# dtw_lb: DTW distance matrix guided by Lemire's improved lower bound In dtwclust: Time Series Clustering Along with Optimizations for the Dynamic Time Warping Distance

 dtw_lb R Documentation

## DTW distance matrix guided by Lemire's improved lower bound

### Description

Calculation of a distance matrix with the Dynamic Time Warping (DTW) distance guided by Lemire's improved lower bound (LB_Improved).

### Usage

```dtw_lb(
x,
y = NULL,
window.size = NULL,
norm = "L1",
error.check = TRUE,
pairwise = FALSE,
dtw.func = "dtw_basic",
nn.margin = 1L,
...
)
```

### Arguments

 `x, y` A matrix or data frame where rows are time series, or a list of time series. `window.size` Window size to use with the LB and DTW calculation. See details. `norm` Either `"L1"` for Manhattan distance or `"L2"` for Euclidean. `error.check` Logical indicating whether the function should try to detect inconsistencies and give more informative errors messages. Also used internally to avoid repeating checks. `pairwise` Calculate pairwise distances? `dtw.func` Which function to use for the core DTW calculations, either "dtw" or "dtw_basic". See `dtw::dtw()` and `dtw_basic()`. `nn.margin` Either 1 to search for nearest neighbors row-wise, or 2 to search column-wise. Only implemented for `dtw.func` = "dtw_basic". `...` Further arguments for `dtw.func` or `lb_improved()`.

### Details

This function first calculates an initial estimate of a distance matrix between two sets of time series using `lb_improved()` (the `proxy::dist()` version). Afterwards, it uses the estimate to calculate the corresponding true DTW distance between only the nearest neighbors of each series in `x` found in `y`, and it continues iteratively until no changes in the nearest neighbors occur.

If only `x` is provided, the distance matrix is calculated between all its time series, effectively returning a matrix filled with the LB_Improved values.

This could be useful in case one is interested in only the nearest neighbor of one or more series within a dataset.

The windowing constraint uses a centered window. The calculations expect a value in `window.size` that represents the distance between the point considered and one of the edges of the window. Therefore, if, for example, `window.size = 10`, the warping for an observation x_i considers the points between x_{i-10} and x_{i+10}, resulting in `10(2) + 1 = 21` observations falling within the window.

### Value

The distance matrix with class `crossdist`.

### Parallel Computing

Please note that running tasks in parallel does not guarantee faster computations. The overhead introduced is sometimes too large, and it's better to run tasks sequentially.

This function uses the `RcppParallel` package for parallelization. It uses all available threads by default (see `RcppParallel::defaultNumThreads()`), but this can be changed by the user with `RcppParallel::setThreadOptions()`.

An exception to the above is when this function is called within a `foreach` parallel loop made by dtwclust. If the parallel workers do not have the number of threads explicitly specified, this function will default to 1 thread per worker. See the parallelization vignette for more information (`browseVignettes("dtwclust")`).

### Note

This function uses a lower bound that is only defined for time series of equal length.

The `proxy::dist()` version simply calls this function.

A considerably large dataset is probably necessary before this is faster than using `dtw_basic()` with `proxy::dist()`. Also note that `lb_improved()` calculates warping envelopes for the series in `y`, so be careful with the provided order and `nn.margin` (see examples).

### Author(s)

Alexis Sarda-Espinosa

### References

Lemire D (2009). “Faster retrieval with a two-pass dynamic-time-warping lower bound .” Pattern Recognition, 42(9), pp. 2169 - 2180. ISSN 0031-3203, doi: 10.1016/j.patcog.2008.11.030, https://www.sciencedirect.com/science/article/pii/S0031320308004925.

`lb_keogh()`, `lb_improved()`

### Examples

```
data(uciCT)

# Reinterpolate to same length
data <- reinterpolate(CharTraj, new.length = max(lengths(CharTraj)))

# Calculate the DTW distance between a certain subset aided with the lower bound
system.time(d <- dtw_lb(data[1:5], data[6:50], window.size = 20L))

# Nearest neighbors
NN1 <- apply(d, 1L, which.min)

# Calculate the DTW distances between all elements (slower)
system.time(d2 <- proxy::dist(data[1:5], data[6:50], method = "DTW",
window.type = "sakoechiba", window.size = 20L))

# Nearest neighbors
NN2 <- apply(d2, 1L, which.min)

# Calculate the DTW distances between all elements using dtw_basic
# (might be faster, see notes)
system.time(d3 <- proxy::dist(data[1:5], data[6:50], method = "DTW_BASIC",
window.size = 20L))

# Nearest neighbors
NN3 <- apply(d3, 1L, which.min)

# Change order and margin for nearest neighbor search
# (usually fastest, see notes)
system.time(d4 <- dtw_lb(data[6:50], data[1:5],
window.size = 20L, nn.margin = 2L))

# Nearest neighbors *column-wise*
NN4 <- apply(d4, 2L, which.min)

# Same results?
identical(NN1, NN2)
identical(NN1, NN3)
identical(NN1, NN4)

```

dtwclust documentation built on Sept. 24, 2022, 5:05 p.m.