Post on 02-Jan-2016
description
Very large data sets
Pasi Fränti
Clustering methods: Part 10
Speech and Image Processing UnitSchool of Computing
University of Eastern Finland
5.5.2014
Methods for large data sets
• Birch
• Clarans
• On-line EM
• Scalable EM
• GMG
Let’s study this(no material for the others)
Gradual model generator (GMG) [Kärkkäinen & Fränti, 2007: Pattern Recognition]
D at a B u ffer M o d el
M o d el s iz ered u ct io n
M o d el gen erat io n
G en erat edm o d el
P o s t p ro ces s in gO u t p u t m o d els
S elec tio n
EM GMG
Goal of the GMG algorithm
EM GMG
Contours of probability density distributions
Before update After update
Model update
• New data points are mapped immediately when input.• Points too far (from any model) will remain in buffer.• Buffered points are re-tested when new models created.
Selected points and a new component
Data in buffer
Generating new components• When buffer full, selected points are used to generate new
components.• Most compact k-neighborhood is selected as seed for a new
component.
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Example
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Example
Example
Example
Example
Example
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Post-processing
Model before processing
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Model before processing Updated model
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Post-processing
Model before processing Updated model + data
Literature
1. I. Kärkkäinen and P. Fränti, "Gradual model generator for single-pass clustering", Pattern Recognition, 40 (3), 784-795, March 2007.
2. P. Bradley, U. Fayyad, C. Reina, Clustering Very Large Databases Using EM Mixture Models, Proc. of the 15th Int. Conf. on Pattern Recognition, vol. 2, 2000, pp. 76-80.
3. R. Ng, J. Han, CLARANS: A Method for Clustering Objects for Spatial Data Mining, IEEE Trans. Knowledge & Data Engineering 14(5) (2002) 1003-1016.
4. M. Sato, S. Ishii, On-line EM Algorithm for the Normalized Gaussian Network, Neural Computation 12(2) (2000) 407-432.
5. T. Zhang, R. Ramakrishnan, M. Livny, BIRCH: A New Data Clustering Algorithm and Its Applications, Data Mining and Knowledge Discovery 1(2) (1997) 141-182.