Model-Based Segmentation and Classification of Gull Trajectories - PowerPoint PPT Presentation

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 Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 1

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

Introduction Segmentation Classification Experiments Example: Brownian bridge movement model (BBMM) Assumption: Entity performs Brownian motion, conditioned on observed locations. Gives (normal) distribution of location at intermediate times. Parameter: Diffusion coefficient σ 2 m (”speed” of entity). Estimate using maximum likelihood method. τ (1) τ b (0) τ b (1) τ (3) τ b (2) τ (0) τ (2) Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 3

Introduction Segmentation Classification Experiments Dynamic Brownian Bridges Idea: Use Brownian bridges, let diffusion coefficient vary. Estimate using sliding window and information criterion. 0 500 km 5 0 km 500 km 500 km 0 0 500 km 500 km 500 km 5 0 km 0 0 20 km 20 km 20 km k k 0 20 km 20 km 20 km k k 0 100 000 00 0 00 00 km 00 0 k 0k 0 km 0 0 k km m m [B. Kranstauber et al., 2012] Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 4

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. Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 5

Introduction Segmentation Classification Experiments Segmentation: Model-based Problem (M ODEL -B ASED -S EGMENTATION ) Input: A trajectory τ , and a penalty factor p ∈ R + . Output: A segmentation S of τ and a parameter value x i for each segment S i ∈ S that minimizes IC ( S ) = − 2 L S + | S |· p . σ 2 m, 3 σ 2 m, 3 σ 2 σ 2 m, 1 σ 2 m, 2 m, 3 σ 2 m, 1 σ 2 m, 1 σ 2 m, 2 σ 2 m, 1 σ 2 m, 1 Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 6

Introduction Segmentation Classification Experiments Segmentation algorithm Discrete set of candidates for diffusion coefficient x 1 ,..., x m . Compute optimal segmentation for a prefix, ending with x j . Two options: Append: Opt i − 1 appended with new segment τ [ i − 1 , i ] . i − 1 i Opt i − 1 Extend: O i − 1 , x with the last segment extended by τ [ i − 1 , i ] . i − 1 j i Opt j O i − 1 ,x Running time O ( nm ) . Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 7

Introduction Segmentation Classification Experiments Classification Problem (C LASSIFICATION ) Input: A set of trajectories T = { τ 1 ,..., τ k } with bitonic likelihood functions, and a penalty factor p ∈ R + . Output: A partition C of T and a parameter value x i for each class C i ∈ C such that IC ( C ) = − 2 L ( C )+ | C |· p is minimized. Classes may not respect the order in which trajectories reach their maximum likelihood. L 1 L 4 L 2 L 3 x 1 x 2 Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 8

Introduction Segmentation Classification Experiments Classification algorithm Discrete set of candidates for diffusion coefficient x 1 ,..., x m . For each x i ∈ { x 1 ,..., x m } : Compute optimal classification Opt i of trajectories reaching maximum likelihood at some x < x i . Extend Opt 1 ,..., Opt i − 1 by a single class at x i . L 2 L 4 L 5 L 1 L 3 x 1 x 2 x 3 x 4 Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 9

Introduction Segmentation Classification Experiments Classification algorithm Discrete set of candidates for diffusion coefficient x 1 ,..., x m . For each x i ∈ { x 1 ,..., x m } : Compute optimal classification Opt i of trajectories reaching maximum likelihood at some x < x i . Extend Opt 1 ,..., Opt i − 1 by a single class at x i . L 2 L 4 L 5 L 1 L 3 x 1 x 2 x 3 x 4 Opt 1 L 1 ( L 2 , L 3 , L 4 , L 5 ) Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 9

