Vector Correlation. Part 1.
GEORGE WASHINGTON UNIV WASHINGTON D C DEPT OF STATISTICS
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It is sometimes of interest to examine whether two sets of unit vectors, paired in some way, are correlated. The two sets of vectors, u1, u2,...,un and v1, v2,...,vn, may for example denote directional data e.g. the direction of magnetization of rock samples before and after laboratory treatment, and one wants to know if u1 is correlated with v1, u2 with v2, etc. A definition of vector correlation is proposed which makes the set v well-correlated with u if an orthogonal transformation can be found to align the vi close to the corresponding ui. This can be sharpened to insist that the necessary transformation be a rotation, or can be adapted to the case where the vectors must be taken as they are, with no rotation permitted. Modified author abstract
- Statistics and Probability