dist.circular {circular}

Distance Matrix Computation for Circular Data

Description

This function computes and returns the distance matrix computed by using the specified distance measure to compute the distances between the rows of a data matrix containing circular data.

Usage

dist.circular(x, method = "correlation", diag = FALSE, upper = FALSE)

Arguments

x

a numeric matrix of class circular.

method

the distance measure to be used. This must be one of "correlation", "angularseparation", "chord", "geodesic". Any unambiguous substring can be given.

diag

logical value indicating whether the diagonal of the distance matrix should be printed by print.dist.

upper

logical value indicating whether the upper triangle of the distance matrix should be printed by print.dist.

Details

Available distance measures are (written for two vectors x and y):

correlation:

\sqrt{1 - \rho} where \rho is the Circular Correlation coefficient defined as

\frac{\sum_{i=1}^n \sin(x_i - \mu_x) \sin(y_i - \mu_y)}{\sqrt{\sum_{i=1}^n \sin^2(x_i - \mu_x) \sum_{i=1}^n \sin^2(y_i - \mu_y)}}

and \mu_x, \mu_y are the mean direction of the two vectors

angularseparation:

\sum_{i=1}^n 1 - cos(x_i - y_i)

chord:

\sum_{i=1}^n \sqrt{2 (1 - \cos(x_i - y_i))}

geodesic:

\sum_{i=1}^n \pi - |\pi - |x_i - y_i|| where the abs(x - y) is expressed with an angle in [-pi,pi]

Missing values are allowed, and are excluded from all computations involving the rows within which they occur. Further, when Inf values are involved, all pairs of values are excluded when their contribution to the distance gave NaN or NA.
If some columns are excluded in calculating the sum is scaled up proportionally to the number of columns used. If all pairs are excluded when calculating a particular distance, the value is NA.

Value

dist.circular returns an object of class "dist".

The lower triangle of the distance matrix stored by columns in a vector, say do. If n is the number of observations, i.e., n <- attr(do, "Size"), then for i < j <= n, the dissimilarity between (row) i and j is do[n*(i-1) - i*(i-1)/2 + j-i]. The length of the vector is n*(n-1)/2, i.e., of order n^2.

The object has the following attributes (besides "class" equal to "dist"):

Size

integer, the number of observations in the dataset.

Labels

optionally, contains the labels, if any, of the observations of the dataset.

Diag, Upper

logicals corresponding to the arguments diag and upper above, specifying how the object should be printed.

call

optionally, the call used to create the object.

method

optionally, the distance method used; resulting from dist.circular(), the (match.arg()ed) method argument.

See Also

dist