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Introduction Segmentation Classification Experiments Model-Based Segmentation and Classification of Gull Trajectories Maike Buchin, Stef Sijben Visually-supported Computational Movement Analysis 14 June 2016 Model-Based Segmentation and

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Introduction Segmentation Classification Experiments Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 1

Model-Based Segmentation and Classification

f Gull Trajectories

Maike Buchin, Stef Sijben

Visually-supported Computational Movement Analysis 14 June 2016

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Introduction Segmentation Classification Experiments

Movement models

Model trajectory between observed locations. Often: Linear interpolation. Random movement models model trajectory as a random walk. Example: Brownian bridge movement model.

A A

Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 2

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Introduction Segmentation Classification Experiments

Example: Brownian bridge movement model (BBMM)

Assumption: Entity performs Brownian motion, conditioned on

bserved locations.

Gives (normal) distribution of location at intermediate times. Parameter: Diffusion coefficient σ 2

m (”speed” of entity).

Estimate using maximum likelihood method.

τ(0) τ(1) τ(2) τ(3) τ b(0) τ b(1) τ b(2)

Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 3

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Introduction Segmentation Classification Experiments

Dynamic Brownian Bridges

Idea: Use Brownian bridges, let diffusion coefficient vary. Estimate using sliding window and information criterion.

100 000 00 00 km m k 0k km m 00 00 0 k 0 km 20 km 20 km k 20 km k 20 km 20 km k 20 km k 500 km 500 km 5 0 km 500 km 500 km 500 km 5 0 km 500 km

[B. Kranstauber et al., 2012]

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Introduction Segmentation Classification Experiments

Segmentation

Goal: Partition trajectory into homogeneous segments. So far: Criterion-based segmentation.

Minimize number of segments while each segment fullfills given criteria.

Example of criteria: Heading range, speed,. . . Efficient algorithms known for many criteria.

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Introduction Segmentation Classification Experiments

Segmentation: Model-based

Problem (MODEL-BASED-SEGMENTATION) Input: A trajectory τ, and a penalty factor p ∈ R+. Output: A segmentation S of τ and a parameter value xi for each segment Si ∈ S that minimizes IC(S ) = −2LS +|S |· p.

σ2

m,1

σ2

m,1

σ2

m,1

σ2

m,1

σ2

m,1

σ2

m,2

σ2

m,2

σ2

m,3

σ2

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σ2

m,3

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Introduction Segmentation Classification Experiments

Segmentation algorithm

Discrete set of candidates for diffusion coefficient x1,...,xm. Compute optimal segmentation for a prefix, ending with xj. Two options:

Append: Opti−1 appended with new segment τ[i − 1,i].

Opti−1 i − 1 i

Extend: Oi−1,x with the last segment extended by τ[i − 1,i].

i − 1 j Optj Oi−1,x i

Running time O(nm).

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Introduction Segmentation Classification Experiments

Classification

Problem (CLASSIFICATION) Input: A set of trajectories T = {τ1,...,τk} with bitonic likelihood functions, and a penalty factor p ∈ R+. Output: A partition C of T and a parameter value xi for each class Ci ∈ C such that IC(C ) = −2L(C )+|C |· p is minimized. Classes may not respect the order in which trajectories reach their maximum likelihood. x1 x2 L1 L2 L3 L4

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Introduction Segmentation Classification Experiments

Classification algorithm

Discrete set of candidates for diffusion coefficient x1,...,xm. For each xi ∈ {x1,...,xm}:

Compute optimal classification Opti of trajectories reaching maximum likelihood at some x < xi. Extend Opt1,...,Opti−1 by a single class at xi. x1 x2 x3 x4 L1 L3 L4 L5 L2

Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 9

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Introduction Segmentation Classification Experiments

Classification algorithm

Discrete set of candidates for diffusion coefficient x1,...,xm. For each xi ∈ {x1,...,xm}:

Compute optimal classification Opti of trajectories reaching maximum likelihood at some x < xi. Extend Opt1,...,Opti−1 by a single class at xi. x1 x2 x3 x4 L1 L2 L3 L4 L5 L1 (L2, L3, L4, L5) Opt1

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Introduction Segmentation Classification Experiments

Classification algorithm

Discrete set of candidates for diffusion coefficient x1,...,xm. For each xi ∈ {x1,...,xm}:

