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Continual Neighborhood Tracking for Moving Objects. Using Adaptive Distances. Yoshiharu Ishikawa Hiroyuki Kitagawa Tooru Kawashima University of Tsukuba, Japan {ishikawa,[email protected] Organization. Background and Overview Our Approach Experiments

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Continual neighborhood tracking for moving objects

Continual Neighborhood Tracking for Moving Objects

Using Adaptive Distances

Yoshiharu Ishikawa

Hiroyuki Kitagawa

Tooru Kawashima

University of Tsukuba, Japan

{ishikawa,[email protected]


Organization
Organization

  • Background and Overview

  • Our Approach

  • Experiments

  • Query Processing with Spatial Indexes

  • Incremental Query Update

  • Conclusions and Future Work


Background
Background

  • Progress of Digital Cartography

  • Development of GPS Technologies

  • Wide Use of PDA and Hand-held Devices

New Types of Information Services: Providing neighborhood information to moving objects (people with PDAs, cars with navigation systems) considering their locations and trajectories


Motivating example 1
Motivating Example (1)

Neighborhood Query:

A user at point x wants

to find nearby gas stations

Typical Approach:

retrieve gas stations

with their distances less

than 200 meters from x

x

A spatial query based on

the Euclidean distance


Motivating example 2

past trajectory

future trajectory

Motivating Example (2)

What’s Wrong?

If we know user’s past and future trajectories,

we can provide more

appropriate information

A


Our idea 1
Our Idea (1)

  • Use of an ellipsoid region to represent a neighborhood query

  • An ellipsoid region is computed based on the past/future trajectories

  • A neighborhood query is specified as a spatial query with an ellipsoid distance

A


Our idea 2

At each sample position, a spatial query is generated

initial query

parameters

start point

destination

: sampled estimated

positions of the

moving object

destination

start point

Our Idea (2)

Neighborhood Info

Retrieval System

: Data objects

  • Sample positions are taken by unit-time basis

  • The system perform queries continuously


Problems and solutions
Problems and Solutions

  • How can we generate appropriate spatial queries?

    • Introduction of influence model of trajectory points

    • Proposal of query derivation models

  • How about efficiency?

    • Use of spatial indexes for efficient query processing

    • Low-cost query update procedure for continuous queries


Organization1
Organization

  • Background and Overview

  • Our Approach

    • Influence model of trajectory points

    • Query derivation model

  • Experiments

  • Query Processing with Spatial Indexes

  • Incremental Query Update

  • Conclusions and Future Work


Representation of LocationInformation (1)

  • Object locations are represented by d-D vectors

: no. of dimensions


Representation of LocationInformation (2)

  • Locations of a moving object:

: departure time

: current time

: estimated arrival time

destination

current point

start point

Assumption:

past/future trajectory points are given in unit-time basis


Influence model of trajectory points 1

current

position

Influence Model of Trajectory Points (1)

  • We usually set high importance on current neighborhood points


Influence model of trajectory points 2

current

position

Influence Model of Trajectory Points (2)

  • A user may be interested in near future neighborhood where he or she will arrive soon


Influence model of trajectory points 3
Influence Model of Trajectory Points (3)

  • The influence model sets the highest weight “1” on location information at time t =  + s(s unit times after the current time )

  • The influence values decay exponentially towards past and future with parameters m and n, respectively

Influence Value

time

τ+σ-2

τ+σ

τ+σ+2

τ+σ-1

τ+σ+1


Influence Model of Trajectory Points (4)

  • Influence value for each point when s = 1

nt’-1

nt’-2

m

m2

1

n

destination

mt

mt+1

current point

n2

highest weight point

since s = 1

start point


Organization2
Organization

  • Background and Overview

  • Our Approach

    • Influence model of trajectory points

    • Query derivation model

  • Experiments

  • Query Processing with Spatial Indexes

  • Incremental Query Update

  • Conclusions and Future Work


Query derivation model

D

q

Query Derivation Model

  • Neighborhood queries for moving objects are issued to a spatial database

  • A spatial query is fixed specifying

    • query center q

      • two models (cur, avg)

    • distance function D

      • three models (EU, OV, HB)

    • query task

      • range query and k-nn query


Derivation of query centers 1

query center q

Derivation of Query Centers (1)

  • Model cur: set the point with the highest importance to the query center

current

position


Derivation of query centers 2
Derivation of Query Centers (2)

