Calibration of self-organizing maps for classification tasks

In many practical applications of self-organizing maps (SOM, Kohonen Feature Maps), these networks are used for classification tasks. In order to be used for classification, the output neurons have to be assigned to classes which correspond to clusters in the input space (feature space) of the SOM (calibration). Usually, a SOM is calibrated after an unsupervised training, when clusters in the input space are represented by clusters in the weight space. The article presents two new calibration algorithms (one-point-algorithm and many-points-algorithm) which are based on statistical assumptions about the shape of the clusters in the weight space. These clusters are modeled by means of multivariate Gaussian distributions, where the unknown parameters of these distributions and the assignment of output neurons to classes (i. e. an appropriate partition of the output neurons) are determined using a maximum likelihood (ML) estimation. The properties of the two iterative algorithms, monotonic decrease with respect to the optimization criterion chosen and termination, are shown by means of benchmark data (PenDigits: classification of handwritten digits).