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K-MST -based clustering

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Title: K-MST-based clustering Author: Thinkpad Last modified by: franti Created Date: 2/15/2010 10:05:41 AM Document presentation format: On-screen Show – PowerPoint PPT presentation

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Title: K-MST -based clustering


1
K-MST -based clustering
  • Caiming Zhong
  • Pasi Franti

2
Outline
  • Minimum spanning tree (MST)
  • MST-based clustering
  • K-MST
  • K-MST-based clustering
  • Fast approximate MST

MST MST-based clustering K-MST K-MST-based
clustering Fast approximate MST
3
Minimum Spanning Tree
  • Spanning tree

Given graph
MST MST-based clustering K-MST K-MST-based
clustering Fast approximate MST
Spanning tree
Non-Spanning tree
4
Minimum Spanning Tree
  • Minimize the sum of weights (Kruskal, Prims
    Algorithm)

MST MST-based clustering K-MST K-MST-based
clustering Fast approximate MST
Given graph G(V,E)
MST T
5
MST-based clustering
  • The most used Method1 removing long MST-edges

MST MST-based clustering K-MST K-MST-based
clustering Fast approximate MST
6
MST MST-based clustering K-MST K-MST-based
clustering Fast approximate MST
7
MST-based clustering
  • Removing long MST-edges doesnt always work

MST MST-based clustering K-MST K-MST-based
clustering Fast approximate MST
8
MST-based clustering
  • The most used Method2 edge inconsistent

Tree edge AB, whose weight W(AB) is significantly
larger than the average of nearby edge weights on
both sides of the edge AB, should be deleted.
MST MST-based clustering K-MST K-MST-based
clustering Fast approximate MST
9
K-MST
  • What is K-MST?
  • Let G (V,E) denote the complete graph
  • Let MST1 denote the MST of G, and it is computed
    as MST1 mst(V, E).
  • Then, MST2 denote the second round of MST of G,
    MST2 mst(V, E- MST1).
  • MSTk mst(V, E- MST1--MSTk-1).

MST MST-based clustering K-MST K-MST-based
clustering Fast approximate MST
10
MST MST-based clustering K-MST K-MST-based
clustering Fast approximate MST
11
K-MST
  • K-MST-based graph

MST MST-based clustering K-MST K-MST-based
clustering Fast approximate MST
12
K-MST
  • Typical clustering problems
  • Separated problems and touching problems.
  • Separated problems includes distance-separated
    problems and density-separated problems.

MST MST-based clustering K-MST K-MST-based
clustering Fast approximate MST
13
K-MST-based clustering
  • Definition of edge weight for separated problems

MST MST-based clustering K-MST K-MST-based
clustering Fast approximate MST
14
Three good features (1) Weights of inter-cluster
edges are quite larger than those of
intra-cluster edges. (2) The inter-cluster edges
are approximately equally distributed to T1 and
T2. (3) Except inter- cluster edges, most of
edges with large weights come from T2.
15
MST MST-based clustering K-MST K-MST-based
clustering Fast approximate MST
16
MST MST-based clustering K-MST K-MST-based
clustering Fast approximate MST
17
K-MST-based clustering
  • Touching problems

MST MST-based clustering K-MST K-MST-based
clustering Fast approximate MST
18
Partition(cut1) and Partition(cut3) are similar
Partition(cut2) and Partition(cut3) are similar
.
19
Fast approximate MST (FAMST)
  • Traditional MST algorithms take O(N2) time, not
    favored by large data sets.
  • In practical application, generally FAMST has as
    same result as exact MST
  • Find a FAMST in O(N1.55)

MST MST-based clustering K-MST K-MST-based
clustering Fast approximate MST
20
Fast approximate MST (FAMST)
  • Scheme Divide-and-Conquer

MST MST-based clustering K-MST K-MST-based
clustering Fast approximate MST
21
Fast approximate MST (FAMST)
  • Performance

MST MST-based clustering K-MST K-MST-based
clustering Fast approximate MST
22
MST MST-based clustering K-MST K-MST-based
clustering Fast approximate MST
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