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DATA MINING van data naar informatie Ronald
Westra Dep. Mathematics Maastricht University
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CLUSTERING AND CLUSTER ANALYSIS

• Data Mining Lecture IV
• Chapter 8 sections 8.4 and Chapter 9 from
  Principles of Data Mining by Hand,, Manilla,
  Smyth

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DATA ANALYSIS AND UNCERTAINTY

• Data Mining Lecture V
• Chapter 4, Hand, Manilla, Smyth

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Random Variables 4.3 multivariate random
variablesmarginal densityconditional density
dependency p(xy) p(x,y) / p(y) example
supermarket purchases
RANDOM VARIABLES
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Example supermarket purchasesX n customers x
p products X(i,j) Boolean variable Has
customer i bought a product of type p ? nA
sum(X(,A)) is number of customers that bought
product AnB sum(X(,B)) is number of customers
that bought product BnAB sum(X(,A).X(,B))
is number of customers that bought product B
Demo matlab conditionaldensity
RANDOM VARIABLES
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(conditionally) independent p(x,y) p(x)p(y)
i.e.  p(xy) p(x)
RANDOM VARIABLES
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RANDOM VARIABLES
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RANDOM VARIABLES
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RANDOM VARIABLES
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SAMPLING
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ESTIMATION
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Maximum Likelihood Estimation
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Maximum Likelihood Estimation
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Maximum Likelihood Estimation
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BAYESIAN ESTIMATION
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BAYESIAN ESTIMATION
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BAYESIAN ESTIMATION
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BAYESIAN ESTIMATION
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BAYESIAN ESTIMATION
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PROBABILISTIC MODEL-BASED CLUSTERING USING
MIXTURE MODELS

• Data Mining Lecture VI
• 4.5, 8.4, 9.2, 9.6, Hand, Manilla, Smyth

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Jensens inequality
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for a concave-down function, the expected value
of the function is less than the function of the
expected value. The gray rectangle along the
horizontal axis represents the probability
distribution of x, which is uniform for
simplicity, but the general idea applies for any
distribution
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