Efficient Determination of Binary Non-negative Vector Neighbors with Regard to Cosine Similarity

Abstract

The cosine and Tanimoto similarity measures are often and successfully applied in classification, clustering and ranking in chemistry, biology, information retrieval, and text mining. A basic operation in such tasks is identification of neighbors. This operation becomes critical for large high dimensional data. The usage of the triangle inequality property was recently offered to alleviate this problem in the case of applying a distance metric. The triangle inequality holds for the Tanimoto dissimilarity, which functionally determines the Tanimoto similarity, provided the underlying data have a form of vectors with binary non-negative values of attributes. Unfortunately, the triangle inequality holds neither for the cosine similarity measure nor for its corresponding dissimilarity measure. However, in this paper, we propose how to use the triangle inequality property and/or bounds on lengths of neighbor vectors to efficiently determine non-negative binary vectors that are similar with regard to the cosine similarity measure.