Indexing Techniques for Non-metric Music Dissimilarity Measures

Abstract

Many dissimilarity measures suitable for music retrieval do not satisfy all properties of a metric. This rules out the use of many established indexing structures, most of which rely on metricity. In this chapter, we give an overview of some existing approaches to building an indexing structure that makes efficient retrieval possible even if the underlying dissimilarity measure is not a metric.

For symmetric prametrics with metric subspaces, a tunneling technique allows one to search a non-metric space efficiently without false negatives. We give a detailed example for this case. In a query-by-example scenario, if queries are already part of a collection, and the triangle inequality is violated, one can enforce it in subsets of the collection by adding a small constant to the distance measure (Linear Constant Embedding). By embedding a non-metric distance function into a metric space in a way that preserves the ordering induced by the function on any query, one can make indexing methods applicable that usually only work for metrics (TriGen). Also, we present several probabilistic methods, including distance based hashing (DBH), clustering (DynDex), and a tree structure with pointers to near neighbours (SASH).