Introduction Segmentation Classification Experiments Classification algorithm Discrete set of candidates for diffusion coefficient x 1 ,..., x m . For each x i ∈ { x 1 ,..., x m } : Compute optimal classification Opt i of trajectories reaching maximum likelihood at some x < x i . Extend Opt 1 ,..., Opt i − 1 by a single class at x i . L 2 L 2 L 4 L 4 L 5 L 5 L 1 L 3 L 3 x 1 x 2 x 3 x 4 Opt 1 L 1 ( L 2 , L 3 , L 4 , L 5 ) ( L 4 , L 5 ) Opt 2 L 1 L 2 , L 3 Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 9

Introduction Segmentation Classification Experiments Classification algorithm Discrete set of candidates for diffusion coefficient x 1 ,..., x m . For each x i ∈ { x 1 ,..., x m } : Compute optimal classification Opt i of trajectories reaching maximum likelihood at some x < x i . Extend Opt 1 ,..., Opt i − 1 by a single class at x i . L 2 L 2 L 4 L 5 L 1 L 3 L 3 x 1 x 2 x 3 x 4 Opt 1 L 1 ( L 2 , L 3 , L 4 , L 5 ) ( L 4 , L 5 ) Opt 2 L 1 L 2 , L 3 ( L 4 , L 5 ) Opt 3 L 1 , L 3 L 2 Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 9

Introduction Segmentation Classification Experiments Classification algorithm Discrete set of candidates for diffusion coefficient x 1 ,..., x m . For each x i ∈ { x 1 ,..., x m } : Compute optimal classification Opt i of trajectories reaching maximum likelihood at some x < x i . Extend Opt 1 ,..., Opt i − 1 by a single class at x i . L 2 L 2 L 4 L 4 L 4 L 5 L 5 L 5 L 1 L 3 L 3 x 1 x 2 x 3 x 4 Opt 1 L 1 ( L 2 , L 3 , L 4 , L 5 ) ( L 4 , L 5 ) Opt 2 L 1 L 2 , L 3 ( L 4 , L 5 ) Opt 3 L 1 , L 3 L 2 ( L 5 ) Opt 4 L 1 L 2 , L 3 L 4 Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 9

Introduction Segmentation Classification Experiments Classification algorithm Discrete set of candidates for diffusion coefficient x 1 ,..., x m . For each x i ∈ { x 1 ,..., x m } : Compute optimal classification Opt i of trajectories reaching maximum likelihood at some x < x i . Extend Opt 1 ,..., Opt i − 1 by a single class at x i . Compute optimal classification of k trajectories in O ( km 2 ) time. Can be improved to O ( m 2 + km ( log m + log k )) . Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 9

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] Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 10

Introduction Segmentation Classification Experiments Experiments 50.4 class Segment input trajectories 2 1 Based on BBMM 7 5 12,787 segments lat 50.1 4 3 Classify resulting segments 20 11 Based on BBMM 40 49.8 19 classes 2.0 2.5 3.0 lon Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 11

Introduction Segmentation Classification Experiments Results: Migration Label each segment migration or non-migration Defined using BBMM home range L902130 L911710 7500000 7000000 7000000 UTM Northing (m) UTM Northing (m) 6500000 6000000 6000000 5500000 5000000 −1e+06 −5e+05 0e+00 5e+05 −1e+06 −5e+05 0e+00 5e+05 UTM Easting (m) UTM Easting (m) Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 12

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 Relative frequency 0.20 Non−migration Migration 0.15 0.10 0.05 0.00 0 3 7 2 9 7 9 3 1 3 9 1 8 2 2 0 8 3 4 . . . . . . . . . . . . . . . . . . . 0 5 2 4 1 7 3 2 5 4 1 0 0 6 8 9 4 5 5 4 4 4 6 5 3 3 9 4 1 3 3 5 2 4 3 4 1 3 6 1 8 7 8 3 1 2 7 6 0 2 7 0 1 1 2 3 5 7 9 1 4 8 6 2 5 1 1 1 2 4 5 4 Diffusion coefficient (m 2 / s) Model-Based Segmentation and Classification of Gull Trajectories VCMA 2016 — Maike Buchin, Stef Sijben 12