# mvm: Minimum Variance Matching algorithm In dtw: Dynamic Time Warping Algorithms

## Description

Step patterns to compute the Minimum Variance Matching (MVM) correspondence between time series

## Usage

 `1` ```mvmStepPattern(elasticity = 20) ```

## Arguments

 `elasticity` integer: maximum consecutive reference elements skippable

## Details

The Minimum Variance Matching algorithm (1) finds the non-contiguous parts of reference which best match the query, allowing for arbitrarily long "stretches" of reference to be excluded from the match. All elements of the query have to be matched. First and last elements of the query are anchored at the boundaries of the reference.

The `mvmStepPattern` function creates a `stepPattern` object which implements this behavior, to be used with the usual `dtw()` call (see example). MVM is computed as a special case of DTW, with a very large, asymmetric-like step pattern.

The `elasticity` argument limits the maximum run length of reference which can be skipped at once. If no limit is desired, set `elasticity` to an integer at least as large as the reference (computation time grows linearly).

## Value

A step pattern object.

Toni Giorgino

## References

Latecki, L. J.; Megalooikonomou, V.; Wang, Q. & Yu, D. An elastic partial shape matching technique Pattern Recognition, 2007, 40, 3069-3080. doi: 10.1016/j.patcog.2007.03.004

Other objects in `stepPattern()`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```## The hand-checkable example given in Fig. 5, ref.  above diffmx <- matrix( byrow=TRUE, nrow=5, c( 0, 1, 8, 2, 2, 4, 8, 1, 0, 7, 1, 1, 3, 7, -7, -6, 1, -5, -5, -3, 1, -5, -4, 3, -3, -3, -1, 3, -7, -6, 1, -5, -5, -3, 1 ) ) ; ## Cost matrix costmx <- diffmx^2; ## Compute the alignment al <- dtw(costmx,step.pattern=mvmStepPattern(10)) ## Elements 4,5 are skipped print(al\$index2) plot(al,main="Minimum Variance Matching alignment") ```