A modified metric to compute distance

摘要

Euclidean distance is used in many practical problems. This paper proposes a new metric which is close to the Euclidean distance and also computationally more efficient. This metric is helpful when the dimension of the data set is large. Bounds of a measure of merit of the new metric as well as of the City-block and Chessboard metrics with respect to the Euclidean metric are analytically established. The utility of this metric is shown on a randomly generated data set in the context of clustering.