1. Data Mining: Concepts and Techniques Classification
November 11, 2018
Data Mining: Concepts and Techniques

2. Chapter 7. Classification and Prediction
What is classification? What is prediction?
Issues regarding classification and prediction
Classification by decision tree induction
Bayesian Classification
Other Classification Methods
Prediction
Classification accuracy
Summary
November 11, 2018
Data Mining: Concepts and Techniques

3. Classification vs. Prediction
predicts categorical class labels
classifies data (constructs a model) based on the training set and the values (class labels) in a classifying attribute and uses it in classifying new data
Prediction:
models continuous-valued functions, i.e., predicts unknown or missing values
Typical Applications
credit approval
target marketing
medical diagnosis
treatment effectiveness analysis
November 11, 2018
Data Mining: Concepts and Techniques

4. Classification—A Two-Step Process
Model construction: describing a set of predetermined classes
Each tuple/sample is assumed to belong to a predefined class, as determined by the class label attribute
The set of tuples used for model construction: training set
The model is represented as classification rules, decision trees, or mathematical formulae
Model usage: for classifying future or unknown objects
Estimate accuracy of the model
The known label of test sample is compared with the classified result from the model
Accuracy rate is the percentage of test set samples that are correctly classified by the model
Test set is independent of training set, otherwise over-fitting will occur
November 11, 2018
Data Mining: Concepts and Techniques

5. Classification Process (1): Model Construction
Algorithms
Training
Data
Classifier
(Model)
IF rank = ‘professor’
OR years > 6
THEN tenured = ‘yes’
November 11, 2018
Data Mining: Concepts and Techniques

6. Classification Process (2): Use the Model in Prediction
Classifier
Testing
Data
Unseen Data
(Jeff, Professor, 4)
Tenured?
November 11, 2018
Data Mining: Concepts and Techniques

7. Supervised vs. Unsupervised Learning
Supervised learning (classification)
Supervision: The training data (observations, measurements, etc.) are accompanied by labels indicating the class of the observations
New data is classified based on the training set
Unsupervised learning (clustering)
The class labels of training data is unknown
Given a set of measurements, observations, etc. with the aim of establishing the existence of classes or clusters in the data
November 11, 2018
Data Mining: Concepts and Techniques

8. Chapter 7. Classification and Prediction
What is classification? What is prediction?
Issues regarding classification and prediction
Classification by decision tree induction
Bayesian Classification
Other Classification Methods
Prediction
Classification accuracy
Summary
November 11, 2018
Data Mining: Concepts and Techniques

9. Issues regarding classification and prediction (1): Data Preparation
Data cleaning
Preprocess data in order to reduce noise and handle missing values
Relevance analysis (feature selection)
Remove the irrelevant or redundant attributes
Data transformation
Generalize and/or normalize data
November 11, 2018
Data Mining: Concepts and Techniques

10. Data Mining: Concepts and Techniques
Issues regarding classification and prediction (2): Evaluating Classification Methods
Predictive accuracy
Speed
time to construct the model
time to use the model
Robustness
handling noise and missing values
Scalability
efficiency in disk-resident databases
Interpretability:
understanding and insight provided by the model
Goodness of rules
decision tree size
compactness of classification rules
November 11, 2018
Data Mining: Concepts and Techniques

11. Chapter 7. Classification and Prediction
What is classification? What is prediction?
Issues regarding classification and prediction
Classification by decision tree induction
Bayesian Classification
Other Classification Methods
Prediction
Classification accuracy
Summary
November 11, 2018
Data Mining: Concepts and Techniques

12. Classification by Decision Tree Induction
A flow-chart-like tree structure
Internal node denotes a test on an attribute
Branch represents an outcome of the test
Leaf nodes represent class labels or class distribution
Decision tree generation consists of two phases
Tree construction
At start, all the training examples are at the root
Partition examples recursively based on selected attributes
Tree pruning
Identify and remove branches that reflect noise or outliers
Use of decision tree: Classifying an unknown sample
Test the attribute values of the sample against the decision tree
November 11, 2018
Data Mining: Concepts and Techniques