Compute optimal classification Opti of trajectories reaching maximum likelihood at some x < xi. Extend Opt1,...,Opti−1 by a single class at xi. x1 x2 x3 x4 L1 L2 L3 L4 L5 L1 (L2, L3, L4, L5) Opt1 Opt2 L1 L2, L3 (L4, L5) L3 L4 L5 L2

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Introduction Segmentation Classification Experiments

Classification algorithm

Discrete set of candidates for diffusion coefficient x1,...,xm. For each xi ∈ {x1,...,xm}:

Compute optimal classification Opti of trajectories reaching maximum likelihood at some x < xi. Extend Opt1,...,Opti−1 by a single class at xi. x1 x2 x3 x4 L1 L2 L3 L4 L5 L1 (L2, L3, L4, L5) Opt1 Opt2 Opt3 L1 L2, L3 (L4, L5) L1, L3 L2 (L4, L5) L2 L3

Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 9

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Introduction Segmentation Classification Experiments

Classification algorithm

Discrete set of candidates for diffusion coefficient x1,...,xm. For each xi ∈ {x1,...,xm}:

Compute optimal classification Opti of trajectories reaching maximum likelihood at some x < xi. Extend Opt1,...,Opti−1 by a single class at xi. x1 x2 x3 x4 L1 L2 L3 L4 L5 L1 (L2, L3, L4, L5) Opt1 Opt2 Opt3 Opt4 L1 L2, L3 (L4, L5) L3 L4 L5 L4 L5 L1, L3 L2 (L4, L5) L1 L2, L3 L4 (L5) L2

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Introduction Segmentation Classification Experiments

Classification algorithm

Discrete set of candidates for diffusion coefficient x1,...,xm. For each xi ∈ {x1,...,xm}:

Compute optimal classification Opti of trajectories reaching maximum likelihood at some x < xi. Extend Opt1,...,Opti−1 by a single class at xi.

Compute optimal classification of k trajectories in O(km2) time. Can be improved to O(m2 + km(logm + logk)).

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Introduction Segmentation Classification Experiments

Dataset

75 Lesser Black-backed Gulls, 26 Herring Gulls 2.5 years 2,485,399 observations 775s mean time between samples

[E. Stienen et al., 2016]

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Introduction Segmentation Classification Experiments

Experiments

Segment input trajectories

Based on BBMM 12,787 segments

Classify resulting segments

Based on BBMM 19 classes

49.8 50.1 50.4 2.0 2.5 3.0

lon lat class

2 1 7 5 4 3 20 11 40

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Introduction Segmentation Classification Experiments

Results: Migration

Label each segment migration or non-migration

Defined using BBMM home range

−1e+06 −5e+05 0e+00 5e+05 5500000 6000000 6500000 7000000 7500000

L902130

UTM Easting (m) UTM Northing (m) −1e+06 −5e+05 0e+00 5e+05 5000000 6000000 7000000

L911710

UTM Easting (m) UTM Northing (m)

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Introduction Segmentation Classification Experiments

Results: Migration

Label each segment migration or non-migration

Defined using BBMM home range

Compare class distribution

Migration has higher diffusion coefficient

Non−migration Migration Relative frequency 0.00 0.05 0.10 0.15 0.20 Diffusion coefficient (m2 / s)

. 5 . 3 4 2 . 7 1 4 4 . 2 3 4 1 . 9 6 6 7 . 7 1 1 5 3 . 9 1 8 3 2 . 3 2 7 3 5 . 1 3 8 9 4 . 3 5 3 4 1 . 9 7 1 1 . 1 9 2 3 . 8 1 1 7 3 6 . 2 1 4 6 5 8 . 2 1 8 2 9 . 2 6 2 4 4 . 8 4 2 7 3 5 . 3 4 5 5 4 5 . 4

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Introduction Segmentation Classification Experiments

Results: Speed

Computed average speed predicted by BBMM Average speed increases with increasing diffusion coefficient

20 40 60 Diffusion coefficient (m2 / s) Average speed (m/s)

5.3 42.7 144.2 341.9 667.7 1153.9 1832.3 2735.1 3894.3 5341.9 7110.1 9230.8 11736.2 14658.2 18029.0 26244.8 42735.3 455045.4

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Introduction Segmentation Classification Experiments

Conclusion

Segmentation, classification based on movement models Detect differences in behaviour Open: Ecological evaluation

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