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Self organizing maps are claimed to be able to visualize/cluster high-dimensional data in a smaller dimensional space. I have some difficulties in understanding this statement.
Consider a six-dimensional data set; the codebook vector/reference vector is also six-dimensional. According to the SOM algorithm, updating these reference vectors is also conducted in the six-dimensional vector space. If we are considering a two dimensional map, how should I understand the map between the six-dimensional data space and two-dimensional map space?