Project Presentation CPSC 695

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Project PresentationCPSC 695

• Prepared By
• Priyadarshi Bhattacharya

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Outline of Talk

• Introduction to clustering and its relevance to
  my research interests.
• Discussion on existing clustering techniques and
  their shortcomings.
• Introduction to a new Delaunay based clustering
  algorithm.
• Experimental Results and comparison with other
  methods.
• Direction of future research.

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Clustering Definition

• Automatic identification of groups of similar
  objects.
• A method of grouping data such that intracluster
  similarity is maximized and intercluster
  similarity is minimized.

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Properties of clustering

• Scalability Clustering performance should
  decrease linearly with data size increase
• Ability to detect clusters of different shapes
• Minimal input parameter
• Robust with regard to noise
• Insensitive to data input order
• Scalability to higher dimensions
• (properties referred from On Data Clustering
  Analysis Scalability, Constraints and
  Validation with minor
• modifications)

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Relevance to my research

• Identification of high-risk areas in the sea
  based on incident data from the Maritime Activity
  and Risk Investigation System (MARIS), maintained
  primarily by the University of Halifax.

Marine Route Planning
Clustering Algorithm
Incident Data
High-risk areas
(ESRI Shape File)
Location of SAR Bases
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Existing clustering algorithms
Clustering
Partitioning
Hierarchical
Density-based
Grid-based
K-Means, K-Medoid
BIRCH, CURE, ROCK, CHAMELEON
DBSCAN, TURN
WaveCluster1, CLIQUE
1WaveCluster A novel clustering approach based
on wavelet transforms. Applies a multi-resolution
grid structure on the data space. For more
details, refer to Wavecluster a
multi-resolution clustering approach for very
large spatial databases, Proc. 24th Conf. on
Very Large Databases.
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Shortcomings of existing methods

• Require large number of parameters to be input by
  user. Example number of clusters, threshold to
  quantify similarity, stopping condition, number
  of nearest neighbors etc.
• Sensitivity to user-supplied parameters.
• Capability of identifying clusters degrades with
  increase in noise.
• Inability to identify clusters of widely varying
  shapes and sizes. Most detect spherical ones
  only.
• Identification of dense clusters in presence of
  sparse ones, clusters connected by multiple
  bridges, closely lying dense clusters remains
  elusive.

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CRYSTAL A new Delaunay based clustering
algorithm

• The algorithm has 3 stages
• Triangulation phase Forms the Delaunay
  Triangulation of the data points and sorts the
  vertices in the order of decreasing average
  length of adjacent edges.
• Grow cluster phase Scans the sorted vertex list
  and grows clusters from the vertices in that
  order, first encompassing first order neighbors,
  then second order neighbors and so on. The growth
  stops when the boundary of the cluster is
  determined.
• Noise removal phase The algorithm identifies
  noise as sparse clusters. They can be easily
  eliminated by removing clusters which are very
  small in size or which have a very low density.

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Description of stage I

• Triangulation phase
• Triangulation is done in O(nlogn) time using
  the incremental
• algorithm.
• An auxiliary grid structure (O(n) in size) is
  used to speed up
• the point location problem in the
  Delaunay Triangulation.
• This considerably reduces length of walk
  in the graph to
• locate the triangle containing the data
  point.
• The well-known Winged-Edge data-structure is
  used to
• represent the Delaunay Triangulation
  because of its
• efficiency in answering proximity
  queries.

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Description of Stage II

• Grow Cluster phase
• A queue is used to maintain a list of
  vertices in order, from which the cluster is
  grown. Only vertices that are not boundary points
  are inserted into the queue.
• To decide whether a point belongs to the
  cluster, the edge length is compared with the
  average edge length of the cluster. To decide
  whether a point is on the boundary of a cluster,
  the average adjacent edge length of the point is
  compared to the average edge length of the
  cluster.

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Description of Stage III

• Noise Removal Phase
• Noise in the data may be in the form of
  isolated data points or scattered throughout the
  data. In the former case,
• cluster based at these data points will not
  be able to grow.
• However, if the noise is scattered uniformly
  throughout the data, our algorithm identifies it
  as a single sparse cluster. This phase simply
  gets rid of noise by eliminating the cluster with
  the highest average edge length. Also any trivial
  clusters (size less than an acceptable number)
  are removed in this phase.

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Complexity Analysis

• The algorithm operates in O(nlogn) time.
• Delaunay Triangulation is generated in
  O(nlogn) time. As a vertex once assigned to a
  cluster is not considered again, the clustering
  is done in O(n) time.

Cluster size (1000) Vs Time consumed (ms)
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Clustering in action
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Experimental Results

• Comparison with K-Means based approaches

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Experimental Results (contd.)
1. Clusters of different shapes 2. Closely
lying dense clusters
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Experimental Results (contd.)
1. Clusters connected by multiple bridges
2. Clusters of widely varying density
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Experimental Results (contd.)
Data set
K-Means
GEM
CRYSTAL
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Experimental Results (contd.)
Results on t7.10k.dat (originally used in
CHAMELEON A Hierarchical Clustering Algorithm
Using Dynamic Modeling)
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Conclusion Future Work

• CRYSTAL is a fast O(nlogn) clustering
  algorithm that
• automatically identifies clusters of widely
  varying shapes, sizes
• and densities without requiring any input from
  user.
• Future work will involve
• Application of the clustering algorithm in
  identification of high-risk areas in the sea
  using the MARIS database.
• Extension of the algorithm to 3D.
• Considering physical constraints in clustering.
  In GIS, physical constraints such as rivers,
  highways, mountain ranges can hinder or alter the
  clustering result.

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References

• G. Papari, N. Petkov Algorithm That Mimics Human
  Perceptual Grouping of Dot Patterns. Lecture
  Notes in Computer Science (2005) 497-506
• Vladimir Estivill-Castro, Ickjai Lee AUTOCLUST
  Automatic Clustering via Boundary Extraction for
  Mining Massive Point-Data Sets. Fifth
  International Conference on Geocomputation (2000)
• Osmar R. Zaiane, Andrew Foss, Chi-Hoon Lee,
  Weinan Wang
• On Data Clustering Analysis Scalability,
  Constraints and Validation.
• Advances in Knowledge Discovery and Data
  Mining, Springer-Verlag (2002 )
• Z.S.H. Chan, N. Kasabov Efficient global
  clustering using the Greedy Elimination Method.
• Electronics Letters 40 25 (2004 )
• Aristidis Likas, Nikos Vlassis, Jakob J. Verbeek
  The global k-means clustering algorithm.
• Pattern Recognition 36 2 (2003 ) 451-461
• Ying Xu, Victor Olman, Dong Xu Minimum Spanning
  Trees for Gene Expression Data Clustering.
  Computational Protein Structure Group, Life
  Sciences Division, Oak Ridge National Laboratory,
  USA
• C. Eldershaw, M. Hegland Cluster Analysis using
  Triangulation. Computational Techniques and
  Applications CTAC97, 201-208. World Scientific,
  Singapore, 1997
• Mir Abolfazl Mostafavi, Christopher Gold, Maciej
  Dakowicz Delete and insert operations in
  Voronoi/Delaunay methods and applications.
  Computers \ Geosciences 29 4 523-530 (2003)
• Atsuyuki Okabe, Barry Boots, Kokichi Sugihara
  Spatial Tessellations Concepts and Applications
  of Voronoi Diagrams.

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Thank You!
All 11 identified by CRYSTAL! Questions?