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

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?

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 3

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

5 Time series f β ∈ β 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 f α ∈ α t0t0 t1t1 Time series f γ ∈ γ for each spatial point x, compare p with the time series of the same variable on x: check each sliding window [t 0,t 1 ] if ( ||f β [t 0 …t 1 ], p|| <δ ) p exists on x in [t 0,t 1 ] A brute force algorithm Trend p ∈ β 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 Compressed Stretched Shifted & Repeated Nonlinearly deformed

7 DTW: Dynamic Time Warping DTW A popular pattern matching method in speech recognition Time complexity O(T 2 ) Invariant under shift/stretch/compression/deform Can DTW be used with the brute force algorithm? Courtsey: E. J. Keogh and M. J. Pazzani. Derivative dynamic time warping. In Proceedings of the First SIAM International Conference on Data Mining, 2001 DTW: mapping time steps from one time series to the other w/ minimal distance

From Brute-force to SUBDTW SUBDTW: our O(T 2 ) trend detection algorithm for each sliding window [t 0,t 1 ] DTW(p, f β [t 0 …t 1 ]) if ( distance after DTW <δ ) p exists in [t 0,t 1 ] A DTW-based brute-force algorithm to detect p in f β [1...T] Time complexity: (#sliding windows) x (DTW time complexity) = O(T 2 ) x O(T 2 ) = O(T 4 ) SUBDTW= Brute force + DTW O(T 2 )O(T 4 )<< Functionality Time complexity

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

Trend Sequence A state machine Each state represents a set of trends The state changes when any trends begin/end 10 Trend A t t t Trend Detection t4t4 t1t1 t3t3 t5t5 t6t6 Time series at x Trend B Trend C time t2t2 Trend Sequence at x t4t4 t1t1 t3t3 t5t5 t6t6 B ABAB A C t2t2

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

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

13 Trend Sequence Icon Encode the state order of a trend sequence t t t #States #Trends Trend A Trend B Trend C t4t4 t1t1 t3t3 t5t5 t6t6 B ABAB A C t2t2

14 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 t1t1 t2t2 t3t3 t4t4 t5t5 t6t6 BA BAC t1t1 t2t2 t3t3 t4t4 t5t5 t6t6 Parallel Coordinates Plot (PCP) t’ 1 t’ 2 t’ 3 t’ 4 t’ 5 t’ 6 Trend sequence A t’ 1 t’ 2 t’ 3 t’ 4 t’ 5 t’ 6 BA BAC Trend sequence B

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 Study Hurricane Isabel A simulation of an intense tropical weather system that occurred in September, 2003, over the west Atlantic region Questions 1.Given a region, do the drop-and-rise patterns appear in both the wind magnitude and the pressure? 2.Will the temperature increase so much only along the hurricane eye? Will it increase in other regions? Testing trends

17 Case Study Hurricane Isabel (contd’) 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? Most common trend sequences Wind Magnitude Pressure Temperature

18 Trend-Sequence-based Transfer Function Reveal the spatial distribution of trend sequences Specification 1.Browse the trend sequence icons to select an icon 2.Select a polyline group on the PCP 3.Specify color and transparency 4.Color the corresponding data points accordingly

19 Case Study Hurricane Isabel (contd’) How does the path of the hurricane eye influence the wind magnitude and pressure? If too distant from the eye, the trends for both variables do not exist. Only the trend for the pressure exists near the path 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?