13. Data Mining: Concepts and Techniques
Training Dataset
This follows an example from Quinlan’s ID3
November 11, 2018
Data Mining: Concepts and Techniques

14. Output: A Decision Tree for “buys_computer”
age?
<=30
overcast
30..40
>40
student?
yes
credit rating? no
yes
excellent
fair no
yes no
yes
November 11, 2018
Data Mining: Concepts and Techniques

15. Algorithm for Decision Tree Induction
Basic algorithm (a greedy algorithm)
Tree is constructed in a top-down recursive divide-and-conquer manner
At start, all the training examples are at the root
Attributes are categorical (if continuous-valued, they are discretized in advance)
Examples are partitioned recursively based on selected attributes
Test attributes are selected on the basis of a heuristic or statistical measure (e.g., information gain)
Conditions for stopping partitioning
All samples for a given node belong to the same class
There are no remaining attributes for further partitioning – majority voting is employed for classifying the leaf
There are no samples left for the branch attribute=ai
November 11, 2018
Data Mining: Concepts and Techniques

16. Attribute Selection Measure
Information gain (ID3/C4.5)
All attributes are assumed to be categorical
Can be modified for continuous-valued attributes
Gini index (IBM IntelligentMiner)
All attributes are assumed continuous-valued
Assume there exist several possible split values for each attribute
May need other tools, such as clustering, to get the possible split values
Can be modified for categorical attributes
November 11, 2018
Data Mining: Concepts and Techniques

17. Data Mining: Concepts and Techniques
Information Gain
Main idea: information conveyed by a message depends on its probability and can be measured in bits as:
Example: if there are 8 equally probable messages, the information conveyed by one of them is:
November 11, 2018
Data Mining: Concepts and Techniques

18. Data Mining: Concepts and Techniques
Information Gain
Assume that there are two classes N and P. Let the set of examples S contain p elements of class P and n elements of class N. Imagine selecting one case at random from a set S and announcing that it belongs to class P. This message has the probability:
The information it conveys is:
The amount of information, needed to decide if an arbitrary example in S belongs to P or N is defined as
November 11, 2018
Data Mining: Concepts and Techniques

19. Information Gain in Decision Tree Induction
Assume that by using attribute A set S will be partitioned into sets {S1, S2 , …, Sv}
If Si contains pi examples of P and ni examples of N, the entropy, or the expected information needed to classify objects in all subtrees Si is
The encoding information that would be gained by branching on A
November 11, 2018
Data Mining: Concepts and Techniques

20. Attribute Selection by Information Gain Computation
Hence
Similarly
Class P: buys_computer = “yes”
Class N: buys_computer = “no”
I(p, n) = I(9, 5) =0.940
Compute the entropy for age:
November 11, 2018
Data Mining: Concepts and Techniques

21. Gini Index (IBM IntelligentMiner)
If a data set T contains examples from n classes, gini index, gini(T) is defined as
where pj is the relative frequency of class j in T.
If a data set T is split into two subsets T1 and T2 with sizes N1 and N2 respectively, the gini index of the split data contains examples from n classes, the gini index gini(T) is defined as
The attribute provides the smallest ginisplit(T) is chosen to split the node (need to enumerate all possible splitting points for each attribute).
November 11, 2018
Data Mining: Concepts and Techniques

22. Extracting Classification Rules from Trees
Represent the knowledge in the form of IF-THEN rules
One rule is created for each path from the root to a leaf
Each attribute-value pair along a path forms a conjunction
The leaf node holds the class prediction
Rules are easier for humans to understand
Example
IF age = “<=30” AND student = “no” THEN buys_computer = “no”
IF age = “<=30” AND student = “yes” THEN buys_computer = “yes”
IF age = “31…40” THEN buys_computer = “yes”
IF age = “>40” AND credit_rating = “excellent” THEN buys_computer = “yes”
IF age = “>40” AND credit_rating = “fair” THEN buys_computer = “no”
November 11, 2018
Data Mining: Concepts and Techniques

