active nearest n eighbor queries for moving objects
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24.11.2002 The Fourth WIM Meeting 1
Active Nearest Neighbor Queries
for Moving Objects
Jan Kolar, Igor Timko
24.11.2002 The Fourth WIM Meeting 2
Outline
Problem StatementSystem Architecture Data ModelTracking Moving Objects NNC Search & Active Result Distance between Moving Points Conclusions Proposals for Bachelor Projects
24.11.2002 The Fourth WIM Meeting 3
Problem Statement Road Network
Copenhagen Moving Data Points
Cars, pedestrians, cyclists, ... Distance along the roads Query Point
A shop assistant Active K-Nearest Neighbor
Query
Monitor 2 nearest shoppers
that need
a nice and cheap dress Active Query Result
T1 : <A, B>
T2 : <B, C>
24.11.2002 The Fourth WIM Meeting 4
Problem Statement Road Network
Copenhagen Moving Data Points
Cars, pedestrians, cyclists, ... Distance along the roads Query Point
A shop assistant Active K-Nearest Neighbor
Query
Monitor 2 nearest shoppers
that need
a nice and cheap dress Active Query Result
T1 : <A, B>
T2 : <B, C>
24.11.2002 The Fourth WIM Meeting 5
Problem Statement Road Network
Copenhagen Moving Data Points
Cars, pedestrians, cyclists, ... Distance along the roads Query Point
A shop assistant Active K-Nearest Neighbor
Query
Monitor 2 nearest shoppers
that need
a nice and cheap dress Active Query Result
T1 : <A, B>
T2 : <B, C>
24.11.2002 The Fourth WIM Meeting 6
Problem Statement Road Network
Copenhagen Moving Data Points
Cars, pedestrians, cyclists, ... Distance along the roads Query Point
A shop assistant Active K-Nearest Neighbor
Query
Monitor 2 nearest shoppers
that need
a nice and cheap dress Active Query Result
T1 : <A, B>
T2 : <B, C>
24.11.2002 The Fourth WIM Meeting 7
Problem Statement Road Network
Copenhagen Moving Data Points
Cars, pedestrians, cyclists, ...
Query Point
A shop assistant Active K-Nearest Neighbor
Query
Monitor 2 nearest shoppers
that need
a nice and cheap dress Active Query Result
T1 : <A, B>
T2 : <B, C>
Distance along the roads
24.11.2002 The Fourth WIM Meeting 8
Problem Statement Road Network
Copenhagen Moving Data Points
Cars, pedestrians, cyclists, ... Distance along the roads Query Point
A shop assistant Active K-Nearest Neighbor
Query
Monitor 2 nearest shoppers
that need
a nice and cheap dress Active Query Result
T1 : <A, B>
T2 : <B, C>
?
A
B
C
24.11.2002 The Fourth WIM Meeting 9
Problem Statement Road Network
Copenhagen Moving Data Points
Cars, pedestrians, cyclists, ... Distance along the roads Query Point
A shop assistant Active K-Nearest Neighbor
Query
Monitor 2 nearest shoppers
that need
a nice and cheap dress Active Query Result
T1 : <A, B>
T2 : <B, C>
?
Time T1
A
B
C
24.11.2002 The Fourth WIM Meeting 10
Problem Statement Road Network
Copenhagen Moving Data Points
Cars, pedestrians, cyclists, ... Distance along the roads Query Point
A shop assistant Active K-Nearest Neighbor
Query
Monitor 2 nearest shoppers
that need
a nice and cheap dress Active Query Result
T1 : <A, B>
T2 : <B, C>
?
Time T1
A
B
C
24.11.2002 The Fourth WIM Meeting 11
Problem Statement Road Network
Copenhagen Moving Data Points
Cars, pedestrians, cyclists, ... Distance along the roads Query Point
A shop assistant Active K-Nearest Neighbor
Query
Monitor 2 nearest shoppers
that need
a nice and cheap dress Active Query Result
T1 : <A, B>
T2 : <B, C>
?
