ML410C

Projects in health informatics – Project and information management

Data Mining

Last time…• Why do we need data analysis?

• What is data mining?

• Examples where data mining has been useful

• Data mining and other areas of computer science and mathematics

• Some (basic) data mining tasks

The Knowledge Discovery ProcessKnowledge Discovery in Databases (KDD) is the nontrivial process of identifying valid, novel, potentially useful, and

ultimately understandable patterns in data.

U.M. Fayyad, G. Piatetsky-Shapiro and P. Smyth, “From Data Mining to Knowledge Discovery in Databases”, AI Magazine 17(3): 37-54 (1996)

CRISP-DM: CRoss Industry Standard Process for Data Mining

Shearer C., “The CRISP-DM model: the new blueprint for data mining”, Journal of Data Warehousing 5 (2000) 13-22 (see also www.crisp-dm.org)

Today

DATE TIME ROOM TOPIC

MONDAY2013-09-09

10:00-11:45 502 Introduction to data mining

WEDNESDAY2013-09-11

09:00-10:45 501 Decision trees, rules and forests

FRIDAY2013-09-13

10:00-11:45 Sal C Evaluating predictive models and tools for data mining

• What is classification

• Overview of classification methods

• Decision trees

• Forests

Today

Predictive data mining

Our task

• Input: data representing objects that have been assigned labels

• Goal: accurately predict labels for new (previously unseen) objects

An example: email classificationFeatures (attributes)

Exam

ples

(obs

erva

tions

)

Ex. Allcaps

No. excl. marks

Missingdate

No. digits in From:

Image fraction

Spam

e1 yes 0 no 3 0 yes

e2 yes 3 no 0 0.2 yes

e3 no 0 no 0 1 no

e4 no 4 yes 4 0.5 yes

e5 yes 0 yes 2 0 no

e6 no 0 no 0 0 no

Decision tree

Spam = yesSpam = no

Spam = yes

Rules

Spam = noSpam = no

Spam = yes Spam = yes Spam = no

Forests

Classification

• What is the class of the following e-mail?

– No Caps: Yes

– No. excl. marks: 0

– Missing date: Yes

– No. digits in From: 4

– Image fraction: 0.3

Classification

• What is classification?• Issues regarding classification and prediction• Classification by decision tree induction• Classification by Naïve Bayes classifier• Classification by Nearest Neighbor• Classification by Bayesian Belief networks

• Classification:

– predicts categorical class labels

– classifies data (constructs a model) based on the training set and the

values (class labels) in a classifying attribute

– uses the model for classifying new data

• Typical Applications

– credit approval

– target marketing

– medical diagnosis

– treatment effectiveness analysis

Classification

• Credit approval– A bank wants to classify its customers based on whether

they are expected to pay back their approved loans

– The history of past customers is used to train the classifier

– The classifier provides rules, which identify potentially

reliable future customers

Why Classification? A motivating application

• Credit approval– Classification rule:

• If age = “31...40” and income = high

• then credit_rating = excellent

– Future customers

• Paul: age = 35, income = high excellent credit rating

• John: age = 20, income = medium fair credit rating

Why Classification? A motivating application

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 formulas

Classification—A Two-Step Process

• Model usage: for classifying future or unknown objects

– Estimate accuracy of the model

• The known label of test samples 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

Classification Process (1): Model Construction

TrainingData

NAME LDL Glu H/ATTACKMike normal 3 noMary high 8 yesBill normal 7 yesJim high 5 yesDave normal 4 no

ClassificationAlgorithms

IF LDL = ‘high’OR Gluc > 6 mmol/litTHEN Heart attack = ‘yes’

Classifier(Model)

Classification Process (2): Use the Model in Prediction

Classifier

TestingData

NAME LDL Glu H/ATTACKTom normal 5.5 noMellisa low 5 noGeorge high 7.5 yesJoseph high 5 yes

Unseen Data

(Jeff, high, 7.5)

Heart attack?

Accuracy=?

