TY - GEN

T1 - A multivariate correlation distance for vector spaces

AU - Connor, Richard

AU - Moss, Robert

PY - 2012/9/3

Y1 - 2012/9/3

N2 - We investigate a distance metric, previously defined for the measurement of structured data, in the more general context of vector spaces. The metric has a basis in information theory and assesses the distance between two vectors in terms of their relative information content. The resulting metric gives an outcome based on the dimensional correlation, rather than magnitude, of the input vectors, in a manner similar to Cosine Distance. In this paper the metric is defined, and assessed, in comparison with Cosine Distance, for its major properties: semantics, properties for use within similarity search, and evaluation efficiency. We find that it is fairly well correlated with Cosine Distance in dense spaces, but its semantics are in some cases preferable. In a sparse space, it significantly outperforms Cosine Distance over TREC data and queries, the only large collection for which we have a human-ratified ground truth. This result is backed up by another experiment over movielens data. In dense Cartesian spaces it has better properties for use with similarity indices than either Cosine or Euclidean Distance. In its definitional form it is very expensive to evaluate for high-dimensional sparse vectors; to counter this, we show an algebraic rewrite which allows its evaluation to be performed more efficiently. Overall, when a multivariate correlation metric is required over positive vectors, SED seems to be a better choice than Cosine Distance in many circumstances.

AB - We investigate a distance metric, previously defined for the measurement of structured data, in the more general context of vector spaces. The metric has a basis in information theory and assesses the distance between two vectors in terms of their relative information content. The resulting metric gives an outcome based on the dimensional correlation, rather than magnitude, of the input vectors, in a manner similar to Cosine Distance. In this paper the metric is defined, and assessed, in comparison with Cosine Distance, for its major properties: semantics, properties for use within similarity search, and evaluation efficiency. We find that it is fairly well correlated with Cosine Distance in dense spaces, but its semantics are in some cases preferable. In a sparse space, it significantly outperforms Cosine Distance over TREC data and queries, the only large collection for which we have a human-ratified ground truth. This result is backed up by another experiment over movielens data. In dense Cartesian spaces it has better properties for use with similarity indices than either Cosine or Euclidean Distance. In its definitional form it is very expensive to evaluate for high-dimensional sparse vectors; to counter this, we show an algebraic rewrite which allows its evaluation to be performed more efficiently. Overall, when a multivariate correlation metric is required over positive vectors, SED seems to be a better choice than Cosine Distance in many circumstances.

KW - cosine distance

KW - distance metric

KW - multivariate correlation

KW - similarity search

KW - vector space

UR - http://www.scopus.com/inward/record.url?scp=84865484370&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-32153-5_15

DO - 10.1007/978-3-642-32153-5_15

M3 - Conference contribution

AN - SCOPUS:84865484370

SN - 9783642321528

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 209

EP - 225

BT - Similarity Search and Applications - 5th International Conference, SISAP 2012, Proceedings

T2 - 5th International Conference on Similarity Search and Applications, SISAP 2012

Y2 - 9 August 2012 through 10 August 2012

ER -