Time T1
A
B
C
24.11.2002 The Fourth WIM Meeting 12
Problem Statement Road Network
Copenhagen Moving Data Points
Cars, pedestrians, cyclists, ... Distance along the roads Query Point
A shop assistant Active K-Nearest Neighbor
Query
Monitor 2 nearest shoppers
that need
a nice and cheap dress Active Query Result
T1 : <A, B>
T2 : <B, C>
?
Time T1
A
B
C
24.11.2002 The Fourth WIM Meeting 13
Problem Statement Road Network
Copenhagen Moving Data Points
Cars, pedestrians, cyclists, ... Distance along the roads Query Point
A shop assistant Active K-Nearest Neighbor
Query
Monitor 2 nearest shoppers
that need
a nice and cheap dress Active Query Result
T1 : <A, B>
T2 : <B, C>
?
Time T2
AB
C
24.11.2002 The Fourth WIM Meeting 14
Problem Statement Road Network
Copenhagen Moving Data Points
Cars, pedestrians, cyclists, ... Distance along the roads Query Point
A shop assistant Active K-Nearest Neighbor
Query
Monitor 2 nearest shoppers
that need
a nice and cheap dress Active Query Result
T1 : <A, B>
T2 : <B, C>
?
Time T2
AB
C
24.11.2002 The Fourth WIM Meeting 15
Problem Statement Road Network
Copenhagen Moving Data Points
Cars, pedestrians, cyclists, ... Distance along the roads Query Point
A shop assistant Active K-Nearest Neighbor
Query
Monitor 2 nearest shoppers
that need
a nice and cheap dress Active Query Result
T1 : <A, B>
T2 : <B, C>
?
Time T2
AB
C
24.11.2002 The Fourth WIM Meeting 16
Problem Statement Road Network
Copenhagen Moving Data Points
Cars, pedestrians, cyclists, ... Distance along the roads Query Point
A shop assistant Active K-Nearest Neighbor
Query
Monitor 2 nearest shoppers
that need
a nice and cheap dress Active Query Result
T1 : <A, B>
T2 : <B, C>
?
Time T2
AB
C
24.11.2002 The Fourth WIM Meeting 17
System Architecture
Active Result
Positioning Unit
Client Position
Visualization
DB of Distances
Road Network
User Query
Result
NNC Search
DB of Moving Points
Road Network
NNC Request
NNC ReplyNNC Refresh
RN Input
Position Update
RN Update
SERVER CLIENT
24.11.2002 The Fourth WIM Meeting 18
System Architecture
Active Result
Positioning Unit
Client Position
Visualization
DB of Distances
Road Network
User Query
Result
NNC Search
DB of Moving Points
Road Network
NNC Request
NNC ReplyNNC Refresh
RN Input
Position Update
RN Update
SERVER CLIENT
24.11.2002 The Fourth WIM Meeting 19
System Architecture
Active Result
Positioning Unit
Client Position
Visualization
DB of Distances
Road Network
User Query
Result
NNC Search
DB of Moving Points
Road Network
NNC Request
NNC ReplyNNC Refresh
RN Input
Position Update
RN Update
SERVER CLIENT
24.11.2002 The Fourth WIM Meeting 20
System Architecture
Active Result
Positioning Unit
Client Position
Visualization
DB of Distances
Road Network
User Query
Result
NNC Search
DB of Moving Points
Road Network
NNC Request
NNC ReplyNNC Refresh
RN Input
Position Update
RN Update
SERVER CLIENT
24.11.2002 The Fourth WIM Meeting 21
Outline
Problem StatementSystem Architecture Data ModelTracking Moving Objects NNC Search & Active Result Distance between Moving Points Conclusions Proposals for Bachelor Projects
24.11.2002 The Fourth WIM Meeting 22
Data Model : Overview
Problem Data Road Network (RN) Data Points (DPs)
2D Representation Captures data in native form Supports positioning and visualization Source for graph representation
Graph Representation Captures data in simpler and more ”compact” form Supports algorithms for NN search
24.11.2002 The Fourth WIM Meeting 23
Data Model : Overview
Problem Data Road Network (RN) Data Points (DPs)
2D Representation Captures data in native form Supports positioning and visualization Source for graph representation
Graph Representation Captures data in simpler and more ”compact” form Supports algorithms for NN search
24.11.2002 The Fourth WIM Meeting 24
Data Model : Overview
Problem Data Road Network (RN) Data Points (DPs)
2D Representation Captures data in native form Supports positioning and visualization Source for graph representation
Graph Representation Captures data in simpler and more ”compact” form Supports algorithms for NN search
24.11.2002 The Fourth WIM Meeting 25
