Download PRESENTATION NAME

Clustering Algorithms Meta
Applier (CAMA) Toolbox
Dmitry S. Shalymov
Kirill S. Skrygan
Dmitry A. Lyubimov
Clustering
• Goals
– To detect the underlying structure in data
– To reduce data set capacity
– To extract unique objects
• Usage
–
–
–
–
–
–
–
Data mining
Machine learning
Financial mathematics
Optimization
Statistics
Pattern recognition
Control strategies development
SYRCoSE’09
Clustering Problem
{x1 , x2 ,..., xn } X
 ( x, x)
A lg : X  Y

W
i j
[ yi  y j ] ( xi , x j )

i j
[ yi  y j ]
 min

B
i j
[ yi  y j ] ( xi , x j )

i j
[ yi  y j ]
 max
Clustering and Classification
SYRCoSE’09
Variety of Clustering Algorithms
• Hierarchical
– Aglomerative
– Partitioning
• Iterative
– Hard (K-means, SVM, SPSA)
– Fuzzy (FCM)
Important parameters
-Distance norm
-Number of clusters
-Initial values of cluster centers
SYRCoSE’09
Cluster Stability Algorithms
• Indexes
• Stability (similarity, merit) functions
• Probabilistic measures assessing the likelihood of a
decision
• Density estimation approaches
SYRCoSE’09
Stochastic Approximation
 * : L /   0
Recursive stochastic approximation
 k 1   k  ak g k ( k )
g ( )  L / 
FDSA
y ( k  ck ei )  y ( k  ck ei )
g ki ( k ) 
2ck
SPSA
y ( k  ck  k )  y ( k  ck  k )
g ki ( k ) 
2ck  ki
k  (k1 , k 2 ,...,  kp )T
SYRCoSE’09
SYRCoSE’09
Effectiveness of SPSA
SYRCoSE’09
Finding the number of clusters in data set
• Run the SPSA algorithm for different numbers of clusters, K, and
calculate the corresponding distortions d K
• Select a transformation power, Y
• Calculate the “jumps” in transformed distortion J K  d
Y
K
 d Y K 1
• Estimate the number of clusters in the data set by
K *  arg max K J K
SYRCoSE’09
Structure of data set detection
SYRCoSE’09
Examples
• Iris (3 clusters, 4
features, 150 instances)
• Wine (3 clusters, 13
features, 178 instances)
• Breast Cancer (2
clusters, 32 features,
569 instances)
• Image Segmentation (7
clusters, 19 features,
2310 instances)
SYRCoSE’09
Software Tools for Clustering Analysis
•
Research
–
–
–
–
–
–
–
–
•
License software
–
–
•
SPSS
STATISTICA
Characteristics
–
–
–
•
COMPACT
DCPR (Data Clustering & Pattern Recognition)
FCDA (Fuzzy Clustering and Data Analysis Toolbox)
ClusterPack Matlab Toolbox
The Curve Clustering Toolbox
SOM (Self-Organizing Map)
Spectral Clustering Toolbox
Yashil's FCM Clustering
Visualization
Efectiveness analysis with patterns
Tools to check performance
Shortcomings
–
–
–
–
Limited number of data sets and algorithms
No possibilities to load own algorithm
No on-line services
MATLAB
SYRCoSE’09
Clustering Algorithms Meta Applier
SYRCoSE’09
Clustering Algorithms Meta Applier
SYRCoSE’09
CAMA. Kernel
SYRCoSE’09
CAMA. Kernel
SYRCoSE’09
CAMA Toolbox
http://ancient.punklan.net:8084/CAMA2/index.jsp
SYRCoSE’09
CAMA Toolbox
SYRCoSE’09
CAMA Toolbox
SYRCoSE’09
Thank you!
SYRCoSE’09