G. Drakopoulos, I. Giannoukou, Ph. Mylonas, S. Sioutas 
On Tensor Distances for Self Organizing Maps: Clustering Cognitive Tasks 
In S. Hartmann et al. (Eds.): DEXA 2020, LNCS 12392, pp. 195–210, 2020, Springer Nature, Switzerland 
ABSTRACT

Self organizing maps (SOMs) are neural networks designed to be in an unsupervised way to create connections, learned through a modified Hebbian rule, between a high (the input vector space) and a lowdimensional space (the cognitive map) based solely on distances in the input vector space. Moreover, the cognitive map is segmentwise continuous and preserves many of the major topological features of the latter. Therefore, neurons, trained using a Hebbian learning rule, can approximate the shape of any arbitrary manifold provided there are enough neurons to accomplish this. Moreover, the cognitive map can be readily used for clustering and visualization. Because of the above properties, SOMs are often used in big data pipelines. This conference paper focuses on a multilinear distance metric for the input vector space which adds flexibility in two ways. First, clustering can be extended to higher order data such as images, graphs, matrices, and time series. Second, the resulting clusters are unions of arbitrary shapes instead of fixed ones such as rectangles in case of 1 norm or circles in case of 2 norm. As a concrete example, the proposed distance metric is applied to an anonymized and open under the Creative Commons license cognitive multimodal dataset of fMRI images taken during three distinct cognitive tasks. Keeping the latter as ground truth, a subset of these images is clustered with SOMs of various configurations. The results are evaluated using the corresponding confusion matrices, topological error rates, activation set change rates, and intracluster distance variations.

27 October , 2020 
G. Drakopoulos, I. Giannoukou, Ph. Mylonas, S. Sioutas, "On Tensor Distances for Self Organizing Maps: Clustering Cognitive Tasks", In S. Hartmann et al. (Eds.): DEXA 2020, LNCS 12392, pp. 195–210, 2020, Springer Nature, Switzerland 
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