Indexing Fingerprint Data with Clustering Approach

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Indexing Fingerprint Data with Clustering Approach

• Wooseok Ryu
• Database Lab.
• September 22, 2007

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Summary of Previous Seminar

• 2 approaches for indexing fingerprint data when
  the number of Access Point is many
• Multi-Dimensional Approach
• Description
• Assign dimension to each Access Point
• The number of dimension is same as the number of
  AP
• Problem
• Curse of dimensionality
• Set of 1-D Index Approach
• Description
• Maintaining one 1-D Index per Access Point
• Merge result of each index
• Problem
• Not faster than M-D Index Approach

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Todays Topic

• Comments at Previous Seminar
• How to reduce dimensions in the Multi-Dimensional
  Approach?
• Index Pruning Approach
• Clustering Approach
• Todays Topic
• Review of Clustering Approach
• Problem of Previous Approach
• Basic Idea for Clustering

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Clustering Approach

• Clustering
• To reduce the computational cost of searching the
  radio map
• A set of locations sharing a common set of access
  points

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Related Work Clustering

• Clustering at the offline phase
• Group locations into clusters according to access
  points that cover the locations
• For a given location l, use the set of the q
  strongest access points covering this location as
  the cluster key
• Use MaxSignal value of each access points
• Do not use weak access points

WLAN Location Determination via Clustering and
Probability Distributions Youssef, Agrawala,
Shankar (PerCom 2003)
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Related Work Clustering

• Online Location Determination Phase
• Determine cluster to search
• Use q strongest access points to determine one
  cluster
• Find most probable location within a cluster
• Use Bayes theorem to estimate the probability of
  each location within the cluster
• Compute each location one by one and choose one
  with highest joint probability

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Related Work Clustering

• Experimental Testbed
• Total 110 locations along the corridors (5 feet
  apart)
• Each location is covered averagely by 4 access
  points

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Related Work Clustering

• Experimental Result
• In the offline phase, number of clusters is 15
  when q is 3
• Average cluster size is about 6 7.
• Clustering reduces the average number of
  operations per location estimate by more than an
  order of magnitude

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Problem of Related Work

• Problem of using only MaxSignal
• Observed vector can fall into wrong cluster
• Because of the characteristics of probability
  distribution
• Simply using q strongest access points to
  determine one cluster cannot guarantee the
  accuracy

Example of off-line Clustering
Example of on-line location determination
C1 AP1, AP2, AP3
C2 AP1, AP2, AP4
AP1
AP2
L1 L2 L3 L4 L5 L6 L7 L8
L9 L10 L11 L12 L13 L14 L15 L16
L17 L18 L19 L20 L21 L22 L23 L24
AP3
AP4
C3 AP1, AP3, AP4
C4 AP2, AP3, AP4
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Problem of Related Work

• Summary
• When choosing q strongest access points at each
  location
• Using just MaxSignal value degrades accuracy
• How to solve the problem?
• we must consider probability distribution
• not only MaxSignal values

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Basic Approach

• Assigning one location into multiple clusters
• Compute possible combination of q strongest
  access points from one locations

3 strongest AP based on Max Signal ? AP1, AP2,
AP3
P
0.5
Possible cases when q is 3
0.4
0.3
0.2
0.1
AP1
AP3
SS at Location 9
-90
-80
-70
-60
-50
-40
-30
-100
AP4
AP2
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Basic Approach

• Multiple Clustering Example
• assign each location into multiple clusters
• Consider all possible combinations

C1 AP1, AP2, AP3
C2 AP1, AP2, AP4
AP1
AP2
L1 L2 L3 L4 L5 L6 L7 L8
L9 L10 L11 L12 L13 L14 L15 L16
L17 L18 L19 L20 L21 L22 L23 L24
AP3
AP4
Location 9 is assigned to cluster C1, C2, C3
C3 AP1, AP3, AP4
C4 AP2, AP3, AP4
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Problem Domain

• Processing Real-Time Phase
• 1. find cluster that contains q strong access
  points
• 2. compute probability distribution of each
  location in the cluster

1. Find matching cluster for received signal
-45, -56, -65, -80
2. In a selected cluster, find best matching
location for signal -45, -56, -65, -80 ?
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First Step Finding matching cluster

• Naïve Approach
• Sequential scan
• Performance degrades when the number of cluster
  is many

Received Signal AP1 -45, AP2 -56, AP3
-65, AP4 -80 3 strongest access points
AP1, AP2, AP3
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First Step Finding matching cluster

• Indexing Cluster Key
• Assign each Access Point to unique number as
  following
• 20, 21, 22, , 2k (k is the number of all access
  points)
• Example
• AP1 20
• AP2 21
• AP3 22
• AP4 23
• Unique number can be assigned to each cluster

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First Step Finding matching cluster

• Indexing Cluster Key is same as indexing Cluster
  Number
• We can use well-known 1-D index structure
• B-Tree for Disk Index
• T-Tree for Main Memory Index

11, C2
7, C1
14, C3
13, C4
Index Representation using Binary Tree
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Second Step Search a best matching location

• Search best matching location in a cluster
• Use q strongest access points, model q1
  dimensional space

Joint Probability
1
0
-100
0
Signal Strength of AP1
-100
0
Signal Strength of AP2
Example value of q is 2, cluster key is AP1,
AP2
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Second Step Search a best matching location

• Example of Joint Probability Distribution over 2
  Access Points

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Second Step Search a best matching location

• Indexing Multi-Dimensional Space
• Use GRID Approach for fast stabbing Query

SS of AP2
-20
-30
MBR7
-40
-50
MBR6
-60
-70
MBR5
-80
-90
SS of AP1
-90
-80
-70
-60
-50
-40
-30
-20
-10
-100
0
MBR4
MBR1
MBR3
MBR2
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Discussion

• Using this Approach
• multi-dimensional index problem can be reduced by
  adopting clustering approach
• Two-step approach
• Finding appropriate cluster
• Search location within one cluster
• Further step
• More efficient access method for a cluster
• How to get optimal q value ?
• Previous approach just showed experimental result
• Optimal value of q highly depends on real
  environment
• This is very critical for performance as well as
  accuracy

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What is optimal q value?

• Real Example showing 24 locations at 6th Bldg
• Too many clusters when q is 3