Attraction and Avoidance Detection from Movements Zhenhui Jessie Li (with Bolin Ding, Fei Wu, Tobias Lei, Roland Kays, Meg Crofoot) Pennsylvania State University VLDB Conference Hangzhou, China September, 2014 1
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Mining Mobility Relationship Problem • Given two trajectories R and S, measure their relationship strength R r5 r4 r6 r2 r1 S r3 s6 s1 s4 s3 s5 s2 * assume synchronized sampling rate 2
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Using Trajectory Similarity as a Measure of Mobility Strength R Meeting (or co-locating) frequency r5 r4 r6 r2 r1 n r3 S X freq ( R, S ) = τ ( r i , s i ) . s6 i =1 ⇢ 1 , s1 | r i − s j | ≤ d ; s4 τ ( r i , s j ) = s3 0 , otherwise . s5 d s2 Vlachos et al., Discovering similar multidimensional trajectories. ICDE’02 Chen et al., Robust and fast similarity search for moving object trajectories. SIGMOD’05 Jeung et al., Discovery of convoys in trajectory database. VLDB’08 3 Li et al., Mining relaxed temporal moving object clusters. VLDB’10
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Meeting Frequency = Relationship Strength? the more frequently you co-locate with another person, less frequently the stronger the mobility relationship is. weaker 4
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Meeting Frequency = Relationship Strength? Example 1. Example 2. A and B are friends A and C are colleagues living in different cities working in the same building attracted to meet avoid meeting Freq(A, B) = 2 Freq(A, C) = 20 Meeting Frequency ≠ Relationship Strength 5
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Consider Mobility Background to Infer Relationship Example 1. Example 2. A and B are friends A and C are colleagues living in different cities working in the same building attracted to meet avoid meeting Freq(A, B) = 2 Freq(A, C) = 20 Mobility background Expect(A, B) = 1 Expect(A, C) = 100 6
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University What happened vs. What is expected to happen Example 1. Example 2. Freq(A, B) = 2 Freq(A, C) = 20 What happened? Expect(A, B) = 1 Expect(A, C) = 100 What is expected? 7
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University What happened vs. What is expected to happen Example 1. Example 2. Freq(A, B) = 2 Freq(A, C) = 20 What happened? larger than smaller than Expect(A, B) = 1 Expect(A, C) = 100 What is expected? How to estimate Attraction Avoidance what is expected? 8
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University How to Estimate Expectation? • Null hypothesis: Two movement sequences R and S are independent. • If we randomly shuffle the sequences, R → σ ( R ) S → σ ( S ) • the meeting frequency should remain the same freq ( R, S ) ≈ freq ( σ ( R ) , σ ( S )) Pr ( freq ( σ ( R ) , σ ( S ) = y )) = Pr ( freq ( R, σ ( S ) = y )) Shuffling two sequences = Shuffling one sequence 9
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Permutation Test to Estimate the Probabilistic Background Model If we randomly shuffle the sequence … r1 r2 r3 r4 r5 r1 r2 r3 r4 r5 R R S σ (S) s1 s2 s3 s4 s5 s5 s1 s3 s4 s2 freq ( R, S ) = 2 freq ( R, σ ( S )) = 0 Z. Li et. al., Int. Conf. on Very Large Data Bases (VLDB'14/PVLDB) 10
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Permutation Test to Estimate the Probabilistic Background Model If we randomly shuffle the sequence … r1 r2 r3 r4 r5 r1 r2 r3 r4 r5 R R S σ (S) s1 s2 s3 s4 s5 s4 s2 s3 s1 s5 freq ( R, S ) = 2 freq ( R, σ ( S )) = 1 Z. Li et. al., Int. Conf. on Very Large Data Bases (VLDB'14/PVLDB) 11
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Permutation Test to Estimate the Probabilistic Background Model …. n! permutations …. generate histogram count freq(R, σ (S)) 12 Z. Li et. al., Int. Conf. on Very Large Data Bases (VLDB'14/PVLDB)
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Compute Degree of the Relationship …. n! permutations …. Expected frequency generate histogram count Actual frequency freq(R, σ (S)) 13 Z. Li et. al., Int. Conf. on Very Large Data Bases (VLDB'14/PVLDB)
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Compute Degree of the Relationship …. n! permutations …. Expected frequency generate histogram Attraction count relationship: 95% significance Actual frequency 95% area freq(R, σ (S)) 14 Z. Li et. al., Int. Conf. on Very Large Data Bases (VLDB'14/PVLDB)
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Compute Degree of the Relationship …. n! permutations …. Expected frequency generate histogram count Actual frequency freq(R, σ (S)) 15 Z. Li et. al., Int. Conf. on Very Large Data Bases (VLDB'14/PVLDB)
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Compute Degree of the Relationship …. n! permutations …. Expected frequency generate histogram Avoidance count relationship: Actual frequency 98% significance 98% area freq(R, σ (S)) 16 Z. Li et. al., Int. Conf. on Very Large Data Bases (VLDB'14/PVLDB)
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Compute Degree of the Relationship …. n! permutations …. Expected frequency generate histogram count avoid attract freq(R, σ (S)) 17 Z. Li et. al., Int. Conf. on Very Large Data Bases (VLDB'14/PVLDB)
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Compute Degree of the Relationship Expected frequency avoid attract sig attract ( R, S ) = Pr [ freq ( R, S ) > freq ( R, σ ( S ))] sig avoid ( R, S ) = Pr [ freq ( R, S ) < freq ( R, σ ( S ))] significant significant freq(R, σ (S)) 18 Z. Li et. al., Int. Conf. on Very Large Data Bases (VLDB'14/PVLDB)
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Monte Carlo Scheme to Approximate Degree • The total number of permutations is factorial n! • Monte Carlo scheme: sample N permutations ✏ 2 ⇢ ln 2 4 N ≥ � guarantee (1 − ✏ ) ⇢ ≤ ˆ ⇢ ≤ (1 + ✏ ) ⇢ with probability 1 − δ Z. Li et. al., Int. Conf. on Very Large Data Bases (VLDB'14/PVLDB) 19
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Experiment on the Monkey dataset 12 monkeys * green line: sig_{attract} > 0.95 11/10/2004 – 04/18/2005 * red line: sig_{avoid} > 0.95 Red: significant avoidance Z. Li et. al., Int. Conf. on Very Large Data Bases (VLDB'14/PVLDB) 20 Green: significant attraction
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Experiment on the Monkey dataset 12 monkeys * green line: sig_{attract} > 0.95 11/10/2004 – 04/18/2005 * red line: sig_{avoid} > 0.95 Red: significant avoidance Z. Li et. al., Int. Conf. on Very Large Data Bases (VLDB'14/PVLDB) 21 Green: significant attraction
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Experiment on the Monkey dataset 12 monkeys * green line: sig_{attract} > 0.95 11/10/2004 – 04/18/2005 * red line: sig_{avoid} > 0.95 Red: significant avoidance Z. Li et. al., Int. Conf. on Very Large Data Bases (VLDB'14/PVLDB) 22 Green: significant attraction
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Comparison with Previous Measures attract avoid Z. Li et. al., Int. Conf. on Very Large Data Bases (VLDB'14/PVLDB) 23
Mining Attraction and Avoidance from Movements Zhenhui Jessie Li, Penn State University Summary and Future Work • Summary: Important to consider background – What happened vs. What is expected to happen – Consider mobility background using permutation test Thanks! Questions? • Permutation test is one way, but not the only way to consider background context – How to deal with “impossible” trajectory? – How to deal with sparse observations? • Rich spatial and temporal context – location semantics – social events 24
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