correlated-timelines

This repository contains the two datasets used for the user study presented in the submitted manucript Investigating Collaboration Coupling Styles in Synchronous Asymmetric Interaction within the context of Collaborative Immersive Analytics by Nico Reski, Aris Alissandrakis, and Andreas Kerren, as well as the R code used to generate them and examples of using the provided functions.

The study required a multivariate spatio-temporal dataset for participants to collaborate on and complete analytics tasks. We came up with the approach of generating correlated (according to a given model) timeline data as a flexible way to have task setups of comparable structure and complexity for when the participants needed to switch interfaces. Please see the article for more details on the study purpose, results, and analysis.

Datasets used

The two datasets used in the study are provieded in the two CSV files fruits_dataset.csv and veggies_dataset.csv.

Each file has four parameters: location (39 names of European countries), dimension (five for plant and two for climate), time (a series of 150 events), and value (values for the dimensions). The two dimensions for climate are sunlight and humidity, and the five for plants are either Apples, Oranges, Bananas, Berries, and Grapes for the fruits dataset, or Tomatoes, Carrots, Potatoes, Cabbages, and Lettuces for the veggies dataset. Each file has 39 locations x 7 dimensions x 150 time events = 40,950 rows.

Independent of the location, the climate and plant data are meant to correlate to each other as follows for the fruits task setup:

	Apples	Oranges	Bananas	Berries	Grapes
humidity	positive	positive	negative	negative	positive
sunlight	positive	negative	negative	positive	positive

and for the veggies task setup:

	Tomatoes	Carrots	Potatoes	Cabbages	Letuces
humidity	negative	positive	positive	positive	negative
sunlight	positive	positive	positive	negative	negative

The pairs of participants, using a combination of immersive and non-immersive interfaces, were asked to collaboratively determine the correlations between the two climate parameters and the five plant ones.

The datasets were generated using the provided R functions -- for each location the humidity and sunlight timelines were generated, and then the timelines for each of the five plants, according to one of the models above (adding the two climate timelines and using the weights from the model, either one or minus one).

The following two figures show that the generated data followed the two models; note that due to randomness in the process, the data for some locations were strongly or moderately correlated (but still along the intended direction). Additionally, for some locations the p-values were above the .01 significance level, and were excluded from shown here (resulting in less than 39 sample sizes in some cases).

Fruits	Veggies

R code

The method used can easily be generalized to have any number of timeline data correlated in various ways, therefore we provide here the R code used. The file correlated-timelines_functions.r includes the code for three useful functions:

• generate_timeline to generate a timeline (a vector of length sample_size) according to various parameters,
  • min_val, max_val -- minimum and maximum values,
  • slope -- regression slope,
  • noise_amount -- amplitude of normally distributed random noise to be added,
  • bumps -- a series of normal distributions to be added to the timeline, defined as a list of vectors containing values for
    • means m (where each bump is centered along the timeline),
    • standard deviation sd (spread of each bump),
    • peak amplitude a of each bump,
• smooth_noise to generate a smoothed spline that can be added as noise to any generated timelines, and
• scale_and_position_timeline to scale and position vertically any previously generated timeline.

Example of use

As an example of using these functions, the following code produced the data shown in the figure below:

example_timeline = generate_timeline()
example_timeline = smooth.spline(example_timeline, df=25)$y
example_timeline = example_timeline + smooth_noise()
example_timeline = scale_and_position_timeline(example_timeline, range=50, position = 75)

Furthermore, the following code produced the data shown in the figure below; two timelines were generated (as above) and then were added in a weighted way to generate a third timeline which then postively correlated with the first and negatively correlated withe the second timeline.

reference_timeline1 = generate_timeline(bumps = list(m=c(25), sd=c(5), a=c(25)), slope=.1)
reference_timeline1 = smooth.spline(reference_timeline1, df=25)$y
reference_timeline1 = reference_timeline1 + smooth_noise()
reference_timeline1 = scale_and_position_timeline(reference_timeline1, range=40, position = 20)

reference_timeline2 = generate_timeline(bumps = list(m=c(125), sd=c(5), a=c(5)), slope=0, noise_amount = .05)
reference_timeline2 = smooth.spline(reference_timeline2, df=25)$y
reference_timeline2 = reference_timeline2 + smooth_noise()
reference_timeline2 = scale_and_position_timeline(reference_timeline2, range=40, position = 40)

correlated_timeline = reference_timeline1*1.0 + reference_timeline2*(-1.0)
correlated_timeline = correlated_timeline + smooth_noise()
correlated_timeline = scale_and_position_timeline(correlated_timeline, range=20, position = 80)

In the above example, the Pearson correlation coefficient and the p-values between the correlated timeline and the timelines to be positively and negatively correlated to are ρ=0.58, p=.00 and ρ=-0.57, p=.00 respectively, confirming statistically the empirical observation that can be obtained by visual inspection.

Note that due to randomness, executing the provieded two snippets of code will not reproduce exactly the same results.