Data Pre-processing• Data Cleaning :

– Eliminating Noise Data (incorrect attribute values, incomplete data items )– Missing data– Redundant data

• Sampling: – selecting appropriate parts of the database for building models– providing error estimation for sample selection

• Dimensionality Reduction and Feature Selection:– identifying the most appropriate attributes in the database being examined– creating important derived attributes

• Data Transformation:– Transforming complex / dynamic data (such as time-series data) into simpler – (static) data

Sampling: Getting representatives • Exhaustive search through the databases available today is not practically

feasible because of their size• A DM system must be able to assist in the selection of appropriate parts

(samples) of the databases to be examined• Random sampling is used most frequently

– not necessarily representative– assumes that the data supporting the various classes/events to be discovered is evenly

distributed. Not the case in many real-world databases.

• Stratified samples: Approximate the percentage of each class (or sub-population of interest) in the overall database (used in conjunction with unevenly distributed data)

• Out-of-sample testing– inductive model is never absolutely correct – testing is to estimate the error rate (uncertainty)

Data Mining Operations and Techniques:

• Predictive Modelling :– Based on the features present in the class_labeled training data,

develop a description or model for each class. It is used for• better understanding of each class, and• prediction of certain properties of unseen data

– If the field being predicted is a numeric (continuous ) variables then the prediction problem is a regression problem

– If the field being predicted is a categorical then the prediction problem is a classification problem

– Predictive Modelling is based on inductive learning (supervised learning)

Predictive Modelling (Classification):

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a*income + b*debt < t => No loan !

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Linear Classifier: Non Linear Classifier:

• Clustering (Segmentation)– Clustering does not specify fields to be predicted but

targets separating the data items into subsets that are similar to each other.

– Clustering algorithms employ a two-stage search:• An outer loop over possible cluster numbers and an inner loop

to fit the best possible clustering for a given number of clusters

– Combined use of Clustering and classification provides real discovery power.

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Supervised vs Unsupervised Learning:

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SupervisedLearning

UnsupervisedLearning

• Associations – relationship between attributes (recurring patterns)

• Dependency Modelling – Deriving causal structure within the data

• Change and Deviation Detection– These methods accounts for sequence information (time-series

in financial applications pr protein sequencing in genome mapping)

– Finding frequent sequences in database is feasible given sparseness in real-world transactional database

Basic Components of Data Mining Algorithms• Model Representation (Knowledge Representation) :

– the language for describing discoverable patterns / knowledge • (e.g. decision tree, rules, neural network)

• Model Evaluation: – estimating the predictive accuracy of the derived patterns

• Search Methods:– Parameter Search : when the structure of a model is fixed, search for the parameters

which optimise the model evaluation criteria (e.g. backpropagation in NN)– Model Search: when the structure of the model(s) is unknown, find the model(s)

from a model class

• Learning Bias– Feature selection– Pruning algorithm

Predictive Modelling (Classification)

TrainingData:

InductiveLearningSystem

Classifiers (Derived Hypotheses)

Data to be classified Classifier Decision on classassignment

• Task: determine which of a fixed set of classes an example belongs to

• Input: training set of examples annotated with class values.

• Output:induced hypotheses (model/concept description/classifiers)

Learning : Induce classifiers from training data

Predication : Using Hypothesis for Prediction: classifying any example described in the same manner

Classification Algorithms

• Decision trees

• Rule-based induction

• Neural networks

• Memory(Case) based reasoning

• Genetic algorithms

• Bayesian networks

Basic Principle (Inductive Learning Hypothesis): Any hypothesis found to approximate the target function well over a sufficiently large set of training examples will also approximate the target function well over other unobserved examples.

Typical Algorithms:

Decision Tree LearningGeneral idea: Recursively partition data into sub-groups

• Select an attribute and formulate a logical test on attribute

• Branch on each outcome of test, move subset of examples (training data) satisfying that outcome to the corresponding child node.

• Run recursively on each child node.

Termination rule specifies when to declare a leaf node.

Decision tree learning is a heuristic, one-step lookahead (hill climbing), non-backtracking search through the space of all possible decision trees.

