Sketches with unbalanced bits for similarity search

Abstract

In order to accelerate efficiency of similarity search, compact bit-strings compared by the Hamming distance, so called sketches, have been proposed as a form of dimensionality reduction. To maximize the data compression and, at the same time, minimize the loss of information, sketches typically have the following two properties: (1) each bit divides datasets approximately in halves, i.e. bits are balanced, and (2) individual bits have low pairwise correlations, preferably zero. It has been shown that sketches with such properties are minimal with respect to the retained information. However, they are very difficult to index due to the dimensionality curse – the range of distances is rather narrow and the distance to the nearest neighbour is high. We suggest to use sketches with unbalanced bits and we analyse their properties both analytically and experimentally. We show that such sketches can achieve practically the same quality of similarity search and they are much easier to index thanks to the decrease of distances to the nearest neighbours.