# Comparative Visualization of Vector Field Ensembles Based on Longest Common Subsequence

### Abstract

We propose a longest common subsequence (LCSS)-based approach to compute the distance among vector field ensembles. By measuring how many common blocks the ensemble pathlines pass through, the LCSS distance defines the similarity among vector field ensembles by counting the number of shared domain data blocks. Compared with traditional methods (e.g., pointwise Euclidean distance or dynamic time warping distance), the proposed approach is robust to outliers, missing data, and the sampling rate of the pathline timesteps. Taking advantage of smaller and reusable intermediate output, visualization based on the proposed LCSS approach reveals temporal trends in the data at low storage cost and avoids tracing pathlines repeatedly. We evaluate our method on both synthetic data and simulation data, demonstrating the robustness of the proposed approach.

**Keywords**: Ensemble visualization, comparative visualization, longest common subsequence

### Figures

Figure 1. Pipeline of our work. We firstly trace pathlines in parallel from the raw ensemble data. By employing the parallel LCSS sequence encoding and distance metric, the generated pathlines then are encoded into LCSS sequences for further visualization and multiscale temporal comparison.

Figure 2. 2D illustration of the block-index encoding and subsequence
comparison for multiscale temporal comparison. The blockindex
sequence of Run 0 is (0, 1, 2, 2, 3, 13, 14, 15, 16, 6, 7, 8, 9).
The sequence of Run 1 is (0, 1, 2, 2, 3, 4, 5, 6, -4, -3, -2, 8, 9).

Figure 3. (a) Similarity field output by LCSS method with the same block size as (h); (b) variation field output by LCSS method with the same
block size as (e); similarity field (c) and variation field (f) output by pointwise method; similarity field (d) and variation field (g) output by DTW
method; similarity field (e) and variation field (h) output by LCSS method; The boxes in (e) and (h) are clustering regions with high LCSS variation.

### Citation

Richen Liu, Hanqi Guo, Jiang Zhang, and Xiaoru Yuan. Comparative Visualization of Vector Field Ensembles Based on Longest Common Subsequence.
In

*Proceedings of IEEE Pacific Visualization Symposium (PacificVis 2016)*, pages 96-103, Taipei, Apr. 19-22, 2016.

### BibTeX

@Article{Liu2016,
Title = {Comparative Visualization of Vector Field Ensembles Based on Longest Common Subsequence},
Author = {Richen Liu, Hanqi Guo, Jiang Zhang, and Xiaoru Yuan},
Booktitle = {Proceedings of {IEEE} Pacific Visualization Symposium 2016},
Year = {2016},
Pages = {96--103},
Bibsource = {dblp computer science bibliography, http://dblp.org}
}