Data Model : Overview
Problem Data Road Network (RN) Data Points (DPs)
2D Representation Captures data in native form Supports positioning and visualization Source for graph representation
Graph Representation Captures data in simpler and more ”compact” form Supports algorithms for NN search
24.11.2002 The Fourth WIM Meeting 26
Data Model : Road Network
2D
Graph
Real-World RN Road segments
2D RN Lines approximate road segments Lines start and end at vertices Vertices have coordinates
Graph RN Edges are obtained from paths Edges start and end at nodes Nodes have no coordinates
RoadNetwork
24.11.2002 The Fourth WIM Meeting 27
Data Model : Road Network
2D
Graph
Real-World RN Road segments
2D RN Lines approximate road segments Lines start and end at vertices Vertices have coordinates
Graph RN Edges are obtained from paths Edges start and end at nodes Nodes have no coordinates
RoadNetwork
24.11.2002 The Fourth WIM Meeting 28
Data Model : Road Network
Graph
Real-World RN Road segments
2D RN Lines approximate road segments Lines start and end at vertices Vertices have coordinates
Graph RN Edges are obtained from paths Edges start and end at nodes Nodes have no coordinates
2D
RoadNetwork
24.11.2002 The Fourth WIM Meeting 29
Data Model : Road Network
Graph
2D
Real-World RN Road segments
2D RN Lines approximate road segments Lines start and end at vertices Vertices have coordinates
Graph RN Edges are obtained from paths Edges start and end at nodes Nodes have no coordinates
RoadNetwork
24.11.2002 The Fourth WIM Meeting 30
Data Model : RN Characteristics
Graph
2D
Real-World RN Road segments have length, maximum
speed, and width
2D RN Lines approximate road segments Lines have length and maximum speed Lines have no width
Graph RN Edges are obtained from paths Edges have edge weight Edge weight is minimal travel time along the
edge – distance in graph Edge weight is calculated by combining line
length and maximum speed
RoadNetwork
24.11.2002 The Fourth WIM Meeting 31
Data Model : RN Characteristics Real-World RN
Road segments have length, maximum speed, and width
2D RN Lines approximate road segments Lines have length and maximum speed Lines have no width
Graph RN Edges are obtained from paths Edges have edge weight Edge weight is minimal travel time along the
edge – distance in graph Edge weight is calculated by combining line
length and maximum speed
RoadNetwork
Graph
2D
24.11.2002 The Fourth WIM Meeting 32
Data Model : RN Characteristics Real-World RN
Road segments have length, maximum speed, and width
2D RN Lines approximate road segments Lines have length and maximum speed Lines have no width
Graph RN Edges are obtained from paths Edges have edge weight Edge weight is minimal travel time along the
edge – distance in graph Edge weight is calculated by combining line
length and maximum speed
RoadNetwork
Graph
2D
L=10 MS=2
L=12 MS=4
L=10 MS=5
24.11.2002 The Fourth WIM Meeting 33
Data Model : RN Characteristics Real-World RN
Road segments have length, maximum speed, and width
2D RN Lines approximate road segments Lines have length and maximum speed Lines have no width
Graph RN Edges are obtained from paths Edges have edge weight Edge weight is minimal travel time along the
edge – distance in graph Edge weight is calculated by combining line
length and maximum speed
RoadNetwork
Graph
2D
W=2+3+5=10
L=10 MS=2
L=12 MS=4
L=10 MS=5
24.11.2002 The Fourth WIM Meeting 34
Data Model : Data Points Real-World DPs
Movement of a DP is a continuous function of time
2D Road DPs A DP at a reference time is given by DP
characteristics (DPC): reference timecoordinatespeed
RoadNetwork
2D
24.11.2002 The Fourth WIM Meeting 35
Data Model : Data Points Real-World DPs
Movement of a DP is a continuous function of time
2D Road DPs A DP at a reference time is given by DP
characteristics (DPC): reference timecoordinatespeed
RoadNetwork
2D
C(12)=(33,60)
24.11.2002 The Fourth WIM Meeting 36
Data Model : Data Points Real-World DPs
Movement of a DP is a continuous function of time
2D Road DPs A DP at a reference time is given by DP
