# Complexity-Invariant Distance Measure For Time Series

### Description

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

### Usage

1 | ```
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 ( diff(x)^2 ) )*

### Value

The computed dissimilarity.

### Author(s)

Pablo Montero Manso, JosÃ© Antonio Vilar.

### 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

`diss`

, `diss.CORT`

### Examples

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