matrix (U-matrix), representing the Euclidean distance between neighbouring neurons, is used as the basic visualization method for SOM, as it depicts the relations between neighbouring data (Ultsch & Siemon, 1990).
Segmenting offshore wind farms for analysing cost reduction opportunities: a case of the North Sea region*
Published in International Journal of Sustainable Energy, 2020
Samira Keivanpour, Amar Ramudhin, Daoud Ait Kadi
The first step of applying the SOM approach is generating a proper neural grid. In this paper, a hexagonal SOM grid is used and trained based on SOM MATLAB Toolbox 2.0 (Vesanto and Alhoniemi 2000). The U-matrix generated from SOM can highlight the different clusters in the data set. Each cluster of the map links to a segment.