23. Avoid Overfitting in Classification
The generated tree may overfit the training data
Too many branches, some may reflect anomalies due to noise or outliers
Result is in poor accuracy for unseen samples
Two approaches to avoid overfitting
Prepruning: Halt tree construction early—do not split a node if this would result in the goodness measure falling below a threshold
Difficult to choose an appropriate threshold
Postpruning: Remove branches from a “fully grown” tree—get a sequence of progressively pruned trees
Use a set of data different from the training data to decide which is the “best pruned tree”
November 11, 2018
Data Mining: Concepts and Techniques

24. Enhancements to basic decision tree induction
Allow for continuous-valued attributes
Dynamically define new discrete-valued attributes that partition the continuous attribute value into a discrete set of intervals
Handle missing attribute values
Assign the most common value of the attribute
Assign probability to each of the possible values
Attribute construction
Create new attributes based on existing ones that are sparsely represented
This reduces fragmentation, repetition, and replication
November 11, 2018
Data Mining: Concepts and Techniques

25. Classification in Large Databases
Classification—a classical problem extensively studied by statisticians and machine learning researchers
Scalability: Classifying data sets with millions of examples and hundreds of attributes with reasonable speed
Why decision tree induction in data mining?
relatively faster learning speed (than other classification methods)
convertible to simple and easy to understand classification rules
can use SQL queries for accessing databases
comparable classification accuracy with other methods
November 11, 2018
Data Mining: Concepts and Techniques

26. Presentation of Classification Results
November 11, 2018
Data Mining: Concepts and Techniques

27. Scalable Decision Tree Induction Methods in Data Mining Studies
SLIQ (EDBT’96 — Mehta et al.)
builds an index for each attribute and only class list and the current attribute list reside in memory
SPRINT (VLDB’96 — J. Shafer et al.)
constructs an attribute list data structure
PUBLIC (VLDB’98 — Rastogi & Shim)
integrates tree splitting and tree pruning: stop growing the tree earlier
RainForest (VLDB’98 — Gehrke, Ramakrishnan & Ganti)
separates the scalability aspects from the criteria that determine the quality of the tree
builds an AVC-list (attribute, value, class label)
November 11, 2018
Data Mining: Concepts and Techniques

28. SLIQ: A Fast Scalable Classifier
Shortcoming of previous classification algorithms
ONLY for memory-resident data
Purpose of SLIQ
scale for LARGE data sets
November 11, 2018
Data Mining: Concepts and Techniques

29. Decision-tree Classification
Tree Building – repeatedly partitioning the training data
evaluation and selection of the best splitting point
creation of partitions using the best split
Tree Pruning -- Minimum Description Length
November 11, 2018
Data Mining: Concepts and Techniques

30. Find Best Splitting Point
Splitting Index ( gini index )  Minimize it
Splits for numeric attributes
Sort on the values of this attribute (v1, v2, ..., vn)
(n -1) possible splits (vi – vi+1)
Splits for categorical attributes (A)
November 11, 2018
Data Mining: Concepts and Techniques

31. Data Mining: Concepts and Techniques
Improvement in SLIQ
Sorting in EVERY node (previous algorithms)
Pre-Sorting Technique (sort only ONCE)
Breadth-First Growth
A fast subsetting algorithm for splitting categorical attributes
A new tree-pruning algorithm
November 11, 2018
Data Mining: Concepts and Techniques

32. Data Structures in SLIQ
Attribute Lists
< attribute value, index into the class list>
Class List
< a class label, reference to a leaf node>
Class Histogram
( to compute frequency for gini splitting index )
numeric attribute: <class, frequency>
categorical attribute: <attribute value, class, frequency>
November 11, 2018
Data Mining: Concepts and Techniques

33. Evaluation of Splitting Points(1)
Splits for all the leaves are simultaneously evaluated .
Evaluate Splits()
for each attribute A do
traverse attribute list of A
for each value v in attribute list
find the corresponding entry in the class list, and
hence the corresponding class and the leaf node (l)
update class histogram in l
if A is a numeric attribute
compute splitting index for test (A <= v) for leaf l
if A is a categorical attribute
for each leaf of the tree do
find subset of A with best split
November 11, 2018
Data Mining: Concepts and Techniques

