Rough Sets and Current Trends in Computing

Volume 7413 of the series Lecture Notes in Computer Science pp 229-236

The Triangle Inequality versus Projection onto a Dimension in Determining Cosine Similarity Neighborhoods of Non-negative Vectors

  • Marzena KryszkiewiczAffiliated withInstitute of Computer Science, Warsaw University of Technology

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In many applications, objects are represented by non-negative vectors and cosine similarity is used to measure their similarity. It was shown recently that the determination of the cosine similarity of two vectors can be transformed to the problem of determining the Euclidean distance of normalized forms of these vectors. This equivalence allows applying the triangle inequality to determine cosine similarity neighborhoods efficiently. Alternatively, one may apply the projection onto a dimension to this end. In this paper, we prove that the triangle inequality is guaranteed to be a pruning tool, which is not less efficient than the projection in determining neighborhoods of non-negative vectors.