Vector Correlation: Review, Exposition, and Geographic Application

Correlation provides one of the most useful and widely employed techniques of data analysis in geography and in the larger scientific community. Most correlation coefficients describe relations among scalar data. Vector-valued data have received less attention despite their obvious geographic importance: vectors can describe motions across the landscape and relations between locations. After a brief review of the meaning and past applications of vector correlation, we present a vector correlation measure for comparing two-dimensional vectors. This vector correlation describes the goodness-of-fit of a relationship between two sets of vectors that includes translation, scaling, and either rotational or reflectional dependency. Linear regression parameters additionally emerge from the computation. We illustrate the properties of the vector correlation using wind velocity data.