Poster Template

1
DATA CLUSTERING WITH KERNAL K-MEANS
Matt Strautmann, Dept. of Electrical and Computer
Engineering
Dr. Donald C. Wunsch II, Dept. of Electrical and
Computer Engineering

• PROJECT OBJECTIVES
• PROJECT GOAL
• Experimentally demonstrate the application of
  Kernel K-Means to non-linearly clusterable data
  sets
• ACADEMIC IMPORTANCE
• Expand the application of the Kernel K-Means
  clustering algorithm to non-traditional uses

PROJECT DATASETS

• DISCUSSION
• Kernel K-Means was found to cluster the test
  datasets in a superior manner over Soft K-Means
• Kernel data-mapping was seen to solve the
  overlapping data sets by
• Mapping the data before clustering to a
  higher-dimensional feature space using a
  nonlinear function
• Partitioning the points with linear separators in
  the new space
• Soft K-Means could not successfully cluster the
  Lung Cancer Dataset results were for one cluster
  out of three successfully clustered
• Soft K-Means clustered the two dimension, two
  cluster Gaussian dataset with only one error out
  of the one thousand data points

Iris Plant Dataset
eleves.ens.fr

• BACKGROUND
• WHAT IS K-MEANS CLUSTERING?
• K-Means clustering aims to divide the dataset
  into clusters (groups) in which each data point
  belongs to the cluster with the nearest mean
  vector.
• WHAT IS KERNAL K-MEANS?
• Sum-of-squares algorithm
• Two step process data point assignment and
  update
• WHAT IS THE PLUS PLUS INITIALIZATION SCHEME?
• The first mean vector is a randomly selected data
  point
• Each subsequent mean vector is created by
  evaluating randomly selected data points against
  a vector weighting probability

2 Dimension, 2 Cluster Dataset (Gaussian 2D2K)
2 Dimension, 2 Cluster Dataset (Gaussian 2D2K)
lans.ece.utexas.edu
lans.ece.utexas.edu

• CONCLUDING REMARKS
• The initialization was seen to be the most
  important factor in the algorithm converging
• The PLUS PLUS cluster mean initialization was
  seen to improve the results
• Kernel assignment works better than the maximum
  responsibility calculation of Soft K-Means
• Kernel K-Means can handle small or large
  dimension datasets well the increase of
  dimensionally seemed to be advantageous for the
  Lung Cancer Dataset (56 dimensions) over the
  lower clustering accuracy of the Iris Plant
  Dataset (4 dimensions)
• Kernel K-Means produced superior results to
  Soft K-Means when clustering the Lung Cancer
  Dataset and demonstrated recognition of all three
  clusters

• SOFT K-MEANS VS. KERNEL K-MEANS

Soft K-Means Clustering Accuracy Average (over ten runs) Standard Deviation of Accuracy Calculation (over ten runs) Variance of Accuracy Calculation (over ten runs)
Iris Plant Dataset 28.00 8.218 2.867
Lung Cancer Dataset 43.75 - -
2D2K Gaussian Dataset 99.00 - -
8D5K Gaussian Dataset 58.50 2.082 0.043
http//en.wikipedia.org/wiki/K-means_clustering
http//en.wikipedia.org/wiki/K-means_clustering
Kernel K-Means Clustering Accuracy Average (over ten runs) Standard Deviation of Accuracy Calculation (over ten runs) Variance of Accuracy Calculation (over ten runs)
Iris Plant Dataset 57.00 5.009 2.238
Lung Cancer Dataset 62.00 6.878 0.473
2D2K Gaussian Dataset 96.50 1.677 0.028
8D5K Gaussian Dataset 76.31 10.366 1.075
2.) Voronoi Diagram Generated by the Means
(data points associated with nearest cluster
mean)
1.) Initial Mean Orientations

• FUTURE WORK
• Further improvement of the mean vector
  initialization is believed possible over the
  PLUS PLUS initialization
• Other options for the mean-squared error
  calculation for data point evaluation are
  possible
• The time analysis of the algorithm must be
  calculate
• The author would like to acknowledge the
  expertise of Dr. Rui Xu in advising this project. 

• RESULTS COMPARISON
• Kernel K-Means clustering accuracy superior in
  all cases except the two dimensional, two cluster
  dataset.
• The clustering accuracy of the datasets
  increased by the following amounts
• Iris Plant 104
• Lung Cancer 38
• 2D2k -2.5
• 8D5K 30

http//en.wikipedia.org/wiki/K-means_clustering
http//en.wikipedia.org/wiki/K-means_clustering
4.) Step 2 and 3 Repeated until Convergence
3.) Cluster Centroid Becomes New Cluster Mean

• APPROACH
• Evaluate standard K-Means (Soft) against 4
  datasets to form benchmark
• Hybridize Soft K-Means with Kernel K-Means to
  form Kernel K-Means
• Test Kernel K-Means on small size, small
  dimension Gaussian, large dimension Gaussian, and
  large size datasets

Acknowledgements