characteristics (DPC): reference timecoordinatespeed
RoadNetwork
C(12)=(33,60)
2D
T=11 C=(34,56) S=3
24.11.2002 The Fourth WIM Meeting 37
Data Model : Data Points 2D Road DPs
A DP at the reference time is given by DP characteristics (DPC):
reference timecoordinatespeed
Graph DPs Movement of a DP is a function of time
(positioning function) Positioning function is a combination of DPC:
reference timeedge initial positiongraph speed
2D
T=11 C=(34,56) S=3
Graph
T=11 E=3 IP=3 GS=3
24.11.2002 The Fourth WIM Meeting 38
Data Model : Data Points 2D Road DPs
A DP at the reference time is given by DP characteristics (DPC):
reference timecoordinatespeed
Graph DPs Movement of a DP is a function of time
(positioning function) Positioning function is a combination of DPC:
reference timeedge initial positiongraph speed
2D
T=11 C=(34,56) S=3
Graph
T=11 E=3 IP=3 GS=3
P(12)=3+3 = 6
24.11.2002 The Fourth WIM Meeting 39
Outline
Problem StatementSystem ArchitectureData ModelTracking Moving Objects NNC Search & Active Result Distance between Moving Points Conclusions Proposals for Bachelor Projects
24.11.2002 The Fourth WIM Meeting 40
System Architecture
Active Result
Positioning Unit
Client Position
Visualization
DB of Distances
Road Network
User Query
Result
NNC Search
DB of Moving Points
Road Network
NNC Request
NNC ReplyNNC Refresh
RN Input
Position Update
RN Update
SERVER CLIENT
24.11.2002 The Fourth WIM Meeting 41
For a DP, its Client DPC are obtained from the Positioning Unit on the Client
For a DP, its Server DPC reside in the DB of Moving Points on the Server
Update Policy Threshold is a maximum allowed deviation between the positions
given by the Client DPC and by the Server DPC
Start
Node Node
End
Deviation
P(S)
Th Th
P(C)
Tracking Moving Points
P(C)=P(S)
Th Th
P(S)
Th Th
P(C)
Deviation
P(C)=P(S)
Th Th
24.11.2002 The Fourth WIM Meeting 43
Outline
Problem Statement Data ModelSystem ArchitectureTracking Moving ObjectsNNC Search & Active Result Distance between Moving Points Conclusions Proposals for Bachelor Projects
24.11.2002 The Fourth WIM Meeting 44
System Architecture
Active Result
Positioning Unit
Client Position
Visualization
DB of Distances
Road Network
User Query
Result
NNC Search
DB of Moving Points
Road Network
NNC Request
NNC ReplyNNC Refresh
RN Input
Position Update
RN Update
SERVER CLIENT
24.11.2002 The Fourth WIM Meeting 45
NNC Search
Searches for some number of DPs that are nearest to the QP
Application of the Best First Search in graphs Extended with “reading” DPs from edges
During the search, all the DPs are fixed at the time when the search starts
24.11.2002 The Fourth WIM Meeting 46
NNC Search
Searches for some number of DPs that are nearest to the QP
Application of the Best First Search in graphs Extended with “reading” DPs from edges
During the search, all the DPs are fixed at the time when the search starts
24.11.2002 The Fourth WIM Meeting 47
NNC Search
Searches for some number of DPs that are nearest to the QP
Application of the Best First Search in graphs Extended with “reading” DPs from edges
During the search, all the DPs are fixed at the time when the search starts
24.11.2002 The Fourth WIM Meeting 48
NNC Search
Searches for some number of DPs that are nearest to the QP
Application of the Best First Search in graphs Extended with “reading” DPs from edges
During the search, all the DPs are fixed at the time when the search starts
24.11.2002 The Fourth WIM Meeting 49
Active Result
Distance between QP and NNCs Sorting NNCs with respect to the distance Estimate of imprecision of NNCs
Expiration Number Distance Limit
24.11.2002 The Fourth WIM Meeting 50
Active Result
Distance between QP and NNCs Sorting NNCs with respect to the distance Estimate of imprecision of NNCs
Expiration Number Distance Limit
24.11.2002 The Fourth WIM Meeting 51
Active Result
Distance between QP and NNCs Sorting NNCs with respect to the distance Estimate of imprecision of NNCs
Expiration Number Distance Limit
24.11.2002 The Fourth WIM Meeting 52
Active Result
Distance between QP and NNCs Sorting NNCs with respect to the distance Estimate of imprecision of NNCs