34. Evaluation of Splitting Points (Numeric)
(age <= 35)
November 11, 2018
Data Mining: Concepts and Techniques

35. Evaluation of Splitting Points (Categorical)
Hybrid approach for categorical attributes:
cardinality of S < threshold,
all the subsets of S are evaluated
cardinality of S >= threshold
a greedy algorithm is used
(starting with an empty subset, and add one element into it, which gives the best split)
November 11, 2018
Data Mining: Concepts and Techniques

36. Updating the Class List
November 11, 2018
Data Mining: Concepts and Techniques

37. Data Mining: Concepts and Techniques
SLIQ Tree Pruning
MDL(Minimum Description Length) principle
cost ( M, D) = cost ( D | M ) + cost ( M )
M: the model encoding the data
D: the data in terms of the model
in decision tree:
M: the result tree after pruning
D: the training set
November 11, 2018
Data Mining: Concepts and Techniques

38. Performance Evaluation (Small Dataset) Classification Accuracy
November 11, 2018
Data Mining: Concepts and Techniques

39. Performance Evaluation (Small Dataset) Pruned-tree Size
November 11, 2018
Data Mining: Concepts and Techniques

40. Performance Evaluation (Small Dataset) Execution Times
November 11, 2018
Data Mining: Concepts and Techniques

41. Performance Evaluation (Scalability)
November 11, 2018
Data Mining: Concepts and Techniques

42. Chapter 7. Classification and Prediction
What is classification? What is prediction?
Issues regarding classification and prediction
Classification by decision tree induction
Bayesian Classification
Other Classification Methods
Prediction
Classification accuracy
Summary
November 11, 2018
Data Mining: Concepts and Techniques

43. Bayesian Classification: Why?
Probabilistic learning: Calculate explicit probabilities for hypothesis, among the most practical approaches to certain types of learning problems
Incremental: Each training example can incrementally increase/decrease the probability that a hypothesis is correct. Prior knowledge can be combined with observed data.
Probabilistic prediction: Predict multiple hypotheses, weighted by their probabilities
Standard: Even when Bayesian methods are computationally intractable, they can provide a standard of optimal decision making against which other methods can be measured
November 11, 2018
Data Mining: Concepts and Techniques

44. Data Mining: Concepts and Techniques
Bayesian Theorem
Given training data D, posteriori probability of a hypothesis h, P(h|D) follows the Bayes theorem
Practical difficulty: require initial knowledge of many probabilities, significant computational cost
November 11, 2018
Data Mining: Concepts and Techniques

45. Bayesian classification
The classification problem may be formalized using a-posteriori probabilities:
P(C|X) = prob. that the sample tuple X=<x1,…,xk> is of class C.
E.g. P(class=N | outlook=sunny,windy=true,…)
Idea: assign to sample X the class label C such that P(C|X) is maximal
November 11, 2018
Data Mining: Concepts and Techniques

46. Estimating a-posteriori probabilities
Bayes theorem:
P(C|X) = P(X|C)·P(C) / P(X)
P(X) is constant for all classes
P(C) = relative freq of class C samples
C such that P(C|X) is maximum = C such that P(X|C)·P(C) is maximum
Problem: computing P(X|C) is unfeasible!
November 11, 2018
Data Mining: Concepts and Techniques

47. Naïve Bayesian Classification
Naïve assumption: attribute independence
P(x1,…,xk|C) = P(x1|C)·…·P(xk|C)
If i-th attribute is categorical: P(xi|C) is estimated as the relative freq of samples having value xi as i-th attribute in class C
If i-th attribute is continuous: P(xi|C) is estimated thru a Gaussian density function
Computationally easy in both cases
November 11, 2018
Data Mining: Concepts and Techniques

