distantia Time Series Dissimilarity

Warning

Version 2.0.0 of distantia is a full re-write of the original package and will break existing workflows before making them better. Please refer to the Changelog for details before updating.

Summary

The R package distantia offers an efficient, feature-rich toolkit for managing, comparing, and analyzing time series data. It is designed to handle a wide range of scenarios, including:

• Multivariate and univariate time series.
• Regular and irregular sampling.
• Time series of different lengths.

Key Features

Comprehensive Analytical Tools

• 10 distance metrics: see distantia::distances.
• The normalized dissimilarity metric psi.
• Free and Restricted Dynamic Time Warping (DTW) for shape-based comparison.
• A Lock-Step method for sample-to-sample comparison
• Restricted permutation tests for robust inferential support.
• Analysis of contribution to dissimilarity of individual variables in multivariate time series.
• Hierarchical and K-means clustering of time series based on dissimilarity matrices.

Computational Efficiency

• A C++ back-end powered by Rcpp.
• Parallel processing managed through the future package.
• Efficient data handling via zoo.

Time Series Management Tools

• Introduces time series lists (TSL), a versatile format for handling collections of time series stored as lists of zoo objects.
• Includes a suite of tsl_...() functions for generating, resampling, transforming, analyzing, and visualizing univariate and multivariate time series.

Citation

If you find this package useful, please cite it as:

Blas M. Benito, H. John B. Birks (2020). distantia: an open-source toolset to quantify dissimilarity between multivariate ecological time-series. Ecography, 43(5), 660-667. doi: 10.1111/ecog.04895.

Blas M. Benito (2024). distantia: A Toolset for Time Series Dissimilarity Analysis. R package version 2.0.0. url: https://blasbenito.github.io/distantia/.

Install

Version 1.0.2 of distantia can be installed from CRAN.

install.packages("distantia")

Version 2.0.0 can be installed from GitHub.

remotes::install_github(
  repo = "blasbenito/distantia", 
  ref = "development"
  )

Getting Started

This section showcases several features of the package distantia. Please, check the Articles section for further details.

Setup

All heavy duty functions in distantia support parallelization via the future package. However, due to the high efficiency of the C++ backend of distantia, parallel execution is only worth it for very large datasets and restricted permutation analyses.

Progress bars provided by the progressr package are also available. Unfortunately, the latter does not work in Rmarkdown documents like this one.

library(distantia, quietly = TRUE)
library(future)
# library(progressr)

#parallelization setup
# future::plan(future::multisession)

#progress bar (does not work in Rmarkdown)
#progressr::handlers(global = TRUE)

Example Data

The albatross data frame contains daily GPS data of 4 individuals of Waved Albatross in the Pacific captured during the summer of 2008. Below are the first 10 rows of this data frame:

#>   name       time         x         y     speed temperature  heading
#> 1 X132 2008-05-31 -89.62097 -1.389512 0.1473333    29.06667 212.0307
#> 2 X132 2008-06-01 -89.62101 -1.389508 0.2156250    28.25000 184.0337
#> 3 X132 2008-06-02 -89.62101 -1.389503 0.2143750    27.68750 123.1269
#> 4 X132 2008-06-03 -89.62099 -1.389508 0.2018750    27.81250 183.4600
#> 5 X132 2008-06-04 -89.62098 -1.389507 0.2256250    27.68750 114.8931
#> 6 X132 2008-06-05 -89.62925 -1.425734 1.3706667    25.73333 245.8033

The code below transforms the data to a Time Series List with tsl_initialize() and applies global scaling and centering with tsl_transform() and f_scale_global to facilitate time series comparisons.

tsl <- tsl_initialize(
  x = distantia::albatross,
  name_column = "name",
  time_column = "time",
  lock_step = TRUE
) |> 
  tsl_transform(
    f = f_scale_global
  )

tsl_plot(
  tsl = tsl,
  ylim = "relative"
)

Dissimilarity Analysis

Lock-Step Analysis

Lock-step analysis performs direct comparisons between samples observed at the same time without any time distortion. It requires time series of the same length preferably observed at the same times.

df_ls <- distantia(
  tsl = tsl,
  lock_step = TRUE
)

df_ls[, c("x", "y", "psi")]
#>      x    y      psi
#> 1 X132 X134 1.888451
#> 3 X132 X153 2.128340
#> 5 X134 X153 2.187862
#> 4 X134 X136 2.270977
#> 2 X132 X136 2.427479
#> 6 X136 X153 2.666099

The “psi” column shows normalized dissimilarity values and is used to sort the data frame from lowest to highest dissimilarity. Hence, the first row shows the most similar pair of time series.

The function distantia_boxplot() enables a quick identification of the time series that are either more dissimilar (top) or similar (bottom) to others.

distantia_boxplot(df = df_ls, text_cex = 0.8)

Dynamic Time Warping

By default, distantia() computes unrestricted dynamic time warping with orthogonal and diagonal least cost paths.

df_dtw <- distantia(
  tsl = tsl
)

df_dtw[, c("x", "y", "psi")]
#>      x    y      psi
#> 1 X132 X134 1.299380
#> 5 X134 X153 2.074241
#> 3 X132 X153 2.091923
#> 4 X134 X136 2.358040
#> 2 X132 X136 2.449381
#> 6 X136 X153 2.666099

The function distantia_dtw_plot() provides detailed insights into the alignment between a pair of time series resulting from DTW.

distantia_dtw_plot(
  tsl = tsl[c("X132", "X153")]
)

Deviations from the perfect diagonal in the least-cost path reveal adjustments made by DTW to align time series by shape rather than time.