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

Issues regarding classification and prediction: 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 (quality)– decision tree size– compactness of classification rules

Classification by Decision Tree Induction• Decision tree

– 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

Training Dataset

age income student credit_rating buys_computer<=30 high no fair no<=30 high no excellent no31…40 high no fair yes>40 medium no fair yes>40 low yes fair yes>40 low yes excellent no31…40 low yes excellent yes<=30 medium no fair no<=30 low yes fair yes>40 medium yes fair yes<=30 medium yes excellent yes31…40 medium no excellent yes31…40 high yes fair yes>40 medium no excellent no

Example

Output: A Decision Tree for “buys_computer”

age?

overcast

student? credit rating?

no yes fairexcellent

<=30 >40

no noyes yes

yes

30..40

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)– Samples are partitioned recursively based on selected attributes– Test (split) 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

Algorithm for Decision Tree Induction (pseudocode)

Algorithm GenDecTree(Sample S, Attlist A)1. create a node N2. If all samples are of the same class C then label N with C; terminate;3. If A is empty then label N with the most common class C in S (majority

voting); terminate;4. Select aA, with the highest information gain; Label N with a;5. For each value v of a:

a. Grow a branch from N with condition a=v;b. Let Sv be the subset of samples in S with a=v;c. If Sv is empty then attach a leaf labeled with the most common class in S;d. Else attach the node generated by GenDecTree(Sv, A-a)

Attribute Selection Measure: Information Gain

Let pi be the probability that an arbitrary tuple in D belongs to class Ci, estimated by |Ci, D|/|D|

- where Ci, D denotes the set of tuples that belong to class Ci

Expected information (entropy) needed to classify a tuple in D:

- where m is the number of classes

)(log)( 21

i

m

ii ppDInfo

Attribute Selection Measure: Information Gain

Information needed (after using A to split D into v partitions) to classify D:

Information gained by branching on attribute A

)(||||

)(1

j

v

j

jA DI

DD

DInfo

(D)InfoInfo(D)Gain(A) A

Attribute Selection: Information Gaing Class P: buys_computer = “yes”g Class N: buys_computer = “no”

age pi ni I(pi, ni)<=30 2 3 0.97131…40 4 0 0>40 3 2 0.971

694.0)2,3(145

)0,4(144)3,2(

145)(

I

IIDInfoage

048.0)_(151.0)(029.0)(

ratingcreditGainstudentGainincomeGain

246.0)()()( DInfoDInfoageGain ageage income student credit_rating buys_computer<=30 high no fair no<=30 high no excellent no31…40 high no fair yes>40 medium no fair yes>40 low yes fair yes>40 low yes excellent no31…40 low yes excellent yes<=30 medium no fair no<=30 low yes fair yes>40 medium yes fair yes<=30 medium yes excellent yes31…40 medium no excellent yes31…40 high yes fair yes>40 medium no excellent no

940.0)145(log

145)

149(log

149)5,9()( 22 IDInfo

)(log)( 21

i

m

ii ppDInfo

)(||||

)(1

j

v

j

jA DI

DD

DInfo

Splitting the samples using age

income student credit_rating buys_computerhigh no fair nohigh no excellent nomedium no fair nolow yes fair yesmedium yes excellent yes

income student credit_rating buys_computerhigh no fair yeslow yes excellent yesmedium no excellent yeshigh yes fair yes

income student credit_rating buys_computermedium no fair yeslow yes fair yeslow yes excellent nomedium yes fair yesmedium no excellent no

age?<=30

30...40

>40

labeled yes

Gini index• If a data set D contains examples from n classes, gini

index, gini(D) is defined as

- where pj is the relative frequency of class j in D

• If a data set D is split on A into two subsets D1 and D2, the gini index gini(D) is defined as

n

jp jDgini1

21)(

)(||||)(

||||)( 2

21

1 DginiDD

DginiDDDginiA

Gini index

• Reduction in Impurity:

• The attribute that provides the smallest ginisplit(D) (or

the largest reduction in impurity) is chosen to split

the node

)()()( DginiDginiAgini A

Gini index (CART, IBM IntelligentMiner)

Example: • D has 9 tuples in buys_computer = “yes” and 5 in “no”

• Suppose that attribute “income” partitions D into 10 records (D1: {low, medium}) and 4 records (D2: {high}).

459.0145

1491)(

22

Dgini

n

jp jDgini1

21)(

Gini index

• Then:

= 0.45

and gini{medium,high} = 0.30

• All attributes are assumed continuous-valued

• May need other tools, e.g., clustering, to get the

possible split values

)(144)(

1410)( 21},{ DGiniDGiniDgini mediumlowincome

Comparing Attribute Selection Measures

• The two measures, in general, return good results but

– Information gain:

• biased towards multivalued attributes

– Gini index:

• biased to multivalued attributes

• has difficulty when # of classes is large

• tends to favor test sets that result in equal-sized partitions and

purity in both partitions

Overfitting due to noise

Decision boundary is distorted by noise point

Overfitting due to insufficient samples

Why?

