Visualization and Exploration of Temporal Trend Relationships in Multivariate Time-Varying Data

1. Visualization and Exploration of Temporal Trend Relationships in Multivariate Time-Varying Data Teng-Yok Lee & Han-Wei Shen

2. Introduction: Temporal Trends in Multivariate Time-Varying Data • Each variable over time on each spatial point forms a time series • Temporal trends • Salient time series patterns • Represent physical phenomena • What are the relationships among these trends on different variables?

3. Motivation • Extract the relationships among user-specified trends in multivariate data • Where, when and how long do they exist? • What’s their order to appear on the same region? • Do they overlap in time/space? • What’s their order to disappear on the same region? • Requirements • Detection of temporal trends • Find and describe their relationship within multivariate data • Effective visualizations and interaction

4. Tend-based Interaction & Visualization Overview User Specification of Temporal Trends Temporal Trend Detection by SUBDTW Temporal Trend Relationship Modeling and Extraction

5. Trend Detection • Trend: a time series of scalars • Given a trend p, how to detect it in a multivariate data set? Time series at x Time series fα∈α Time series fβ∈β for each spatial point x, • compare p with the time series of the same variable on x: • check each sliding window [t0,t1] • if ( ||fβ[t0…t1], p|| <δ ) • pexists on x in [t0,t1] Time series fγ∈γ t0 t1 Trend p∈β A brute force algorithm t

6. Trend Detection: Challenge • The trend can be deformed over time • Conventional distance metrics cannot work • How do other communities handle this problem? • DTW in speech recognition Original Trend Stretched Nonlinearly deformed Shifted & Repeated Compressed

7. DTW: Dynamic Time Warping • DTW • A popular pattern matching method in speech recognition • Time complexity O(T2) • Invariant under shift/stretch/compression/deform • Can DTW be used with the brute force algorithm? • DTW: mapping time steps from one time series to the other w/ minimal distance Courtsey: E. J. Keogh and M. J. Pazzani. Derivative dynamic time warping. In Proceedings of the First SIAM International Conference on Data Mining, 2001

8. SUBDTW: ourO(T2) trend detectionalgorithm for each sliding window [t0,t1] DTW(p, fβ[t0…t1]) if ( distance after DTW <δ ) p exists in [t0,t1] From Brute-force to SUBDTW • Time complexity: • (#slidingwindows) • x (DTW time complexity) • = O(T2) x O(T2) • = O(T4) A DTW-based brute-force algorithm to detect p in fβ[1...T] Brute force + DTW SUBDTW = Functionality Time complexity O(T2) << O(T4)

9. Trend Relationship Model • Given a spatial location, various relationships among the trends exist • Which trends occur? • What’s their temporal order? • How long are their durations? • Do their durations overlap? • Trend sequence • Our formal model to describe the trend relationships

10. Trend Sequence • A state machine • Each state represents a set of trends • The state changes when any trends begin/end Trend A Time series at x Trend Detection t Trend B t Trend C t time t1 t2 t3 t4 t5 t6 B A B A C t6 t2 t3 t4 t5 t1 Trend Sequence at x

11. Trend Sequence Clustering • Extract the most common ones from millions of trend sequences • A 1-pass clustering algorithm Trend Sequences B AB A C C B AB A C B A B A B A B A C C root C A A C B A B A C Clustered State Diagram B A B A C B A B A

12. Visualization Parallel Coordinate Plots (PCP): represents the transition times in the trend sequences Trend sequence Icon: encodes the order of the trend sequences Trend-sequence-based transfer function: reveals the spatial and temporal information of the trend sequences

13. #States #Trends Trend Sequence Icon • Encode the state order of a trend sequence Trend A t Trend B t Trend C t • B • A • B • A • C t6 t2 t3 t4 t5 t1

14. Parallel Coordinates Plot (PCP) t6 t5 t4 t3 t’6 t’5 t’4 t’3 t’2 t’1 t2 t1 t’1 t’2 t’3 t’4 t’5 t’6 B A B A C Trend sequence B Visualizing Trend Sequence Times • In the same cluster, trend sequences can have different transition times • From times to high dim vectors • Each trend sequence w/ n states has n+1 time steps. • Use PCP w/ n+1 axes to visually compare the trend sequences in the same cluster t1 t2 t3 t4 t5 t6 B A B A C Trend sequence A

15. Visualizing Trend Sequence Times (contd’) • Different techniques can be applied to enhance the PCP By blending the polylines, the visual clutters can be reduced and the polylines can be visually grouped. The groups can be then filtered out and colored

16. Case StudyHurricane Isabel • A simulation of an intense tropical weather system that occurred in September, 2003, over the west Atlantic region • Questions • Given a region, do the drop-and-rise patterns appear in both the wind magnitude and the pressure? • Will the temperature increase so much only along the hurricane eye? Will it increase in other regions? Testing trends

17. Case StudyHurricane Isabel (contd’) Most common trend sequences • Observations • The wind magnitude and the pressure will not always drop together • If they drop together, where? • The rising of temperature can occur in other regions • Where? Wind Magnitude Pressure Temperature

18. Trend-Sequence-based Transfer Function • Reveal the spatial distribution of trend sequences • Specification • Browse the trend sequence icons to select an icon • Select a polyline group on the PCP • Specify color and transparency • Color the corresponding data points accordingly

19. Case StudyHurricane Isabel (contd’) • How does the path of the hurricane eye influence the wind magnitude and pressure? Only the trend for the pressure exists near the path If too distant from the eye, the trends for both variables do not exist. The trends for both variables coexist along the path of the hurricane eye Wind Magnitude Pressure

20. Conclusion • Contributions • A new way to explore/understand multivariate time-varying data • A model to describe trend relationships and an efficient clustering algorithm • A new algorithm to detect time series patterns Any questions?