# diss.CORT: Dissimilarity Index Combining Temporal Correlation and Raw... In TSclust: Time Series Clustering Utilities

## Description

Computes an adaptive dissimilarity index between two time series that covers both dissimilarity on raw values and dissimilarity on temporal correlation behaviors.

## Usage

 1 diss.CORT(x, y, k = 2, deltamethod="Euclid")

## Arguments

 x Numeric vector containing the first of the two time series. y Numeric vector containing the second of the two time series. k Parameter controlling the weight of the dissimilarity between dynamic behaviors (See Details). deltamethod Defines the method for the raw data discrepancy. Either "Euclid", "Frechet" or "DTW".

## Details

The dissimilarity between time series x and y is given by:

d(x,y) = Φ[CORT(x,y)] δ(x,y)

where:

CORT(x,y) measures the proximity between the dynamic behaviors of x and y by means of the first order temporal correlation coefficient defined by:

CORT(x,y) = ∑ ( ( x_(t+1) - x_t ) ( y_(t+1) - y_t ) ) / (√( ∑ (x_(t+1) - x_t)^2) √( ∑ (y_(t+1) - y_t)^2))

Φ[u] is an adaptive tuning function taking the form:

2/(1+exp(ku))

with k ≥q 0 so that both Φ and k modulate the weight that CORT(x,y) has on d(x,y).

δ(x,y) denotes a dissimilarity measure between the raw values of series x and y, such as the Euclidean distance, the Frechet distance or the Dynamic Time Warping distance. Note that d(x,y) = δ(x,y) if k=0.

More details of the procedure can be seen in Chouakria-Douzal and Nagabhushan (2007).

deltamethod (δ) can be either Euclidean (deltamethod = "Euclid"), Frechet ( deltamethod = "Frechet") or Dynamic Time Warping (deltamethod ="DTW") distances. When calling from dis.CORT, DTW uses Manhattan as local distance.

## Value

The computed distance.

## Author(s)

Pablo Montero Manso, José Antonio Vilar.

## References

Chouakria-Douzal, A. and Nagabhushan P. N. (2007) Adaptive dissimilarity index for measuring time series proximity. Adv. Data Anal. Classif., 1(1), 5–21.

Montero, P and Vilar, J.A. (2014) TSclust: An R Package for Time Series Clustering. Journal of Statistical Software, 62(1), 1-43. http://www.jstatsoft.org/v62/i01/.

## Examples

 1 2 3 4 5 6 7 8 9 10 11 12 13 ## Create three sample time series x <- cumsum(rnorm(100)) y <- cumsum(rnorm(100)) z <- sin(seq(0, pi, length.out=100)) ## Compute the distance and check for coherent results diss.CORT(x, y, 2) diss.CORT(x, z, 2) diss.CORT(y, z, 2) #create a dist object for its use with clustering functions like pam or hclust ## Not run: diss( rbind(x,y,z), "CORT", k=3, deltamethod="DTW") ## End(Not run)

### Example output

Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE