FUNTA (version 0.1.0)

FUNTA: Obtain FUNTA pseudo-depth values

Description

For a given dataset, FUNTA pseudo-depth values can be obtained. FUNTA is a functional data depth that is based on the intersection angles that the centered functions form with each other.

Usage

FUNTA(Data, centered = FALSE, give.angles = FALSE, tick.dist = 1)

Arguments

Data

a matrix. Enter the discretized values of a functional data set in a n times T matrix, where n is the number of functional observations and T is the number of time points.

centered

boolean. If the data are already centered, that means, the mean of each row of Data is 0, this can be set to TRUE to save computation time. Default value is FALSE.

give.angles

boolean. If the intersection angles of each function with the other functions are to be displayed, set to TRUE. Default value is FALSE.

tick.dist

atomic vector. The distance between two neighbored time points can be set here. Default value is 1.

Value

give.angles = TRUE, a list of two elements FUNTA and Angles. Otherwise only the first element of that list is returned.

FUNTA

Vector of FUNTA values. First row of Data corresponds to first element of FUNTA.

Angles

List of intersection angles. First element of list corresponds to the intersection angles that the first row of Data has with every other row of Data, ordered by time point of intersection.

Details

The larger the value of FUNTA is, the less it can be regarded as a shape outlier, and vice versa. The values are bounded by 0 and 1.

References

Kuhnt, S.; Rehage, A. (2016) An angle-based multivariate functional pseudo-depth for shape outlier detection. Journal of Multivariate Analysis 146, 325-340.

Examples

x <- seq(0, 2*pi, by = 0.01)
y1 <- sin(x)
y2 <- sin(1.02*x)
y3 <- cos(x)
y <- rbind(y1, y2, y3)
FUNTA(y, tick.dist = 0.01)