# diss.CID

##### Complexity-Invariant Distance Measure For Time Series

Computes the distance based on the Euclidean distance corrected by the complexity estimation of the series.

##### Usage

`diss.CID(x, y)`

##### Arguments

- x
Numeric vector containing the first of the two time series.

- y
Numeric vector containing the second of the two time series.

##### Details

This distance is defined $$CID(x,y) = ED(x,y) \times CF(x,y)$$ where \(CF(x,y)\) is a complexity correction factor defined as: $$ max(CE(x), CE(y)) / min(CE(x), CE(y)) $$ and \(CE(x)\) is a compexity estimate of a time series \(x\). `diss.CID`

therefore increases the distance between series with different complexities. If the series have the same complexity estimate, the distance defenerates Euclidean distance. The complexity is defined in `diss.CID`

as:
$$ CE(x) = \sqrt{ \sum_{t=1} (x_{t+1} - x_t)^2 } $$

##### Value

The computed dissimilarity.

##### References

Batista, G. E., Wang, X., & Keogh, E. J. (2011). A Complexity-Invariant Distance Measure for Time Series. In SDM (Vol. 31, p. 32).

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/.

##### See Also

##### Examples

```
# NOT RUN {
n = 100
x <- rnorm(n) #generate sample series, white noise and a wiener process
y <- cumsum(rnorm(n))
diss.CID(x, y)
z <- rnorm(n)
w <- cumsum(rnorm(n))
series = rbind(x, y, z, w)
diss(series, "CID")
# }
```

*Documentation reproduced from package TSclust, version 1.2.4, License: GPL-2*