This document summarizes research on using time curves to visualize patterns of temporal evolution in data. Time curves represent temporal data as curved lines, with position on the x-axis indicating time and y-axis position indicating similarity between data points. This allows visualization of trends and outliers over time. Examples of use cases include exploring document edit histories, analyzing video recordings, and visualizing dynamic networks in neuroscience research. The technique works by computing distances between data points over time, positioning points using multidimensional scaling, and drawing curves between points.

1. Time Curves: Folding Time to Visualize Patterns of
Temporal Evolution in Data
Benjamin Bach, Conglei Shi, Nicolas Heulot, Tara Madhyastha, Tom Grabowski, Pierre Dragicevic
IEEE Transactions on Visualization and Computer Graphics
2016 published, 89 cited

2. 1
Motivation
• Costly and impractical to develop specialized visualization tools for each possible
domain and type of dataset can be costly and impractical 
• Develop more visual representations of temporal data that can be applied to a
range of datasets.
• Focus on time and similarity
• Offer a generic way of producing simple visual overviews for range of temporal
dataset

3. 2
Use Case Scenarios 1: Exploring Document Histories
• Progress and Stagnation
 Zig-zag patterns = controversial stage
 Cluster = maturity (consensus)
 Alternating curve = “edit war”
• Similar and Identical Revisions
 Dense cluster = stabilization
 Blue halo = superimposed
• User Contributions
 Use different color encodings
• Vandalism
 Entire article is removed = outlier
• Visual Signatures
 Use as thumbnail

4. 3
Use Case Scenarios 2: Video Recordings
• Surveillance Videos
 Show outlying frames
• Movie Analysis
 Overview of dynamic structure of a movie
 Provide recognizable visual landmarks

5. 4
Use Case Scenarios 3: Analyzing Dynamic Visualization
• Animated visualization
• Precipitation Patterns
 January to December = 1 cycle
 October/November = March/April
• Temperature Patterns
 Stable (1941-1991)
 Rapid progression (1991-2012)

6. 5
Time Curves in Neuroscience Research
• Functional brain connectivity = network of
correlation between activity
 Measured in blood-oxygen-level dependent signal
 Using fMRI, hundreds of time points each with 2-3
seconds apart are collected
• Used ME-ICA denoising method
• Comparing connectivity across individual becomes
possible
 Disjoint = difference in individuals physiological function

7. 6
Time Curve Characteristics and Patterns 1
• Time Point Distances
 Rank distance: number of time points between A and B
 Curvilinear distance: length of the curve segment
between A and B (Accumulated amount of change)
 Spatial distance: 2D Euclidean distance between A and B
(Similarity)

8. 7
Time Curve Characteristics and Patterns 2
Unpredictable
Many changes
Many reversals
Unstable
No long-term change
• Geometric Characteristics of Curves
• Patterns

9. 8
Implementing Time Curves 1
• Temporal Dataset
 Time points P = p0, p1 , . . . , pn
 pi = (Time points ti, data snapshot si)
• Temporal similarity dataset PD : temporal dataset P with a distance matrix D
• Distance Matrix
 Wikipedia histories: edit distance of pairs of revisions
 Videos: pairwise frame distance by computing normalized absolute pixel difference
 Dynamic networks: Euclidean distance between adjacency matrics
• Positioning Time point
 Classical MDS algorithm
 Multidimensional scaling (MDS): a means of visualizing the level of similarity of individual
cases of a dataset

10. 9
Implementing Time Curves 2
• Drawing curves
 Model curve as a string
 Join all time points using Bezier curves
• Removing time points overlap
 Highlight displaced point with a halo
• Rotating Curves
 Initial time points to the left

11. 10
Limitation & Future work
• Not convey all information in temporal datasets
 Convey ordinal aspect of time, rather than quantitative aspects
• Highly dependent on the distance metric chosen
• Major bottleneck in a computation
 MDS algorithm should improve
• The effect of such visualization is not proved
 No user study
• Can apply designing method to new type of visualization