Trajectory Bayesian Indexing : The Airport Ground Traffic Case

Trajectory Bayesian Indexing : The Airport Ground Traffic Case

Cynthia Delauney, Nicolas Baskiotis and Vincent Guigue

IEEE 19th International Conference on Intelligent Transportation Systems Rio de Janeiro, Brazil

November 2^nd, 2016

C

:

-

Issues :

◦ Clustering/categorization [Jiang et al. 08]

◦ Anomaly detection [Bu et al. 09]

◦ Indexing[Guttman et al. 84, Chakka et al. 03, Zheng et al. 11]

Challenges :

◦ Variable size

◦ Noise(s)

◦ Data amount

M

:

&

Query What is close to agiven situation?

Analysis What are thecommon featuresshared by close trajectories?

Predict Does the current trajectorybecome closer to a risk situation?

Paris international airport

◦ Which trajectoryrepresentation?

◦ Whichmetricsbetween trajectories?

R

D

1 year∼130 000 trajectories

∼350 Gb (with a rich context)

|T_k| ∼1000in average

Trajectory samples:

T_k={c,(t₁, `<sub>1</sub>, . . . , t<sub>|Tk|</sub>, `_|Tk|)} t∈R, `∈R²

c: context,t_i : time,`_i: location

D

& B

W

S×6velocites×8directions

⇒Fixed dimensions Z S= 30×30⇒Z = 43200

Word definition:

w_i=(`,v,d)∈N³ location,velocity,direction

↓

T_k={c,w}, w∈N^Z Frequency normalization:↓

w_i ⇒w_i^f = w_i P

jw_j ∈R+

↓ T_k={c,w^f}

D

& B

W

S×6velocites×8directions

⇒Fixed dimensions Z S= 30×30⇒Z = 43200

Word definition:

w_i=(`,v,d)∈N³ location,velocity,direction

↓

T_k={c,w}, w∈N^Z Frequency normalization:↓

w_i ⇒w_i^f = w_i P

jw_j ∈R+

↓ T_k={c,w^f}

⇒

Z

N

trajectory i

N

B

M

Z = 43200

Multinomial model:

Θ =







...

θ_i=p(w_i|`) ...





∈R^Z

p(w_i|`) = P

kw^(k)_i X

k

X

{j|`∈wj}

w^(k)_j

N

B

M

Z = 43200

Multinomial model:

Θ =







...

θ_i=p(w_i|`) ...





∈R^Z

p(w_i|`) = P

kw^(k)_i X

k

X

{j|`∈wj}

w^(k)_j

Vincent Guigue Trajectory Bayesian Indexing 6/16

⇒

Z

N

trajectory i

Introduction Representation Requˆete D´etection d’anomalies Conclusion

N^AIVEB^AYESM^ODELING

Z= 43200

Multinomial model:

⇥ = 2 66 4

...

✓i=p(wi|`) ...

3 77 52R^Z

p(wi|`) = P

kw^(k)_i X

k

X

{j|`2wj}

w_j^(k) +

E

:

Parking (green)

High entropy Runway (yellow) Low entropy

Local normalization procedure : θ_i=p(w_i|`)

| {z } likelihood

⇒ θ_i= p(w_i|`) max

{i|`∈w<sup>k</sup><sub>i</sub>}p(w<sub>i</sub>|`)

| {z }

locally norm. likelihood

L

Yellow

Cyan

Blue

Green

Magenta

Red

L

⇒

Spatial caracterization:

Introduction Representation Query Traj. analysis Conclusion

Q

◦ Query : 1 trajectory

◦ Answers :k(= 3)Nearest Neighbors(Euclidian distance)

Query in the original representation space

◦ Query = region`(all velocit./dir.)

◦ Sorted answers:

4 Lowest likelihood

Query in representation space + likelihood

Q

◦ Query : 1 trajectory

◦ Answers :k(= 3)Nearest Neighbors(Euclidian distance)

Query in the original representation space

Smartquery:

◦ Query = region`(all velocit./dir.)

◦ Sorted answers:

4 Lowest likelihood

Query in representation space + likelihood

C

T-SNE projection (2D)

◦ Unsupervised learning...

difficult to evaluate

◦ Colors=

airport configurations - 4 runways

- East or west direction

⇒Clear latent space division

C

T-SNE projection (2D)

Fine analysis of the

magenta cluster:

◦ left sub-cluster

◦ right sub-cluster

Introduction Representation Query Traj. analysis Conclusion

[P

.]

1 Clustering of the parkings

3 Late = last percentile

⇒10 clusters

Introduction Representation Query Traj. analysis Conclusion

[P

.]

1 Clustering of the parkings

2 Taxiing duration pdf estimate

Raw estimate Smoothed estimate (Parzen)

[P

.]

1 Clustering of the parkings

2 Taxiing duration pdf estimate

3 Late = last percentile

Smoothed estimate (Parzen) + last percentiles of each cluster

L

T-SNE projection (2D)

We detect some regularities in late trajectories

Outliers (often) correspond to late trajectories

S

Trajectory = series ofwords⇒series oflikelihoods T ={w_t1, . . . ,w_t|T|} ⇒ {L(w_t1), . . . ,L(w_t|T|)} Likelihood course of a late trajectory:

S

Spatialmapping Velocitymapping

The plane had an abnormallowvelocityin3 spatial tilesof the grid

S

Finding trajectories with:

anomaly in the region`

& velocity>ML velocity

C

& P

◦ Very lightway to index trajectories

◦ Consistent

◦ (Local)likelihood

◦ Many possible coding (presence, frequency, tf-idf...)

inspired from text indexing Perspectives

◦ Indexing⇒categorization withcontinuous modeling (neural network)

◦ Identifyingprecursory eventsof abnormal situations

◦ Trajectory⇒Situation(multiple vehicles)

bigram?