  • Model avg: weighted average based on influence values

Setting of parameters m and n

changes the query center

current

position

query center q


Query derivation model1

D

q

Query Derivation Model

  • Neighborhood queries for moving objects are issued to a spatial database

  • A spatial query is fixed specifying

    • query center q

      • two models (cur, avg)

    • distance function D

      • three models (EU, OV, HB)

    • query task

      • range query and k-nn query


Distance function derivation models 1
Distance Function Derivation Models (1)

  • Model EU: Euclid distance-based model

  • Pros

    • - simple and intuitive

    • - easy to compute

  • Cons

    • - do not consider past/future

    • - trajectory information


Ellipsoid distance
Ellipsoid Distance

Appropriate setting of the distance

matrix A allows flexible

tuning of distances

We derive an appropriate matrix

A using past/future trajectory

information


Distance function derivation models 2
Distance Function Derivation Models (2)

  • Model OV: ellipsoid distance-based model

derive a distance matrix M that reflects the sample point

distribution nearby the query point [19]

C is the weighted covariance matrix


Distance function derivation models 3
Distance Function Derivation Models (3)

  • Model OV: ellipsoid distance-based model

    • pros

      • allows retrieval along the trajectory since the derived distance is an extended version of the Mahalanobis distance [8, 20]

    • cons: not robust compared to the Euclidean distance

      • When an object is moving along a straight line or staying in some place, the matrix C becomes an ill-conditioned matrix: therefore, we cannot derive the distance matrix M!


regularization

: unit matrix

Distance Function Derivation Models (4)

  • Model HB: hybrid model

    • integrates the benefits of EU and OV models

becomes an regular matrix


Query derivation model2

D

q

Query Derivation Model

  • Neighborhood queries for moving objects are issued to a spatial database

  • A spatial query is fixed specifying

    • query center q

      • two models (cur, avg)

    • distance function D

      • three models (EU, OV, HB)

    • query task

      • range query and k-nn query


Query task 1
Query Task (1)

  • Range Query: At each point, retrieve objects within distance e


Query task 2
Query Task (2)

  • k-Nearest Neighbor Query: At each point retrieve nearest k objects

when k = 3


Organization3
Organization

  • Background and Overview

  • Our Approach

  • Experiments

  • Query Processing with Spatial Indexes

  • Incremental Query Update

  • Conclusions and Future Work


Experiment 1 observation of behaviors
Experiment 1: Observation of Behaviors

  • Query generation example for the trajectory (blue line)

  • Target points are shown in green points

  • Queries are generated based on the hybrid model


Experiment 1 1

x

Experiment 1 (1)

  • Comparison of Euclidean distance and ellipsoid distance


Experiment 1 2

y

modified parameters

σ= 5 , μ=0.4

ν=0.4, λ= 1.0

Experiment 1 (2)

  • Set the “near future” point as query center

initial parameters

σ= 0 , μ=0.5

ν=0.5, λ= 1.0

x


Experiment 1 3

refined parameters

σ= 0 , μ=0.4

ν=0.9, λ= 1.0

Experiment 1 (3)

  • Set high weights on future trajectory

initial parameters

σ= 0 , μ=0.4

ν=0.4, λ= 1.0

x


Experiment 1 4

refined parameters

σ= 0 , μ=0.4

ν=0.4, λ= 0.7

Experiment 1 (4)

  • Use of the regularization parameter l

initial parameters

σ= 0 , μ=0.4

ν=0.4, λ= 1.0

x


Experiment 2 simulation based on trace data 1
Experiment 2: Simulation Based on Trace Data (1)

  • Car driving trace data is used to compute queries


Experiment 2 simulation based on trace data 2
Experiment 2: Simulation Based on Trace Data (2)

  • Each isosurface represents the query generated at the point


Organization4
Organization

  • Background and Overview

  • Our Approach

  • Experiments

  • Query Processing with Spatial Indexes

  • Incremental Query Update

  • Conclusions and Future Work


Query processing based on spatial indexes
Query Processing Based on Spatial Indexes

  • Most of spatial indexes do not support ellipsoid distance-based queries

  • We extend the approach of Seidl & Kriegel [30] to support ellipsoid distance-based queries with conventional spatial indexes

  • Assumptions: only three generic retrieval functions are supported by the underlying spatial indexes


Generic retrieval functions 1

r

Generic Retrieval Functions (1)