Expiration Number Distance Limit
24.11.2002 The Fourth WIM Meeting 53
Active Result: Procedure
Distance from QP 1 3 5 8 9
Expired DP false false false false false
Distance Limit = 10
Expiration Number = 2
Number of Expired DP = 0
NNC is Valid: YES
1 2 3 4 52 1 4 3 5Time = 1
Number of Expired DP = 1
Time = 2
1371112Distance from QP
falsefalsetruefalsefalseExpired DP
NNC is Valid: NO
15121613Distance from QP
truetruetruefalsefalseExpired DP
Time = 3
Number of Expired DP = 3
2 1 4 3 5
New NNC Request
24.11.2002 The Fourth WIM Meeting 54
Outline
Problem StatementSystem Architecture Data ModelTracking Moving Objects NNC Search & Active Result Distance between Moving Points Conclusions Proposals for Bachelor Projects
24.11.2002 The Fourth WIM Meeting 55
Definition Distance between two DPs is the shortest path
between the DPs
Difficulty The shortest path between two DPs changes as
the DPs move
Distance between Moving Points
24.11.2002 The Fourth WIM Meeting 56
Definition Distance between two DPs is the shortest path
between the DPs
Difficulty The shortest path between two DPs changes as
the DPs move
Distance between Moving Points
24.11.2002 The Fourth WIM Meeting 57
Definition Distance between two DPs is the shortest path
between the DPs
Difficulty The shortest path between two DPs changes as
the DPs move
Distance between Moving Points
24.11.2002 The Fourth WIM Meeting 58
5
1
13
2
3
6
1
4
6
7
Distance between Moving Points
QD
QD
Q
D
24.11.2002 The Fourth WIM Meeting 59
Distance between Moving Points
Requirement Find the shortest path quickly
Idea DB of Distances: pre-compute shortest distances
between each pair of nodes Reduces the distance calculation to several
arithmetic operations
24.11.2002 The Fourth WIM Meeting 60
Distance between Moving Points
Requirement Find the shortest path quickly
Idea DB of Distances: pre-compute shortest distances
between each pair of nodes Reduces the distance calculation to several
arithmetic operations
24.11.2002 The Fourth WIM Meeting 61
Distance between Moving Points
Requirement Find the shortest path quickly
Idea DB of Distances: pre-compute shortest distances
between each pair of nodes Reduces the distance calculation to several
arithmetic operations
24.11.2002 The Fourth WIM Meeting 62
Distance between moving DP: Procedure
5
1
2 1
6
4
6
Q
D
A B
X
Y
|AX|
|AY|
|BX|
|BY|Aq
Aq
Aq
Bq
Bq
Bq
Xd
Xd
Xd
Yd
Yd
Yd
D = min
24.11.2002 The Fourth WIM Meeting 63
Outline
Problem StatementSystem Architecture Data ModelTracking Moving ObjectsNNC Search & Active Result Distance between Moving PointsConclusions Proposals for Bachelor Projects
24.11.2002 The Fourth WIM Meeting 64
Conclusions
Reusable data model Applicable for other NN, and non-NN problems
Classical algorithm for the NNC search An extension of the Best First Search
Simple idea for maintaining the active result Sort NNCs with respect to the distance to the QP Ask for new NNCs, if the current ones get too far from the QP
Efficient algorithm for the distance calculation Uses the pre-computed shortest distances between each pair of
nodes Reduces the distance calculation to several arithmetic operations
24.11.2002 The Fourth WIM Meeting 65
Conclusions
Reusable data model Applicable for other NN, and non-NN problems
Classical algorithm for the NNC search An extension of the Best First Search
Simple idea for maintaining the active result Sort NNCs with respect to the distance to the QP Ask for new NNCs, if the current ones get too far from the QP
Efficient algorithm for the distance calculation Uses the pre-computed shortest distances between each pair of
nodes Reduces the distance calculation to several arithmetic operations
24.11.2002 The Fourth WIM Meeting 66
Conclusions
Reusable data model Applicable for other NN, and non-NN problems
Classical algorithm for the NNC search An extension of the Best First Search
Simple idea for maintaining the active result Sort NNCs with respect to the distance to the QP Ask for new NNCs, if the current ones get too far from the QP
Efficient algorithm for the distance calculation Uses the pre-computed shortest distances between each pair of
