Chapter 6 Classification and Prediction Dr Bernard Chen

Chapter 6 Classification and Prediction Dr. Bernard Chen Ph. D. University of Central Arkansas

Outline n n n Classification Introduction Decision Tree Classifier Accuracy Measures

Classification and Prediction n n Classification and Prediction are two forms of data analysis that can be used to extract models describing important data classes or to predict future data trends For example: n n n Bank loan applicants are “safe” or “risky” Guess a customer will buy a new computer? Analysis cancer data to predict which one of three specific treatments should apply

Classification n Classification is a Two-Step Process n n Learning step: 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 step: predicts categorical class labels (discrete or nominal)

Learning step: Model Construction Training Data Classification Algorithms Classifier (Model) IF rank = ‘professor’ OR years > 6 THEN tenured = ‘yes’

Learning step n Model construction: describing a set of predetermined classes n n n 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 is training set The model is represented as classification rules, decision trees, or mathematical formulae

Prediction step: Using the Model in Prediction Classifier Testing Data Unseen Data (Jeff, Professor, 4) Tenured?

Prediction step n Estimate accuracy of the model n The known label of test sample is compared with the classified result from the model n Accuracy rate is the percentage of test set samples that are correctly classified by the model n Test set is independent of training set, otherwise over-fitting will occur

N-fold Cross-validation n n In order to solve over-fitting problem, n-fold crossvalidation is usually used For example, 7 fold cross validation: n n Divide the whole training dataset into 7 parts equally Take the first part away, train the model on the rest 6 portions After the model is trained, feed the first part as testing dataset, obtain the accuracy Repeat step two and three, but take the second part away and so on…

Supervised learning VS Unsupervised learning n n Because the class label of each training tuple is provided, this step is also known as supervised learning It contrasts with unsupervised learning (or clustering), in which the class label of each training tuple is unknown

Issues: Data Preparation n Data cleaning n n Relevance analysis (feature selection) n n Preprocess data in order to reduce noise and handle missing values Remove the irrelevant or redundant attributes Data transformation n Generalize and/or normalize data

Issues: Evaluating Classification Methods n n Accuracy Speed n n n time to construct the model (training time) time to use the model (classification/prediction time) Robustness: handling noise and missing values Scalability: efficiency in disk-resident databases Interpretability

Outline n n n Classification Introduction Decision Tree Classifier Accuracy Measures

Decision Tree n n Decision Tree induction is the learning of decision trees from class-labeled training tuples A decision tree is a flowchart-like tree structure, where each internal node denotes a test on an attribute Each Branch represents an outcome of the test Each Leaf node holds a class label

Decision Tree Example

Decision Tree Algorithm n Basic algorithm (a greedy algorithm) n n Tree is constructed in a top-down recursive divideand-conquer manner At start, all the training examples are at the root Attributes are categorical (if continuous-valued, they are discretized in advance) Test attributes are selected on the basis of a heuristic or statistical measure (e. g. , information gain)

Attribute Selection Measure: Information Gain (ID 3/C 4. 5) n n n Select the attribute with the highest information gain Let pi be the probability that an arbitrary tuple in D belongs to class Ci, estimated by |Ci, D|/|D| Expected information (entropy) needed to classify a tuple in D:

Attribute Selection Measure: Information Gain (ID 3/C 4. 5) n n Information needed (after using A to split D into v partitions) to classify D: Information gained by branching on attribute A

Decision Tree

Decision Tree n n means “age <=30” has 5 out of 14 samples, with 2 yes’s and 3 no’s. I(2, 3) = -2/5 * log(2/5) – 3/5 * log(3/5)

Tools n n http: //www. ehow. com/how_5144933_calculatelog. html http: //web 2. 0 calc. com/

Decision Tree n Infoage (D)= 5/14 I(2, 3)+4/14 I(4, 0)+ 5/14 I(3, 2) = 5/14 * ( )+ 4/14 * (0)+ 5/14 * ( )=0. 694 For type in http: //web 2. 0 calc. com/: -2/5*log 2(2/5)-3/5*log 2(3/5)

Decision Tree (0. 940 - 0. 694) n Similarily, we can compute n n Gain(income)=0. 029 Gain(student)=0. 151 Gain(credit_rating)=0. 048 Since “student” obtains highest information gain, we can partition the tree into:

Decision Tree n Infoincome (D)= 4/14 I(3, 1)+6/14 I(4, 2)+ 4/14 I(2, 2) = 4/14 * ( )+ 6/14 * ( )+ 4/14 * (1)= 0. 232+0. 393+0. 285=0. 911 n Gain(income)=0. 940 -0. 911=0. 029

Decision Tree

Another Decision Tree Example

Decision Tree Example n n Info(Tenured)=I(3, 3)= log 2(12)=log 12/log 2=1. 07918 /0. 30103=3. 584958.

Decision Tree Example n Info. RANK (Tenured)= 3/6 I(1, 2) + 2/6 I(1, 1) + 1/6 I(1, 0)= 3/6 * ( ) + 2/6 (1) + 1/6 (0)= 0. 79 n 3/6 I(1, 2) means “Assistant Prof” has 3 out of 6 samples, with 1 n 2/6 I(1, 1) means “Associate Prof” has 2 out of 6 samples, with 1 n 1/6 I(1, 0) means “Professor” yes’s and 2 no’s. yes’s and 1 no’s. yes’s and 0 no’s. has 1 out of 6 samples, with 1

Decision Tree Example n n Info. YEARS (Tenured)= 1/6 I(1, 0) + 2/6 I(0, 2) + 1/6 I(0, 1) + 2/6 I (2, 0)= 0 1/6 I(1, 0) means “years=2” has 1 out of 6 samples, with 1 yes’s and 2/6 I(0, 2) means “years=3” has 2 out of 6 samples, with 0 yes’s and 1/6 I(0, 1) means “years=6” has 1 out of 6 samples, with 0 yes’s and 2/6 I(2, 0) means “years=7” has 2 out of 6 samples, with 2 yes’s and 0 no’s. n 2 no’s. n 1 no’s. n 0 no’s.

Group Practice Example

Outline n n n Classification Introduction Decision Tree Classifier Accuracy Measures

Classifier Accuracy Measures classes (Real) buy computer = yes (Real) buy computer = no total (Predict) buy computer = yes 6954 412 7366 (Predict) buy computer = no 46 2588 2634 total 7000 (Buy Computer) 3000 (Does not buy Computer) 10000

Classifier Accuracy Measures n Alternative accuracy measures (e. g. , for cancer diagnosis) sensitivity = t-pos/pos = 6954/7000 specificity = t-neg/neg = 2588/3000 precision = t-pos/(t-pos + f-pos) = 6954/7366 accuracy =