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Note 1: Sparse data.

If the data set is sparse, consisting only of a few samples per map unit, it becomes more difficult to measure topology preservation. A judgment of the continuity of the mapping based on a sum over the data samples may become inaccurate. It may then be useful to consider, along with the distance between the nearest and second-nearest reference vector as was done in Publication 7, the distance to the third-closest reference vector etc., weighted suitably.

Sami Kaski
Mon Mar 31 23:43:35 EET DST 1997