  • rect_search(r): retrieve objects within the specified rectangle region r


Generic retrieval functions 2

Generic Retrieval Functions (2)

  • dist_search(q, ):retrieve objects within distance e from q using the Euclidean distance


Generic retrieval functions 3
Generic Retrieval Functions (3)

  • knn_search(q, k): retrieve nearest k objects from the query center q using the Euclidean distance


Minimal bounding box mbb for ellipsoid isosurface 30
Minimal Bounding Box (MBB) for Ellipsoid Isosurface [30]

  • MBB that tightly encloses the ellipsoid ellip(M, q, e)

ellip(M, q, e)

j-th dimension

: (i, i) element of

the inverse of M

i-th dimension


Minimal bounding sphere mbs for ellipsoid isosuraface 30
Minimal Bounding Sphere (MBS) for Ellipsoid Isosuraface [30]

  • MBS that tightly encloses the ellipsoid ellip(M, q, e)

ellip(M, q, e)

: the smallest

eigenvalue of M


Query processing 1

e

Query Processing (1)

  • Range query processing with MBB approximation


Query processing 11

e

Query Processing (1)

  • Range query processing with MBB approximation


Query processing 2
Query Processing (2)

  • k-NN query (k = 3)


Query processing 21
Query Processing (2)

  • k-NN query (k = 3)

  • Perform k-NN query

  • based on the Euclidean

  • distance

2. Derive an ellipsoid that

tightly encloses k-NN

objects

3. Perform a range query

with MBS (or MBB) that

tightly encloses the

ellipsoid region

4. Select nearest k objects

from the retrieved objects

using the ellipsoid distance


Experiment retrieval i o cost with spatial indexes 1
Experiment: Retrieval I/O Cost with Spatial Indexes (1)

  • I/O cost evaluation using R-tree (GiST)

    • Target dataset (green points): 39,226 crossroad points of Maryland County in U.S.

    • Query: 62 blue points along the road

  • I/O costs are compared for

    • sequential scan

    • ellipsoid distance query with the support of spatial indexes

  • k-NN (k = 1, 10, …, 150) results are shown



Organization5
Organization

  • Background and Overview

  • Our Approach

  • Examples

  • Query Processing with Spatial Indexes

  • Incremental Query Update

  • Conclusions and Future Work


Query update
Query Update

  • In each query point, a slightly different query is generated

    • The query center and the distance function will change

  • Naïve update strategy

    • Derive the query center and the distance function from scratch

    • The generation cost is quite large

      • It requires calculation from past/future trajectory information

  • Can we update queries incrementally?

    • Answer: Yes, but periodic reorganization is required


Incremental query update 1
Incremental Query Update (1)

  • Basic Idea

    • Decompose statistics used to generate a query into past part and future part

    • At each update, make “one step shift” from the future part to the past part

    • Exponential decay factors allow a simple and efficient procedure


Incremental query update 2
Incremental Query Update (2)

  • Example: Incremental update of query center for model avg

    • Decompose x|t as


Incremental query update 3
Incremental Query Update (3)

  • Then update using the following formulas

  • We can make an incremental update for covariance matrix (C) in a similar manner


Incremental query update 4
Incremental Query Update (4)

  • Incremental query update procedure allows constant update cost for fixed dimensionality d

  • Bad news: two problems

    • A moving object may reach early or late to the next point. Moreover, it may change the estimated route.

    • A number of incremental updates will result in incorrect query generation since the proposed incremental update procedure amplifies the noise.

  • Practical update procedure

    • Use incremental update procedure for short period and recalculate statistics periodically


Organization6
Organization

  • Background and Overview

  • Our Approach

  • Examples

  • Query Processing with Spatial Indexes

  • Incremental Query Update

  • Conclusions and Future Work


Conclusions
Conclusions

  • Generation of Neighborhood Tracking Queries Based on Adaptive Distances (Ellipsoid Distances)

    • Introduction of Influence Decay Model of Trajectory Points

    • Proposal of Spatial Query Generation Models

  • Efficient Query Evaluation with Spatial Indexes

  • Query Update Method for Continual Query Processing


Future work
Future Work

  • Development of parameter set-up method that considers query workloads and query tasks

  • Use of previous query results (cached results) for efficient continual query processing

  • Development of Prototype System


Prototype system
Prototype System

Under

development

on top of

ArcView GIS

Support of

dynamic

location feeding

from GPS


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