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Politecnico di Milano School of Industrial and Information Engineering Data Mining and Text Mining Prof. Pier Luca Lanzi & Ing. Daniele Loiacono July 4, 2016 NAME CODICE PERSONA/ID • Answers must be clearly written inside the problem box. All the answers must be adequately motivated. • Pencils are not allowed. The midterm consists of 3 sheets of paper. It must be returned with all the 3 sheets. No any other sheet can be added. No sheet can be removed. • This is a closed-book/closed-notes exam. • Only non-programmable calculators are allowed. • Notes/books/mobile phones are not allowed. • If you are caught using forbidden material, the exam will immediately end and an RP grade will be recorded; then, your Data Mining exam will consist of an oral examination from then on. • Scoring o A problem left unsolved will amount to zero points. o A completely wrong solution will amount to -3 points Grades Problem 1. (7 points) Consider the following dataset where the last column represents the class attribute. (1) show which decision will be chosen at the root of the decision tree using information gain and Gini index. Show all split points for all attributes. (2) What happens to the purity if we use Instance as another attribute? Do you think this attribute should be used for a decision in the tree? Instance a1 a2 a3 Class 1 T T 5.0 Y 2 T T 7.0 Y 3 T F 8.0 N 4 F F 3.0 Y 5 F T 7.0 N 6 F T 4.0 N 7 F F 5.0 N 8 T F 6.0 Y 9 F T 1.0 N Write the values of the Information Gain and Gini Index in the following boxes. a1 a2 a3 Information Gain Gini Index Information Gain Splits Problem 1 (continued) Gini Index Splits Problem 2. (7pts) Given the following graph, cluster the graph into two clusters using simple cut and normalized cut (conductance). Problem 3 (5pts). The company StereotypeThis…