Data Mining

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3. Classification Methods

• Patterns and Models
• Regression, NBC
• k-Nearest Neighbors
• Decision Trees and Rules
• Large size data

2
Models and Patterns

• A model is a global description of data, or an
  abstract representation of a real-world process
• Estimating parameters of a model
• Data-driven model building
• Examples Regression, Graphical model (BN), HMM
• A pattern is about some local aspects of data
• Patterns in data matrices
• Predicates (age lt 40) (income lt 10)
• Patterns for strings (ASCII characters, DNA
  alphabet)
• Pattern discovery rules

3
Performance Measures

• Generality
• How many instances are covered
• Applicability
• Or is it useful? All husbands are male.
• Accuracy
• Is it always correct? If not, how often?
• Comprehensibility
• Is it easy to understand? (a subjective measure)

4
Forms of Knowledge

• Concepts
• Probabilistic, logical (proposition/predicate),
  functional
• Rules
• Taxonomies and Hierarchies
• Dendrograms, decision trees
• Clusters
• Structures and Weights/Probabilities
• ANN, BN

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Induction from Data

• Inferring knowledge from data - generalization
• Supervised vs. unsupervised learning
• Some graphical illustrations of learning tasks
  (regression, classification, clustering)
• Any other types of learning?
• Compare The task of deduction
• Infer information/fact that is a logical
  consequence of facts in a database
• Who is Johns grandpa? (deduced from e.g. Mary is
  Johns mother, Joe is Marys father)
• Deductive databases extending the RDBMS

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The Classification Problem

• From a set of labeled training data, build a
  system (a classifier) for predicting the class of
  future data instances (tuples).
• A related problem is to build a system from
  training data to predict the value of an
  attribute (feature) of future data instances.

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What is a bad classifier?

• Some simplest classifiers
• Table-Lookup
• What if x cannot be found in the training data?
• We give up!?
• Or, we can
• A simple classifier Cs can be built as a
  reference
• If it can be found in the table (training data),
  return its class otherwise, what should it
  return?
• A bad classifier is one that does worse than Cs.
• Do we need to learn a classifier for data of one
  class?

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Many Techniques

• Decision trees
• Linear regression
• Neural networks
• k-nearest neighbour
• Naïve Bayesian classifiers
• Support Vector Machines
• and many more ...

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Regression for Numeric Prediction

• Linear regression is a statistical technique when
  class and all the attributes are numeric.
• y a ßx, where a and ß are regression
  coefficients
• We need to use instances ltxi,ygt to find a and ß
• by minimizing SSE (least squares)
• SSE S(yi-yi)2 S(yi- a - ßxi)2
• Extensions
• Multiple regression
• Piecewise linear regression
• Polynomial regression

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Nearest Neighbor

• Also called instance based learning
• Algorithm
• Given a new instance x,
• find its nearest neighbor ltx,ygt
• Return y as the class of x
• Distance measures
• Normalization?!
• Some interesting questions
• Whats its time complexity?
• Does it learn?

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Nearest Neighbor (2)

• Dealing with noise k-nearest neighbor
• Use more than 1 neighbor
• How many neighbors?
• Weighted nearest neighbors
• How to speed up?
• Huge storage
• Use representatives (a problem of instance
  selection)
• Sampling
• Grid
• Clustering

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Naïve Bayes Classification

• This is a direct application of Bayes rule
• P(Cx) P(xC)P(C)/P(x)
• x - a vector of x1,x2,,xn
• Thats the best classifier you can ever build
• You dont even need to select features, it takes
  care of it automatically
• But, there are problems
• There are a limited number of instances
• How to estimate P(xC)

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NBC (2)

• Assume conditional independence between xis
• We have P(Cx) P(x1C) P(xiC) (xnC)P(C)
• How good is it in reality?
• Lets build one NBC for a very simple data set
• Estimate the priors and conditional probabilities
  with the training data
• P(C1) ? P(C2) ? P(x11C1)? P(x12C1)?
• What is the class for x(1,2,1)?
• P(1x) P(x111) P(x221) P(x311) P(1),
  P(2x)
• What is the class for (1,2,2)?

