On Not Making Dissimilarities Euclidean
Non-metric dissimilarity measures may arise in practice e.g. when objects represented by sensory measurements or by structural descriptions are compared. It is an open issue whether such non-metric measures should be corrected in some way to be metric or even Euclidean. The reason for such corrections is the fact that pairwise metric distances are interpreted in metric spaces, while Euclidean distances can be embedded into Euclidean spaces. Hence, traditional learning methods can be used.
The k-nearest neighbor rule is usually applied to dissimilarities. In our earlier study [2,3], we proposed some alternative approaches to general dissimilarity representations (DRs). They rely either on an embedding to a pseudo-Euclidean space and building classifiers there or on constructing classifiers on the representation directly. In this paper, we investigate ways of correcting DRs to make them more Euclidean (metric) either by adding a proper constant or by some concave transformations. Classification experiments conducted on five dissimilarity data sets indicate that non-metric dissimilarity measures can be more beneficial than their corrected Euclidean or metric counterparts. The discriminating power of the measure itself is more important than its Euclidean (or metric) properties.
KeywordsEuclidean Space Average Error Negative Eigenvalue Handwritten Digit Deformable Template
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