Classification

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• Classification

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Classification

• Task Given a set of pre-classified examples,
  build a model or classifier to classify new
  cases.
• Supervised learning classes are known for the
  examples used to build the classifier.
• A classifier can be a set of rules, a decision
  tree, a neural network, etc.
• Typical applications credit approval, direct
  marketing, fraud detection, medical diagnosis,
  ..

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Simplicity first

• Simple algorithms often work very well!
• There are many kinds of simple structure, eg
• One attribute does all the work
• All attributes contribute equally independently
• A weighted linear combination might do
• Instance-based use a few prototypes
• Use simple logical rules
• Success of method depends on the domain

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Inferring rudimentary rules

• 1R learns a 1-level decision tree
• I.e., rules that all test one particular
  attribute
• Basic version
• One branch for each value
• Each branch assigns most frequent class
• Error rate proportion of instances that dont
  belong to the majority class of their
  corresponding branch
• Choose attribute with lowest error rate
• (assumes nominal attributes)

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Pseudo-code for 1R
For each attribute, For each value of the attribute, make a rule as follows count how often each class appears find the most frequent class make the rule assign that class to this attribute-value Calculate the error rate of the rules Choose the rules with the smallest error rate

• Note missing is treated as a separate
  attribute value

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Evaluating the weather attributes
Attribute Rules Errors Total errors
Outlook Sunny ? No 2/5 4/14
Overcast ? Yes 0/4
Rainy ? Yes 2/5
Temp Hot ? No 2/4 5/14
Mild ? Yes 2/6
Cool ? Yes 1/4
Humidity High ? No 3/7 4/14
Normal ? Yes 1/7
Windy False ? Yes 2/8 5/14
True ? No 3/6
Outlook Temp Humidity Windy Play
Sunny Hot High False No
Sunny Hot High True No
Overcast Hot High False Yes
Rainy Mild High False Yes
Rainy Cool Normal False Yes
Rainy Cool Normal True No
Overcast Cool Normal True Yes
Sunny Mild High False No
Sunny Cool Normal False Yes
Rainy Mild Normal False Yes
Sunny Mild Normal True Yes
Overcast Mild High True Yes
Overcast Hot Normal False Yes
Rainy Mild High True No

• indicates a tie

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Dealing withnumeric attributes

• Discretize numeric attributes
• Divide each attributes range into intervals
• Sort instances according to attributes values
• Place breakpoints where the class changes(the
  majority class)
• This minimizes the total error
• Example temperature from weather data

Outlook Temperature Humidity Windy Play
Sunny 85 85 False No
Sunny 80 90 True No
Overcast 83 86 False Yes
Rainy 75 80 False Yes

64 65 68 69 70 71 72 72 75 75 80 81 83 85 Yes No Yes Yes Yes No No Yes Yes Yes No Yes Yes No
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The problem of overfitting

• This procedure is very sensitive to noise
• One instance with an incorrect class label will
  probably produce a separate interval
• Also time stamp attribute will have zero errors
• Simple solutionenforce minimum number of
  instances in majority class per interval

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Discretization example

• Example (with min 3)
• Final result for temperature attribute

64 65 68 69 70 71 72 72 75 75 80 81 83 85 Yes No Yes Yes Yes No No Yes Yes Yes No Yes Yes No
64 65 68 69 70 71 72 72 75 75 80 81 83 85 Yes No Yes Yes Yes No No Yes Yes Yes No Yes Yes No
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With overfitting avoidance

• Resulting rule set

Attribute Rules Errors Total errors
Outlook Sunny ? No 2/5 4/14
Overcast ? Yes 0/4
Rainy ? Yes 2/5
Temperature ? 77.5 ? Yes 3/10 5/14
gt 77.5 ? No 2/4
Humidity ? 82.5 ? Yes 1/7 3/14
gt 82.5 and ? 95.5 ? No 2/6
gt 95.5 ? Yes 0/1
Windy False ? Yes 2/8 5/14
True ? No 3/6
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• Missing Values

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Missing Values

• Many data sets are plagued by the problem of
  missing values
• missing values can be a result of manual data
  entry, incorrect measurements, equipment errors,
  etc.
• they are usually denoted by special characters
  such as
• NULL
• ?

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Table 2.1
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Missing Values

• imputation (filling-in) of missing data
• We will use two ways of single imputation
• Single Imputation
• Hot Deck Imputation

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Missing Values

• single imputation
• mean imputation method uses the mean of values of
  a feature that contains missing data
• in case of a symbolic/categorical feature, a mode
  (the most frequent value) is used
• the algorithm imputes missing values for each
  attribute separately

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Table 2.2
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Missing Values

• - single imputation
• hot deck imputation for each object that
  contains missing values the most similar object
  (according to some distance function) is found,
  and the missing values are imputed from that
  object
• if the most similar record also contains missing
  values for the same feature then it is discarded
  and another closest object is found
• the procedure is repeated until all the missing
  values are imputed
• when no similar object is found, the closest
  object with the minimum number of missing values
  is chosen to impute the missing values

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Table 2.3
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Noise
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Noise

• Def. Noise in the data is defined as a value
  that is a random error or variance in a measured
  feature
• the amount of noise in the data can jeopardize
  the entire KDP results
• the influence of noise on the data can be
  prevented by imposing constraints on features to
  detect anomalies when the data is entered
• for instance, DBMS usually provides facility to
  define constrains for individual attributes

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Noise Detection

• In manual inspection, the user checks feature
  values against predefined constraints and
  manually detects the noise
• For example, for object 5 in table 2.3 , the
  cholesterol value is 45.0, which is outside the
  predefined acceptable interval for this feature,
  namely, within 50.0, 600.0.

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Noise

• Noise can be removed using
• Binning
• Requires ordering values of the noisy feature and
  then substituting the values with a mean or
  median value for predefined bins
• In table 2.3, the attribute of Cholesterol
  contains the value of 45 which is a noise.
  Binning first orders the values of the noisy
  feature and then replaces the values with a mean
  or median value for the predefined bins. As an
  example, let us consider the cholesterol feature,
  with its values 45.0, 261.2, 331.2, and 407.5. If
  the bin size equals two, two bins are created
  bin1 with 45.0 and 261.2, and bin2 with 331.2 and
  407.5. For bin1 the mean value is 153.1, and for
  bin2 it is 369.4. Therefore the values 45.0 and
  261.2 would be replaced with 153.1 and the values
  331.2 and 407.5 with 369.4. Note that the two new
  values are within the acceptable interval.