Overfitting due to insufficient samples

Lack of data points in the lower half of the diagram makes it difficult to predict correctly the class labels of that region

- Insufficient number of training records in the region causes the decision tree to predict the test examples using other training records that are irrelevant to the classification task

Overfitting and Tree Pruning

• Overfitting: An induced tree may overfit the training data – Too many branches, some may reflect anomalies due to noise or outliers

– 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

Occam’s Razor• Given two models of similar generalization errors, one should prefer the

simpler model over the more complex model• Therefore, one should include model complexity when evaluating a model

“entia non sunt multiplicanda praeter ecessitatem”,

which translates to:

“entities should not be multiplied beyond necessity”.

Pros and Cons of decision trees

• Cons– Cannot handle complicated

relationship between features– simple decision boundaries– problems with lots of missing

data

• Pros+ Reasonable training time+ Fast application+ Easy to interpret+ Easy to implement+ Can handle large number

of features

Some well-known decisiontree learning implementations

CART Breiman L, Friedman JH, Olshen RA, Stone CJ (1984) Classification and Regression Trees. Wadsworth

ID3 Quinlan JR (1986) Induction of decision trees. Machine Learning 1:81–106

C4.5 Quinlan JR (1993) C4.5: Programs for machine learning. Morgan Kaufmann

J48 Implementation of C4.5 in WEKA

Handling missing values

• Remove attributes with missing values

• Remove examples with missing values

• Assume most frequent value

• Assume most frequent value given a class

• Learn the distribution of a given attribute

• Find correlation between attributes

Handling missing values

Example A 1 … Class

e1 yes +

e2 no +

e3 yes -

e4 ? -

A1

yes no

e1 (w=1)e3 (w=1)e4 (w=2/3)

e2 (w=1)e4 (w=1/3)

k-nearest neighbor classifiers

X X X

(a) 1-nearest neighbor (b) 2-nearest neighbor (c) 3-nearest neighbor

k-nearest neighbors of a record x are data points that have the k smallest distance to x

k-nearest neighbor classification

• Given a data record x find its k closest points– Closeness: ?

• Determine the class of x based on the classes in the neighbor list– Majority vote– Weigh the vote according to distance

• e.g., weight factor, w = 1/d2

Characteristics of nearest-neighbor classifiers

• No model building (lazy learners)– Lazy learners: computational time in classification– Eager learners: computational time in model

building• Decision trees try to find global models, k-NN

take into account local information• K-NN classifiers depend a lot on the choice of

proximity measure

Condorcet’s jury theorem

• If each member of a jury is more likely to be right than wrong,

• then the majority of the jury, too, is more likely to be right than wrong

• and the probability that the right outcome is supported by a majority of the jury is a (swiftly) increasing function of the size of the jury,

• converging to 1 as the size of the jury tends to infinity

Condorcet, 1785

0

0.05

0.1

0.15

0.2

0.25

0.3

0 5 10 15 20

No. of jury members

Prob

abili

ty o

f err

or

Condorcet’s jury theorem

Random forests

Random forests (Breiman 2001) are generated by

combining two techniques:

• bagging (Breiman 1996)

• the random subspace method (Ho 1998)

L. Breiman. Random forests. Machine Learning, 45(1):5–32, 2001

L. Breiman. Bagging predictors. Machine Learning, 24(2):123–140, 1996

T. K. Ho. The random subspace method for constructing decision forests, IEEE Transactions on Pattern Analysis and Machine Intelligence, 20(8):832-844, 1998

Bagging

A bootstrap replicate E’ of a set of examples E is created by randomly selecting n = |E| examples from E with replacement.

Ex. Other Bar Fri/Sat Hungry Guests Wait

e1 yes no no yes some yes

e2 yes no no yes full no

e3 no yes no no some yes

e4 yes no yes yes full yes

e5 yes no yes no none no

e6 no yes no yes some yes

Ex. Other Bar Fri/Sat Hungry Guests Wait

e2 yes no no yes full no

e2 yes no no yes full no

e3 no yes no no some yes

e4 yes no yes yes full yes

e4 yes no yes yes full yes

e6 no yes no yes some yes

Forests

• What is classification

• Overview of classification methods

• Decision trees

• Forests

Today

Next time

DATE TIME ROOM TOPIC

MONDAY2013-09-09

10:00-11:45 502 Introduction to data mining

WEDNESDAY2013-09-11

09:00-10:45 501 Decision trees, rules and forests

FRIDAY2013-09-13

10:00-11:45 Sal C Evaluating predictive models and tools for data mining