48. Play-tennis example: estimating P(xi|C)
outlook
P(sunny|p) = 2/9
P(sunny|n) = 3/5
P(overcast|p) = 4/9
P(overcast|n) = 0
P(rain|p) = 3/9
P(rain|n) = 2/5
temperature
P(hot|p) = 2/9
P(hot|n) = 2/5
P(mild|p) = 4/9
P(mild|n) = 2/5
P(cool|p) = 3/9
P(cool|n) = 1/5
humidity
P(high|p) = 3/9
P(high|n) = 4/5
P(normal|p) = 6/9
P(normal|n) = 2/5
windy
P(true|p) = 3/9
P(true|n) = 3/5
P(false|p) = 6/9
P(false|n) = 2/5
P(p) = 9/14
P(n) = 5/14
November 11, 2018
Data Mining: Concepts and Techniques

49. Play-tennis example: classifying X
An unseen sample X = <rain, hot, high, false>
P(X|p)·P(p) = P(rain|p)·P(hot|p)·P(high|p)·P(false|p)·P(p) = 3/9·2/9·3/9·6/9·9/14 =
P(X|n)·P(n) = P(rain|n)·P(hot|n)·P(high|n)·P(false|n)·P(n) = 2/5·2/5·4/5·2/5·5/14 =
Sample X is classified in class n (don’t play)
November 11, 2018
Data Mining: Concepts and Techniques

50. The independence hypothesis…
… makes computation possible
… yields optimal classifiers when satisfied
… but is seldom satisfied in practice, as attributes (variables) are often correlated.
Attempts to overcome this limitation:
Bayesian networks, that combine Bayesian reasoning with causal relationships between attributes
Decision trees, that reason on one attribute at the time, considering most important attributes first
November 11, 2018
Data Mining: Concepts and Techniques

51. Bayesian Belief Networks (I)
Family
History
Smoker
(FH, S)
(FH, ~S)
(~FH, S)
(~FH, ~S) LC
0.8
0.5
0.7
0.1
LungCancer
Emphysema
~LC
0.2
0.5
0.3
0.9
The conditional probability table for the variable LungCancer
PositiveXRay
Dyspnea
Bayesian Belief Networks
November 11, 2018
Data Mining: Concepts and Techniques

52. Bayesian Belief Networks (II)
Joint probability of a tuple is computed as:
Bayesian belief network allows a subset of the variables conditionally independent
A graphical model of causal relationships
November 11, 2018
Data Mining: Concepts and Techniques

53. Chapter 7. Classification and Prediction
What is classification? What is prediction?
Issues regarding classification and prediction
Classification by decision tree induction
Bayesian Classification
Other Classification Methods
Prediction
Classification accuracy
Summary
November 11, 2018
Data Mining: Concepts and Techniques

54. Other Classification Methods
k-nearest neighbor classifier
Case-based reasoning
Genetic algorithm
Rough set approach
Fuzzy set approaches
November 11, 2018
Data Mining: Concepts and Techniques

55. Chapter 7. Classification and Prediction
What is classification? What is prediction?
Issues regarding classification and prediction
Classification by decision tree induction
Bayesian Classification
Other Classification Methods
Prediction
Classification accuracy
Summary
November 11, 2018
Data Mining: Concepts and Techniques

56. Data Mining: Concepts and Techniques
What Is Prediction?
Prediction is similar to classification
First, construct a model
Second, use model to predict unknown value
Major method for prediction is regression
Linear and multiple regression
Non-linear regression
Prediction is different from classification
Classification refers to predict categorical class label
Prediction models continuous-valued functions
November 11, 2018
Data Mining: Concepts and Techniques

57. Data Mining: Concepts and Techniques
Regress Analysis
Linear regression: Y =  +  X
Two parameters ,  and  specify the line and are to be estimated by using the data at hand.
using the least squares criterion to the known values of Y1, Y2, …, X1, X2, ….
Multiple regression: Y = b0 + b1 X1 + b2 X2.
Many nonlinear functions can be transformed into the above.
November 11, 2018
Data Mining: Concepts and Techniques

58. Data Mining: Concepts and Techniques
A simple example
If the university authorities want to predict a student's grade on a freshman college calculus midterm based on his/her SAT score, then they may apply linear regression.
November 11, 2018
Data Mining: Concepts and Techniques

