Cluster Analysis

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Cluster Analysis

• Lecture Notes for Chapter 8

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Announcements

• Assignment update
• Paper for next time
• Focus on sections 1-3
• Projects 10 days (have datasets ready)

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Hierarchical Clustering Group Average
Dist(3, 6, 4, 2, 5) (Dist(3,2)Dist(3,5)Dis
t(6,2)Dist(6,5) Dist(4,2) Dist(4,5)/(32)
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Hierarchical Clustering Group average
Proximity of two clusters is the average of
pairwise proximity between points in the two
clusters.
Dist(3,6,4,1) (0.22 0.37 0.23)/(31)
0.28
Dist(2, 5,1) (0.24 0.34)/(21)
0.29
Dist(3, 6, 4, 2, 5) (0.15 0.28 0.25
0.39 0.20 0.29)/(32)
0.26
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Exercise
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Hierarchical Clustering Group Average

• Compromise between Single and Complete Link
• Strengths
• Less susceptible to noise and outliers
• Limitations
• Biased towards globular clusters

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Hierarchical Clustering Comparison
MIN
MAX
Group Average
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Hierarchical Clustering Problems and Limitations

• Once a decision is made to combine two clusters,
  it cannot be undone
• No objective function is directly minimized
• Different schemes have problems with one or more
  of the following
• Sensitivity to noise and outliers
• Difficulty handling different sized clusters and
  convex shapes
• Breaking large clusters

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DBSCAN

• DBSCAN is a density-based algorithm.
• Density number of points within a specified
  radius (Eps)
• A point is a core point if it has more than a
  specified number of points (MinPts) within Eps
• Including core point itself
• These are points that are at the interior of a
  cluster
• A border point has fewer than MinPts within Eps,
  but is in the neighborhood of a core point
• A noise point is any point that is not a core
  point or a border point.

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DBSCAN Core, Border, and Noise Points
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DBSCAN Algorithm

• Label all points as core, border or noise
• Eliminate noise points
• Put an edge between core points that are within
  Eps of each other
• Make each group of connected points into a
  separate cluster
• Assign each border point to one of the clusters
  of its associated core points

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DBSCAN Core, Border and Noise Points
Original Points
Point types core, border and noise
Eps 10, MinPts 4
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When DBSCAN Works Well
Original Points

• Resistant to Noise
• Can handle clusters of different shapes and sizes

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When DBSCAN Does NOT Work Well
If Eps is low? If Eps is high? Varying densities