The Fourth WIM Meeting 1 Active Nearest Neighbor Queries for Moving Objects Jan Kolar, Igor Timko

The Fourth WIM Meeting 2 Outline  Problem Statement  System Architecture  Data Model  Tracking Moving Objects  NNC Search & Active Result  Distance between Moving Points  Conclusions  Proposals for Bachelor Projects

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 T 1 : T 2 :

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 T 1 : T 2 :

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 T 1 : T 2 :

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 T 1 : T 2 :

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 T 1 : T 2 :  Distance along the roads

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 T 1 : T 2 : ? A B C

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 T 1 : T 2 : ? Time T 1 A B C

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 T 1 : T 2 : ? Time T 1 A B C

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 T 1 : T 2 : ? Time T 1 A B C

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 T 1 : T 2 : ? Time T 1 A B C

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 T 1 : T 2 : ? Time T 2 A B C

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 T 1 : T 2 : ? Time T 2 A B C

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 T 1 : T 2 : ? Time T 2 A B C

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 T 1 : T 2 : ? Time T 2 A B C

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 Reply NNC Refresh RN Input Position Update RN Update SERVERCLIENT

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 Reply NNC Refresh RN Input Position Update RN Update SERVERCLIENT

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 Reply NNC Refresh RN Input Position Update RN Update SERVERCLIENT

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 Reply NNC Refresh RN Input Position Update RN Update SERVERCLIENT

The Fourth WIM Meeting 21 Outline Problem Statement System Architecture  Data Model  Tracking Moving Objects  NNC Search & Active Result  Distance between Moving Points  Conclusions  Proposals for Bachelor Projects

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

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

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

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

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 Road Network

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 Road Network

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 Road Network

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 Road Network

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 Road Network

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 Road Network Graph 2D

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 Road Network Graph 2D L=10 MS=2 L=12 MS=4 L=10 MS=5

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 Road Network Graph 2D W=2+3+5=10 L=10 MS=2 L=12 MS=4 L=10 MS=5

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 time  coordinate  speed Road Network 2D

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 time  coordinate  speed Road Network 2D C(12)=(33,60)

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 time  coordinate  speed Road Network C(12)=(33,60) 2D T=11 C=(34,56) S=3

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 time  coordinate  speed  Graph DPs  Movement of a DP is a function of time (positioning function)  Positioning function is a combination of DPC:  reference time  edge  initial position  graph speed 2D T=11 C=(34,56) S=3 Graph T=11 E=3 IP=3 GS=3

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 time  coordinate  speed  Graph DPs  Movement of a DP is a function of time (positioning function)  Positioning function is a combination of DPC:  reference time  edge  initial position  graph speed 2D T=11 C=(34,56) S=3 Graph T=11 E=3 IP=3 GS=3 P(12)=3+3 = 6

The Fourth WIM Meeting 39 Outline Problem Statement System Architecture Data Model  Tracking Moving Objects  NNC Search & Active Result  Distance between Moving Points  Conclusions  Proposals for Bachelor Projects

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 Reply NNC Refresh RN Input Position Update RN Update SERVERCLIENT

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 End Deviation P(S) Th P(C) Tracking Moving Points P(C)=P(S) Th P(S) Th P(C) Deviation P(C)=P(S) Th

The Fourth WIM Meeting 42  After a DP traverses to a new edge, its Server DPC expires  Update policies  Update immediately after traversing to a new edge  Update after the threshold is exceeded Tracking Moving Points – Passing a Node P(C) P(S) Th Deviation P(S) P(C) Deviation Th P(S) P(C) Deviation Th DPC Update P(C) Th P(S)

The Fourth WIM Meeting 43 Outline Problem Statement Data Model System Architecture Tracking Moving Objects  NNC Search & Active Result  Distance between Moving Points  Conclusions  Proposals for Bachelor Projects

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 Reply NNC Refresh RN Input Position Update RN Update SERVERCLIENT

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

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

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

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

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

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

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

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

The Fourth WIM Meeting 53 Active Result: Procedure Distance from QP13589 Expired DPfalse Distance Limit = 10 Expiration Number = 2 Number of Expired DP = 0 NNC is Valid: YES Time = 1 Number of Expired DP = 1 Time = Distance from QP false truefalse Expired DP NNC is Valid: NO Distance from QP true false Expired DP Time = 3 Number of Expired DP = New NNC Request

The Fourth WIM Meeting 54 Outline Problem Statement System Architecture Data Model Tracking Moving Objects NNC Search & Active Result  Distance between Moving Points  Conclusions  Proposals for Bachelor Projects

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

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

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

The Fourth WIM Meeting Distance between Moving Points Q D Q D Q D

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

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

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

The Fourth WIM Meeting 62 Distance between moving DP: Procedure Q D A B X Y |AX| |AY| |BX| |BY| D = min

The Fourth WIM Meeting 63 Outline Problem Statement System Architecture Data Model Tracking Moving Objects NNC Search & Active Result Distance between Moving Points  Conclusions  Proposals for Bachelor Projects

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

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

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

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

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

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

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

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

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

The Fourth WIM Meeting 73 Outline Problem Statement Data Model NNC Search & Active Result Distance between Moving Points System Architecture Conclusions  Proposals for Bachelor Projects

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

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

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

The Fourth WIM Meeting 77 Active Nearest Neighbor Queries for Moving Objects Jan Kolar, Igor Timko

The Fourth WIM Meeting 78 Uncertainty in the NN problem Igor Timko

The Fourth WIM Meeting 79 Outline  Uncertainty  Handling Location Uncertainty  Conclusions

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

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

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

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

The Fourth WIM Meeting 84 Outline  Uncertainty  Handling Location Uncertainty  Conclusions

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

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

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

The Fourth WIM Meeting 88 Measuring the Uncertainty  Bounded normal distribution Mean is at the distance value Deviation is the update threshhold D1D1 D2D2 D3D3 Th

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

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

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

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

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

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

The Fourth WIM Meeting 95 Uncertainty in the NN problem Igor Timko

The Fourth WIM Meeting 96 Outline  Uncertainty  Handling Location Uncertainty  Conclusions

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

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

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

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

The Fourth WIM Meeting 101 Outline  Uncertainty  Handling Location Uncertainty  Conclusions

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

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

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

The Fourth WIM Meeting 105 Measuring the Uncertainty  Bounded normal distribution Mean is at the distance value Deviation is the update threshhold D1D1 D2D2 D3D3 Th

The Fourth WIM Meeting 106 Measuring the Uncertainty  Bounded normal distribution Mean is at the distance value Deviation is the update threshhold D1D1 D2D2 D3D3 Th

The Fourth WIM Meeting 107 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

The Fourth WIM Meeting 108 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

The Fourth WIM Meeting 109 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

The Fourth WIM Meeting 110 Outline  Uncertainty  Handling Location Uncertainty  Conclusions

The Fourth WIM Meeting 111 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

The Fourth WIM Meeting 112 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

The Fourth WIM Meeting 113 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

The Fourth WIM Meeting 114 Uncertainty in the NN problem Igor Timko