R: Global constraints and windowing functions for DTW

dtwWindowingFunctions {dtw} | R Documentation

## Global constraints and windowing functions for DTW

### Description

Various global constraints (windows) which can be applied to the `window.type` argument of `dtw()`, including the Sakoe-Chiba band, the Itakura parallelogram, and custom functions.

### Usage

    sakoeChibaWindow(iw, jw, window.size, ...)

    slantedBandWindow(iw, jw, query.size, reference.size, window.size, ...)

    itakuraWindow(iw, jw, query.size, reference.size, ...)

    dtwWindow.plot(fun, query.size = 200, reference.size = 220, ...)

    noWindow(iw, jw, ...)

### Arguments

`iw` | index in the query (row) – automatically set
`jw` | index in the reference (column) – automatically set
`window.size` | window size, used by some windowing functions – must be set
`...` | additional arguments passed to windowing functions
`query.size` | size of the query time series – automatically set
`reference.size` | size of the reference time series – automatically set
`fun` | a windowing function

### Details

Windowing functions can be passed to the `window.type` argument in `dtw()` to put a global constraint to the warping paths allowed. They take two integer arguments (plus optional parameters) and must return a boolean value `TRUE` if the coordinates fall within the allowed region for warping paths, `FALSE` otherwise.

User-defined functions can read variables `reference.size`, `query.size` and `window.size`; these are pre-set upon invocation. Some functions require additional parameters which must be set (e.g. `window.size`). User-defined functions are free to implement any window shape, as long as at least one path is allowed between the initial and final alignment points, i.e., they are compatible with the DTW constraints.

The `sakoeChibaWindow` function implements the Sakoe-Chiba band, i.e. `window.size` elements around the `main` diagonal. If the window size is too small, i.e. if `reference.size`-`query.size` > `window.size`, warping becomes impossible.

An `itakuraWindow` global constraint is still provided with this package. See example below for a demonstration of the difference between a local the two.

The `slantedBandWindow` (package-specific) is a band centered around the (jagged) line segment which joins element `[1,1]` to element `[query.size,reference.size]`, and will be `window.size` columns wide. In other words, the "diagonal" goes from one corner to the other of the possibly rectangular cost matrix, therefore having a slope of `M/N`, not 1.

`dtwWindow.plot` visualizes a windowing function. By default it plots a 200 x 220 rectangular region, which can be changed via `reference.size` and `query.size` arguments.

### Value

Windowing functions return `TRUE` if the coordinates passed as arguments fall within the chosen warping window, `FALSE` otherwise. User-defined functions should do the same.

### Note

Although `dtwWindow.plot` resembles object-oriented notation, there is not a such a dtwWindow class currently.

A widely held misconception is that the "Itakura parallelogram" (as described in reference 2) is a global constraint, i.e. a window. To the author's knowledge, it instead arises from the local slope restrictions imposed to the warping path, such as the one implemented by the `typeIIIc()` step pattern.

### Author(s)

Toni Giorgino

### References

1. Sakoe, H.; Chiba, S., Dynamic programming algorithm optimization for spoken word recognition, Acoustics, Speech, and Signal Processing, IEEE Transactions on , vol.26, no.1, pp. 43-49, Feb 1978 doi: 10.1109/TASSP.1978.1163055

2. Itakura, F., Minimum prediction residual principle applied to speech recognition, Acoustics, Speech, and Signal Processing, IEEE Transactions on , vol.23, no.1, pp. 67-72, Feb 1975. doi: 10.1109/TASSP.1975.1162641

### Examples

    ## Display some windowing functions
    dtwWindow.plot(itakuraWindow, main="So-called Itakura parallelogram window")
    dtwWindow.plot(slantedBandWindow, window.size=2,
      reference=13, query=17, main="The slantedBandWindow at window.size=2")

    ## Asymmetric step with Sakoe-Chiba band

    idx<-seq(0,6.28,len=100);
    query<-sin(idx)+runif(100)/10;
    reference<-cos(idx);

    asyband<-dtw(query,reference,keep=TRUE,
                 step=asymmetric,
                 window.type=sakoeChibaWindow,
                 window.size=30                  );

    dtwPlot(asyband,type="density",main="Sine/cosine: asymmetric step, S-C window")

[Package dtw version 1.22-3 Index]