nodes Reduces the distance calculation to several arithmetic operations
24.11.2002 The Fourth WIM Meeting 67
Conclusions
Reusable data model Applicable for other NN, and non-NN problems
Classical algorithm for the NNC search An extension of the Best First Search
Simple idea for maintaining the active result Sort NNCs with respect to the distance to the QP Ask for new NNCs, if the current ones get too far from the QP
Efficient algorithm for the distance calculation Uses the pre-computed shortest distances between each pair of
nodes Reduces the distance calculation to several arithmetic operations
24.11.2002 The Fourth WIM Meeting 68
Conclusions
Reusable data model Applicable for other NN, and non-NN problems
Classical algorithm for the NNC search An extension of the Best First Search
Simple idea for maintaining the active result Sort NNCs with respect to the distance to the QP Ask for new NNCs, if the current ones get too far from the QP
Efficient algorithm for the distance calculation Uses the pre-computed shortest distances between each pair of
nodes Reduces the distance calculation to several arithmetic operations
24.11.2002 The Fourth WIM Meeting 69
Conclusions
Reasonable system architecture Based on the client-server architecture Distributes the tasks in an efficient way
“Balanced” handling of position updates Updates are not performed continuously Threshold controls precision
Prototype Single-process system that simulates the real application Experiment results show that the solutions are
reasonable
24.11.2002 The Fourth WIM Meeting 70
Conclusions
Reasonable system architecture Based on the client-server architecture Distributes the tasks in an efficient way
“Balanced” handling of position updates Updates are not performed continuously Threshold controls precision
Prototype Single-process system that simulates the real application Experiment results show that the solutions are
reasonable
24.11.2002 The Fourth WIM Meeting 71
Conclusions
Reasonable system architecture Based on the client-server architecture Distributes the tasks in an efficient way
“Balanced” handling of position updates Updates are not performed continuously Threshold controls precision
Prototype Single-process system that simulates the real application Experiment results show that the solutions are
reasonable
24.11.2002 The Fourth WIM Meeting 72
Conclusions
Reasonable system architecture Based on the client-server architecture Distributes the tasks in an efficient way
“Balanced” handling of position updates Updates are not performed continuously Threshold controls precision
Prototype Single-process system that simulates the real application Experiment results show that the solutions are
reasonable
24.11.2002 The Fourth WIM Meeting 73
Outline
Problem Statement Data ModelNNC Search & Active Result Distance between Moving PointsSystem Architecture Conclusions Proposals for Bachelor Projects
24.11.2002 The Fourth WIM Meeting 74
Proposals for Bachelor Projects
Implementation, experiments, and improvements NNC search Active result Distance calculation Complete architecture
Extending the settings: influence on the algorithms,
the architecture, and the data model “Richer” model Uncertainty of Query Results Pre-Defined Routes Dynamic Weights
24.11.2002 The Fourth WIM Meeting 75
Proposals for Bachelor Projects
Implementation, experiments, and improvements NNC search Active result Distance calculation Complete architecture
Extending the settings: influence on the algorithms,
the architecture, and the data model “Richer” model Uncertainty of Query Results Pre-Defined Routes Dynamic Weights
24.11.2002 The Fourth WIM Meeting 76
Proposals for Bachelor Projects
Implementation, experiments, and improvements NNC search Active result Distance calculation Complete architecture
Extending the settings: influence on the algorithms,
the architecture, and the data model “Richer” model Uncertainty of Query Results Pre-Defined Routes Dynamic Weights
24.11.2002 The Fourth WIM Meeting 77
Active Nearest Neighbor Queries
for Moving Objects
