A Tunneling-Vantage Indexing Method for Non-Metrics

We consider an instance of the Earth Mover’s Distance (EMD) useful for comparing rhythmical patterns. To make searches for r-near neighbours efficient, we decompose our search space into disjoint metric subspaces, in each of which the EMD reduces to the l1 norm. We then use a combined approach of two methods, one for searching within the subspaces, the other for searching between them. For the former, we show how one can use vantage indexing without false positives nor false negatives for solving the exact rnear neighbour problem, and find an optimum number and placement of vantage objects for this result. For searching between subspaces, where the EMD is not a metric, we show how one can guarantee that still no false negatives occur, and the percentage of false positives is reduced as the search radius is increased.