README.md

In yingtliu/distPack: Evaluate distance matrice based on points in coordinates by different methods

distPack

A package bundles functions to evaluate distance matrices by different methods.

Methods included

• Euclidean: between two points in Euclidean space is a number, the length of a line segment between the two points. Formula: sqrt(sum((x - y)^ 2)). [https://en.wikipedia.org/wiki/Euclidean_distance]

• Manhattan: the distance between two points is the sum of the absolute differences of their Cartesian coordinates. Formula: sum(abs(x - y)).[https://en.wikipedia.org/wiki/Taxicab_geometry]

• Minkowski: a metric in a normed vector space which can be considered as a generalization of both the Euclidean distance and the Manhattan distance. Formula: sum(abs(x - y)^p)^(1/p) [https://en.wikipedia.org/wiki/Minkowski_distance]

• Chebyshev: a metric defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension. Formula: max(abs(x - y)) [https://en.wikipedia.org/wiki/Chebyshev_distance]

• Cosine: a measure of distance between two non-zero vectors of an inner product space. Formula: 1- Cosine similarity. [https://en.wikipedia.org/wiki/Cosine_similarity]

• Correlation: subtracted mean form of cosine distance. [https://github.com/JuliaStats/Distances.jl]

• Chi-square: The Euclidean distance between the components of the profiles of frequence table is called the chi-square distance. Formula: sum((x - y)^2 / (x + y)) [https://link.springer.com/referenceworkentry/10.1007%2F978-0-387-32833-1_53]

Accuracy

Since not all functions are available in R packages, I used a julia package called 'Distance'[https://github.com/JuliaStats/Distances.jl], which includes many distance functions. All provide good accuracy.

Efficiency

The functions are optimized by vectorization and minimize use of loops. The functions are tested with matrix in size 100 x 100 with 10000 elements. The elapsed time consumed are:

• euclidean: 0.08s
• manhattan: 0.11s
• cos_dis: 0.06s
• corr_dis: 0.07s
• chebyshev: 0.08s
• chiSq_dis: 0.06s
• minkowski: 0.10s

yingtliu/distPack documentation built on Jan. 1, 2021, 1:45 p.m.