Performance of Minkowski-type Distances in Similarity Search - A Geometrical Approach

This work is an attempt at exploring distances, in the context of Similarity Search (SS), where an approximate match for a given query q is sought from a given dataset X. One view is that the query q itself is a noise η corrupted version of an x ∈ X. Recently, François et al., [1] had studied the efficacy of Minkowski-type distances in retrieving the x given q in the presence of both white and highly coloured noise η. Noting that not all conclusions in [1] hold true, in high dimensions, in this work, we have undertaken a similar study but that which differs in the following way: Taking into account various other factors not considered in [1]. Our geometric approach to these investigations have revealed hitherto unknown impact of both the domain geometry and denseness of the data set and has led us to propose an index which aids in explaining the simulation results obtained and in understanding the impact of the 3D's of Dimensionality, Domain geometry and Denseness of the data on the appropriateness of a Distance function in the setting of SS algorithms.