The article Dynamic Time Warping vs Lock-Step provides further insights on the advantages and disadvantages of each method in different scenarios.

Permutation Test

The function distantia() implements restricted permutation tests to assess the significance of dissimilarity scores. It provides several setups to support different assumptions.

For example, the configuration below rearranges complete rows within 7-day blocks, assuming strong dependencies within rows and between observations that are close in time.

future::plan(future::multisession)

df_dtw <- distantia(
  tsl = tsl,
  repetitions = 1000,
  permutation = "restricted_by_row",
  block_size = 7 #one week
)

future::plan(future::sequential)

df_dtw[, c("x", "y", "psi", "p_value")]
#>      x    y      psi p_value
#> 1 X132 X134 1.299380   0.001
#> 5 X134 X153 2.074241   0.001
#> 3 X132 X153 2.091923   0.001
#> 4 X134 X136 2.358040   0.184
#> 2 X132 X136 2.449381   0.499
#> 6 X136 X153 2.666099   0.007

The “p_value” column represents the fraction of permutations yielding a psi score lower than the observed value, and indicates the strength of similarity between two time series. A significance threshold (e.g., 0.05, depending on iterations) helps identifying pairs of time series with a robust similarity.

Variable Importance

When comparing multivariate time series, certain variables contribute more to similarity or dissimilarity. The momentum() function uses a leave-one-out algorithm to quantify each variable’s contribution to the overall dissimilarity between two time series.

df_importance <- momentum(
  tsl = tsl
)

df_importance[, c("x", "y", "variable", "importance", "effect")]
#>       x    y    variable   importance               effect
#> 1  X132 X134           x   87.6066043 decreases similarity
#> 2  X132 X134           y   93.9587187 decreases similarity
#> 3  X132 X134       speed  -21.9171171 increases similarity
#> 4  X132 X134 temperature   72.8121621 decreases similarity
#> 5  X132 X134     heading  -38.0165137 increases similarity
#> 6  X132 X136           x   48.3845903 decreases similarity
#> 7  X132 X136           y   93.5214543 decreases similarity
#> 8  X132 X136       speed  -61.1729252 increases similarity
#> 9  X132 X136 temperature  356.8824838 decreases similarity
#> 10 X132 X136     heading -102.9830173 increases similarity
#> 11 X132 X153           x  427.7381576 decreases similarity
#> 12 X132 X153           y  156.1285451 decreases similarity
#> 13 X132 X153       speed  -40.9249630 increases similarity
#> 14 X132 X153 temperature  -14.2831545 increases similarity
#> 15 X132 X153     heading  -79.3532025 increases similarity
#> 16 X134 X136           x   61.3361468 decreases similarity
#> 17 X134 X136           y  108.9650664 decreases similarity
#> 18 X134 X136       speed  -59.2603918 increases similarity
#> 19 X134 X136 temperature  310.6812842 decreases similarity
#> 20 X134 X136     heading  -90.2797292 increases similarity
#> 21 X134 X153           x  592.0783167 decreases similarity
#> 22 X134 X153           y  116.4310429 decreases similarity
#> 23 X134 X153       speed  -52.4149093 increases similarity
#> 24 X134 X153 temperature    0.9936944 decreases similarity
#> 25 X134 X153     heading  -85.0271172 increases similarity
#> 26 X136 X153           x  507.6153648 decreases similarity
#> 27 X136 X153           y   56.6957442 decreases similarity
#> 28 X136 X153       speed  -65.4516103 increases similarity
#> 29 X136 X153 temperature  240.9053814 decreases similarity
#> 30 X136 X153     heading -116.2461929 increases similarity

Positive “importance” values indicate variables contributing to dissimilarity, while negative values indicate contribution to similarity. The function documentation provides more details on how importance scores are computed.

The momentum_boxplot() function provides a quick insight into which variables contribute the most to similarity or dissimilarity across all pairs of time series.

momentum_boxplot(
  df = df_importance
)

Clustering

The package distantia provides tools to group together time series by dissimilarity using hierarchical or K-means clustering. The example below applies the former to the albatross dataset to find out groups of individuals with the most similar movement time series.

dtw_hclust <- distantia_cluster_hclust(
  df = df_dtw,
  clusters = NULL, #automatic mode
  method = NULL    #automatic mode
  )

#cluster object
dtw_hclust$cluster_object
#> 
#> Call:
#> stats::hclust(d = d_dist, method = method)
#> 
#> Cluster method   : ward.D 
#> Number of objects: 4

#number of clusters
dtw_hclust$clusters
#> [1] 2

#clustering data frame
#group label in column "cluster"
#negatives in column "silhouette_width" higlight anomalous cluster assignation
dtw_hclust$df
#>   name cluster silhouette_width
#> 1 X132       1        0.3077225
#> 2 X134       1        0.2846556
#> 3 X136       2        0.0000000
#> 4 X153       1        0.2186781

#tree plot
par(mar=c(3,1,1,3))

plot(
  x = stats::as.dendrogram(
    dtw_hclust$cluster_object
    ),
  horiz = TRUE
)

This is just a summary of the features implemented in the package. Please visit the Articles section to find out more about distantia.

Getting help

If you encounter bugs or issues with the documentation, please file a issue on GitHub.