Global Collaboration through Local Interaction in Competitive Learning

The Self Organizing Map (SOM) is a competitive, unsupervised learningalgorithm capable of creating a low dimensional and discrete representation of high dimensional data. Sinceits initial conception, SOM has found broad application indata analytics, mainly for data clustering, function approximation, and dimensionality reduction (see [5, 8] for examples of applications). A SOM consists of a population of adaptive, interacting agents dubbed units. Each unit is represented in the sample spaceby vector (called weight) and it influences set of other units (neighbors). For each sample, the unit with the most similar weight is found (called the best matching unit - BMU), and its similarity to the sample is increased by altering itsweight. Subsequently, the neighbors of the BMU are also influenced by increasing their similarity to the sample - albeit to a lesser extend. Given enough data, the units' weight may converge to a low dimensional discrete representation of the data - called a feature map. Additionally, the units' weight will be placed meaningfully: neighboring units should contain similar features, sinceneighborhoods move en masse, a property known as topological preservation. It is possible however for this process to go awry; for example, limiting the influence of a unit over its neighbors may compromise the topological preservation[5, 4].