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 low-dimensional 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 \(\ell _1\) norm or circles in case of \(\ell _2\) 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 intra-cluster distance variations.
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Acknowledgment
This conference paper is part of the Interreg V-A Greece-Italy Programme 2014-2020 project “Fostering capacities and networking of industrial liaison offices, exploitation of research results, and business support” (ILONET), co-funded by the European Union, European Regional Development Funds (ERDF), and by the national funds of Greece and Italy.
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Drakopoulos, G., Giannoukou, I., Mylonas, P., Sioutas, S. (2020). On Tensor Distances for Self Organizing Maps: Clustering Cognitive Tasks. In: Hartmann, S., Küng, J., Kotsis, G., Tjoa, A.M., Khalil, I. (eds) Database and Expert Systems Applications. DEXA 2020. Lecture Notes in Computer Science(), vol 12392. Springer, Cham. https://doi.org/10.1007/978-3-030-59051-2_13
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