Creating Self-Organizing Maps

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The algorithm that creates a self-organizing map starts by creating a grid of hexagonal bins arranged in a square. The dimensions of the square are $n\times n$ , where $n=\sqrt{Numberofdesignpo\mathrm{int}s}$ . The maximum value of $n$ is 25. (If the data set contains more than 625 data points, Results Analytics positions the data in a 25 × 25 grid.)

The Preserve topology of sample space technique tries to minimize the topology error.

The Maximize resolution of fit technique tries to determine the quality of the fit.

The maximum iterations are the maximum number of times Results Analytics runs the outer loop of the self-organizing map algorithm with a new set of random weight vectors. For more information, see The Self-Organizing Maps Algorithm.

The learning rate controls the amount of deformation experienced by each node in the mesh. For the self-organizing map to converge, Results Analytics decreases the learning rate exponentially with time.

The default is 0.8, which means that a node is moved by a maximum of 80% toward the training data point during the first iteration. Higher values for the learning rate result in arriving at the correct self-organizing map quickly, but they can sometimes produce enormous deformations (invalid self-organizing maps).

The neighborhood radius identifies the nodes in the neighborhood that are affected by a training data point. Similar to the learning rate, this radius is also reduced exponentially with time.

The default is 0.8, which means that nodes that lie within 80% of the span of the self-organizing map are influenced by the training data point in the first iteration, but that range of influence decreases very quickly in subsequent iterations. Low values for neighborhood radius can produce faster convergence, which in some cases can be premature (invalid self-organizing maps).

When a SOM is initialized with a random map, the seed value is used to generate the random data for the initial random map. The SOM can appear different for the same data set with different random initializations (controlled by the seed value), but the trends between parameters in the data set are preserved.

To create self-organizing maps, Results Analytics creates an initial map that is trained with the data set. The initial map can be generated with random data or with the linear correlations among the parameters in the training data set obtained through Principal Component Analysis (PCA). When the linear correlations are used to generate the map, a substantial aspect of the data trend is already captured before beginning the training iterations. The nonlinear trends are captured during the training iterations.

Using PCA, a good self-organizing map can be obtained with fewer iterations. However, for certain data sets the linear trends can be misleading and dominate the self-organizing map. In such cases, random initialization is preferred along with increasing maximum number of iterations to ensure convergence.

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