Day Outlook Temperature Humidity Wind Play Tennis1 Sunny Hot High Weak No2 Sunny Hot High Strong No3 Overcast Hot High Weak Yes4 Rain Mild High Weak Yes5 Rain Cool Normal Weak Yes6 Rain Cool Normal Strong No7 Overcast Cool Normal Strong Yes8 Sunny Mild High Weak No9 Sunny Cool Normal Weak Yes10 Rain Mild Normal Weak Yes11 Sunny Mild Normal Strong Yes12 Overcast Mild High Strong Yes13 Overcast Hot Normal Weak Yes14 Rain Mild High Strong No

Outlook

Sunny Overcast Rain

Humidity Yes Wind

High Normal

No Yes No Yes

Strong Weak

Decision Tree: Example

DecisionTree(examples) =Prune (Tree_Generation(examples))

Tree_Generation (examples) =IF termination_condition (examples)

THEN leaf ( majority_class (examples) )ELSE LETBest_test = selection_function (examples)IN FOR EACH value v OF Best_test Let subtree_v = Tree_Generation ({ e example| e.Best_test = v )

IN Node (Best_test, subtree_v )

Definition :selection: used to partition training datatermination condition: determines when to stop partitioningpruning algorithm: attempts to prevent overfitting

Decision Tree : Training

The basic approach to select a attribute is to examine each attribute and evaluate its likelihood for improving the overall decision performance of the tree.

The most widely used node-splitting evaluation functions work by reducing the degree of randomness or ‘impurity” in the current node:

Entropy function (C4.5):

Information gain :

• ID3 and C4.5 branch on every value and use an entropy minimisation heuristic to select best attribute.

• CART branches on all values or one value only, uses entropy minimisation or gini function.

• GIDDY formulates a test by branching on a subset of attribute values (selection by entropy minimisation)

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Selection Measure : the Critical Step

Outlook

Sunny Overcast Rain

Yes?

?

{1, 2,8,9,11 } {4,5,6,10,14}

(Sunny, Humidity) = 0.97 - 3/5*0 - 2/5*0 = 0.97(Sunny,Temperature) = 0.97-2/5*0 - 2/5*1 - 1/5*0.0 = 0.57(Sunny,Wind)= 0.97 -= 2/5*1.0 - 3/5*0.918 = 0.019

The algorithm searches through the space of possible decision trees from simplest to increasingly complex, guided by the information gain heuristic.

Tree Induction:

Overfitting

• Consider eror of hypothesis H over – training data : error_training (h)– entire distribution D of data : error_D (h)

Hypothesis h overfits training data if there is an alternative hypothesis h’ such that

error_training (h) < error_training (h’)

error_D (h) > error (h’)

Preventing Overfitting

• Problem: We don’t want to these algorithms to fit to ``noise’’• Reduced-error pruning :

– breaks the samples into a training set and a test set. The tree is induced completely on the training set.

– Working backwards from the bottom of the tree, the subtree starting at each nonterminal node is examined.

• If the error rate on the test cases improves by pruning it, the subtree is removed. The process continues until no improvement can be made by pruning a subtree,

• The error rate of the final tree on the test cases is used as an estimate of the true error rate.

Decision Tree Pruning:

physician fee freeze = n:| adoption of the budget resolution = y: democrat (151.0)| adoption of the budget resolution = u: democrat (1.0)| adoption of the budget resolution = n:| | education spending = n: democrat (6.0)| | education spending = y: democrat (9.0)| | education spending = u: republican (1.0)physician fee freeze = y:| synfuels corporation cutback = n: republican (97.0/3.0)| synfuels corporation cutback = u: republican (4.0)| synfuels corporation cutback = y:| | duty free exports = y: democrat (2.0)| | duty free exports = u: republican (1.0)| | duty free exports = n:| | | education spending = n: democrat (5.0/2.0)| | | education spending = y: republican (13.0/2.0)| | | education spending = u: democrat (1.0)physician fee freeze = u:| water project cost sharing = n: democrat (0.0)| water project cost sharing = y: democrat (4.0)| water project cost sharing = u:| | mx missile = n: republican (0.0)| | mx missile = y: democrat (3.0/1.0)| | mx missile = u: republican (2.0)

Simplified Decision Tree:

physician fee freeze = n: democrat (168.0/2.6)physician fee freeze = y: republican (123.0/13.9)physician fee freeze = u:| mx missile = n: democrat (3.0/1.1)| mx missile = y: democrat (4.0/2.2)| mx missile = u: republican (2.0/1.0)

Evaluation on training data (300 items):

Before Pruning After Pruning ---------------- --------------------------- Size Errors Size Errors Estimate

25 8( 2.7%) 7 13( 4.3%) ( 6.9%) <

False Positives

True Positives

False Negatives

Actual

Predicted

Evaluation of Classification Systems

Training Set: examples with class values for learning.

Test Set: examples with class values for evaluating.

Evaluation: Hypotheses are used to infer classification of examples in the test set; inferred classification is compared to known classification.

Accuracy: percentage of examples in the test set that are classified correctly.