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Example of NBC
C 1 2
7 4 3
A10 2 0
A11 2 1
A12 0 2
A20
A21
A22
A31
A32
A1 A2 A3 C
1 2 1 1
0 0 1 1
2 1 2 2
1 2 1 2
0 1 2 1
2 2 2 2
1 0 1 1
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Golf Data
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Decision Trees

• A decision tree

Outlook
sunny
overcast
rain
Humidity
Wind
YES
high
normal
strong
weak
NO
YES
NO
YES
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How to grow a tree?

• Randomly ? Random Forests (Breiman, 2001)
• What are the criteria to build a tree?
• Accurate
• Compact
• A straightforward way to grow is
• Pick an attribute
• Split data according to its values
• Recursively do the first two steps until
• No data left
• No feature left

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Discussion

• There are many possible trees
• lets try it on the golf data
• How to find the most compact one
• that is consistent with the data?
• Why the most compact?
• Occams razor principle
• Issue of efficiency w.r.t. optimality
• One attribute at a time or

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Grow a good tree efficiently

• The heuristic to find commonality in feature
  values associated with class values
• To build a compact tree generalized from the data
• It means we look for features and splits that can
  lead to pure leaf nodes.
• Is it a good heuristic?
• What do you think?
• How to judge it?
• Is it really efficient?
• How to implement it?

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Lets grow one

• Measuring the purity of a data set Entropy
• Information gain (see the brief review)
• Choose the feature with max gain

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Different numbers of values

• Different attributes can have varied numbers of
  values
• Some treatments
• Removing useless attributes before learning
• Binarization
• Discretization
• Gain-ratio is another practical solution
• Gain root-Info InfoAttribute(i)
• Split-Info -?((Ti/T)log2 (Ti/T))
• Gain-ratio Gain / Split-Info

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Another kind of problems

• A difficult problem. Why is it difficult?
• Similar ones are Parity, Majority problems.

XOR problem 0 0 0 0 1 1 1 0 1 1
1 0
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Tree Pruning

• Overfitting Model fits training data too well,
  but wont work well for unseen data.
• An effective approach to avoid overfitting and
  for a more compact tree (easy to understand)
• Two general ways to prune
• Pre-pruning stop splitting further
• Any significant difference in classification
  accuracy before and after division
• Post-pruning to trim back

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Rules from Decision Trees

• Two types of rules
• Order sensitive (more compact, less efficient)
• Order insensitive
• The most straightforward way is
• Class-based method
• Group rules according to classes
• Select most general rules (or remove redundant
  ones)
• Data-based method
• Select one rule at a time (keep the most general
  one)
• Work on the remaining data until all data is
  covered

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Variants of Decision Trees and Rules

• Tree stumps
• Holtes 1R rules (1992)
• For each attribute A
• Sort according to its values v
• Find the most frequent class value c for each v
• Breaking tie with coin flipping
• Output the most accurate rule as if Av then c
• An example (the Golf data)

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Handling Large Size Data

• When data simply cannot fit in memory
• Is it a big problem?
• Three representative approaches
• Smart data structures to avoid unnecessary
  recalculation
• Hash trees
• SPRINT
• Sufficient statistics
• AVC-set (Attribute-Value, Class label) to
  summarize the class distribution for each
  attribute
• Example RainForest
• Parallel processing
• Make data parallelizable

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Ensemble Methods

• A group of classifiers
• Hybrid (Stacking)
• Single type
• Strong vs. weak learners
• A good ensemble
• Accuracy
• Diversity
• Some major approaches form ensembles
• Bagging
• Boosting

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Bibliography

• I.H. Witten and E. Frank. Data Mining Practical
  Machine Learning Tools and Techniques with Java
  Implementations. 2000. Morgan Kaufmann.
• M. Kantardzic. Data Mining Concepts, Models,
  Methods, and Algorithms. 2003. IEEE.
• J. Han and M. Kamber. Data Mining Concepts and
  Techniques. 2001. Morgan Kaufmann.
• D. Hand, H. Mannila, P. Smyth. Principals of Data
  Mining. 2001. MIT.
• T. G. Dietterich. Ensemble Methods in Machine
  Learning. I. J. Kittler and F. Roli (eds.) 1st
  Intl Workshop on Multiple Classifier Systems, pp
  1-15, Springer-Verlag, 2000.