Jan Kolar, Igor Timko
24.11.2002 The Fourth WIM Meeting 78
Uncertainty in the NN problem
Igor Timko
24.11.2002 The Fourth WIM Meeting 79
Outline
UncertaintyHandling Location UncertaintyConclusions
24.11.2002 The Fourth WIM Meeting 80
Uncertainty
Sources of the uncertainty Location of DPs NNCs Dynamic weights Partial NNC search Partial DB of distances Communication network
Problem with the uncertainty Imprecise query result
Handling the uncertainty Calculate the probabilistic NN neighbor
24.11.2002 The Fourth WIM Meeting 81
Uncertainty
Sources of the uncertainty Location of DPs NNCs Dynamic weights Partial NNC search Partial DB of distances Communication network
Problem with the uncertainty Imprecise query result
Handling the uncertainty Calculate the probabilistic NN neighbor
24.11.2002 The Fourth WIM Meeting 82
Uncertainty
Sources of the uncertainty Location of DPs NNCs Dynamic weights Partial NNC search Partial DB of distances Communication network
Problem with the uncertainty Imprecise query result
Handling the uncertainty Calculate the probabilistic NN neighbor
24.11.2002 The Fourth WIM Meeting 83
Uncertainty
Sources of the uncertainty Location of DPs NNCs Dynamic weights Partial NNC search Partial DB of distances Communication network
Problem with the uncertainty Imprecise query result
Handling the uncertainty Calculate the probabilistic NN neighbor
24.11.2002 The Fourth WIM Meeting 84
Outline
UncertaintyHandling Location UncertaintyConclusions
24.11.2002 The Fourth WIM Meeting 85
Handling Location Uncertainty Old active result procedure
Obtain NNCs Calculate distances between the NNCs and the QP Sort the NNCs
Identifying the uncertainty Calculated distances are uncertain, because locations of NNCs are uncertain
24.11.2002 The Fourth WIM Meeting 86
Handling Location Uncertainty Old active result procedure
Obtain NNCs Calculate distances between the NNCs and the QP Sort the NNCs
Identifying the uncertainty Calculated distances are uncertain, because locations of NNCs are uncertain
24.11.2002 The Fourth WIM Meeting 87
Handling Location Uncertainty Old active result procedure
Obtain NNCs Calculate distances between the NNCs and the QP Sort the NNCs
Identifying the uncertainty Calculated distances are uncertain, because locations of NNCs are uncertain
24.11.2002 The Fourth WIM Meeting 88
Measuring the Uncertainty
Bounded normal distribution• Mean is at the distance value• Deviation is the update threshhold
D1 D2 D3
Th Th
24.11.2002 The Fourth WIM Meeting 89
New Active Result Procedure New active result procedure
Obtain NNCs For each NNC
• calculate distances between it and the QP• construct the probability distribution• calculate the probability of being NN
24.11.2002 The Fourth WIM Meeting 90
New Active Result Procedure New active result procedure
Obtain NNCs For each NNC
• calculate distances between it and the QP• construct the probability distribution• calculate the probability of being NN
24.11.2002 The Fourth WIM Meeting 91
Conclusions
There are many sources of the uncertainty in the NN problem
The uncertainty makes the NN query result imprecise
The uncertainty is handled by the probabilistic NN queries
24.11.2002 The Fourth WIM Meeting 92
Conclusions
There are many sources of the uncertainty in the NN problem
The uncertainty makes the NN query result imprecise
The uncertainty is handled by the probabilistic NN queries
24.11.2002 The Fourth WIM Meeting 93
Conclusions
There are many sources of the uncertainty in the NN problem
The uncertainty makes the NN query result imprecise
The uncertainty is handled by the probabilistic NN queries
24.11.2002 The Fourth WIM Meeting 94
Conclusions
There are many sources of the uncertainty in the NN problem
The uncertainty makes the NN query result imprecise
The uncertainty is handled by the probabilistic NN queries
24.11.2002 The Fourth WIM Meeting 95
Uncertainty in the NN problem
Igor Timko
24.11.2002 The Fourth WIM Meeting 96
Outline
UncertaintyHandling Location UncertaintyConclusions
24.11.2002 The Fourth WIM Meeting 97
Uncertainty