59. Linear Regression result:
Y = X
November 11, 2018
Data Mining: Concepts and Techniques

60. NBA Salary Prediction Example
Use player’s game statistics data to determine if their salaries are due to performance or just popularity.
Consider variables that affect salaries positively:
Minutes per game
Points per game
Assists per game
Rebounds per game.
Try to find the most significant variables that can predict the player’s salary.
We felt that minutes per game was important in our analysis because we felt the more minutes the athlete played, the more he should earn. Points per game was included as a variable because we thought it to be a measure of the worth of that player to the team
Rebounds and assists are also important in judging the athlete's worth to the team.
November 11, 2018
Data Mining: Concepts and Techniques

61. Data Mining: Concepts and Techniques
NBA Statistics Data
November 11, 2018
Data Mining: Concepts and Techniques

62. Variable Selection and Statistical Significance
Linear Regression:
Y = A-.0756M+.742P
Only the variable points-per-game is significant.
Adjusted model:
Y = P
The usual interpretation of R2 is as the relative amount of variance of the dependent variable y explained or accounted for by the explanatory variables x1, x2,..., xq. For example, if R2 = we say that the explanatory variables "explains" 76.2 % of the variance of y.
), the squared multiple correlation also called the coefficient of determination is defined as
 R2 = 1 - Var(e)/Var(y). E is the error. Y dependent variable.
November 11, 2018
Data Mining: Concepts and Techniques

63. Data Mining: Concepts and Techniques
Model analysis
In the previous NBA salary example,
Y = P
Statistics R2 = So, only 45.8 % of the salary is caused by Points-Per-Game.
For further analysis, we may examine the player's popularity, the impact of their agent, the perceived added income they bring to the team, as well as other, qualitative, variables.
November 11, 2018
Data Mining: Concepts and Techniques

64. Issues of regression analysis in large data sets
Regression analysis handles a data set as a whole.
Not realistic to assume a single model can fit a large data set.
Stringent model assumptions fail in the real world.
November 11, 2018
Data Mining: Concepts and Techniques

65. Data Mining: Concepts and Techniques
A new method
Regression-class mixture decomposition method ( RCMD)
View a complicated data set as a mixture of a finite number of regression models.
Goal: Identification of these models.
November 11, 2018
Data Mining: Concepts and Techniques

66. Chapter 7. Classification and Prediction
What is classification? What is prediction?
Issues regarding classification and prediction
Classification by decision tree induction
Bayesian Classification
Classification by backpropagation
Classification based on concepts from association rule mining
Other Classification Methods
Prediction
Classification accuracy
Summary
November 11, 2018
Data Mining: Concepts and Techniques

67. Classification Accuracy: Estimating Error Rates
Partition: Training-and-testing
use two independent data sets, e.g., training set (2/3), test set(1/3)
used for data set with large number of samples
Cross-validation
divide the data set into k subsamples
use k-1 subsamples as training data and one sub-sample as test data --- k-fold cross-validation
iterate k times
November 11, 2018
Data Mining: Concepts and Techniques

68. Data Mining: Concepts and Techniques
Boosting
Boosting increases classification accuracy
Applicable to decision trees or Bayesian classifier
Learn a series of classifiers, where each classifier in the series pays more attention to the examples misclassified by its predecessor
Boosting requires only linear time and constant space
November 11, 2018
Data Mining: Concepts and Techniques

69. Chapter 7. Classification and Prediction
What is classification? What is prediction?
Issues regarding classification and prediction
Classification by decision tree induction
Bayesian Classification
Classification by backpropagation
Classification based on concepts from association rule mining
Other Classification Methods
Prediction
Classification accuracy
Summary
November 11, 2018
Data Mining: Concepts and Techniques

70. Data Mining: Concepts and Techniques
Summary
Classification is an extensively studied problem (mainly in statistics, machine learning & neural networks)
Classification is probably one of the most widely used data mining techniques with a lot of extensions
Scalability is still an important issue for database applications: thus combining classification with database techniques should be a promising topic
Research directions: classification of non-relational data, e.g., text, spatial, multimedia, etc..
November 11, 2018
Data Mining: Concepts and Techniques