Sources of the uncertainty Location of DPs NNCs Dynamic weights Partial NNC search Partial DB of distances Communication network
Problem with the uncertainty Imprecise query result
Handling the uncertainty Calculate the probabilistic NN neighbor
24.11.2002 The Fourth WIM Meeting 98
Uncertainty
Sources of the uncertainty Location of DPs NNCs Dynamic weights Partial NNC search Partial DB of distances Communication network
Problem with the uncertainty Imprecise query result
Handling the uncertainty Calculate the probabilistic NN neighbor
24.11.2002 The Fourth WIM Meeting 99
Uncertainty
Sources of the uncertainty Location of DPs NNCs Dynamic weights Partial NNC search Partial DB of distances Communication network
Problem with the uncertainty Imprecise query result
Handling the uncertainty Calculate the probabilistic NN neighbor
24.11.2002 The Fourth WIM Meeting 100
Uncertainty
Sources of the uncertainty Location of DPs NNCs Dynamic weights Partial NNC search Partial DB of distances Communication network
Problem with the uncertainty Imprecise query result
Handling the uncertainty Calculate the probabilistic NN neighbor
24.11.2002 The Fourth WIM Meeting 101
Outline
UncertaintyHandling Location UncertaintyConclusions
24.11.2002 The Fourth WIM Meeting 102
Handling Location Uncertainty Old active result procedure
Obtain NNCs Calculate distances between the NNCs and the QP Sort the NNCs
Identifying the uncertainty Calculated distances are uncertain, because locations of NNCs are uncertain
24.11.2002 The Fourth WIM Meeting 103
Handling Location Uncertainty Old active result procedure
Obtain NNCs Calculate distances between the NNCs and the QP Sort the NNCs
Identifying the uncertainty Calculated distances are uncertain, because locations of NNCs are uncertain
24.11.2002 The Fourth WIM Meeting 104
Handling Location Uncertainty Old active result procedure
Obtain NNCs Calculate distances between the NNCs and the QP Sort the NNCs
Identifying the uncertainty Calculated distances are uncertain, because locations of NNCs are uncertain
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Measuring the Uncertainty
Bounded normal distribution• Mean is at the distance value• Deviation is the update threshhold
D1 D2 D3
Th Th
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Measuring the Uncertainty
Bounded normal distribution• Mean is at the distance value• Deviation is the update threshhold
D1 D2 D3
Th Th
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New Active Result Procedure New active result procedure
Obtain NNCs For each NNC
• calculate distances between it and the QP• construct the probability distribution• calculate the probability of being NN
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New Active Result Procedure New active result procedure
Obtain NNCs For each NNC
• calculate distances between it and the QP• construct the probability distribution• calculate the probability of being NN
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Conclusions
There are many sources of the uncertainty in the NN problem
The uncertainty makes the NN query result imprecise
The uncertainty is handled by the probabilistic NN queries
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Outline
UncertaintyHandling Location UncertaintyConclusions
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Conclusions
There are many sources of the uncertainty in the NN problem
The uncertainty makes the NN query result imprecise
The uncertainty is handled by the probabilistic NN queries
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Conclusions
There are many sources of the uncertainty in the NN problem
The uncertainty makes the NN query result imprecise
The uncertainty is handled by the probabilistic NN queries
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Conclusions
There are many sources of the uncertainty in the NN problem
The uncertainty makes the NN query result imprecise
The uncertainty is handled by the probabilistic NN queries
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Uncertainty in the NN problem
Igor Timko
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