2: Data Preprocessing Release Date: September 27, 2016 Due Date: October 6, 2016 (upon the start of class) 1. (30 points) Suppose the data for analysis includes an attribute Age and a binary class attribute (with values Y and N). The age values for the data records (in increasing order) and their corresponding class values are as follows. Age: 10, 13, 15, 16, 16, 19, 20, 20, 20, 22, 27, 27, 27, 27, 27, 34, 42, 42, 42, 45, 52, 60, 65, 70 Class: Y, Y , Y , N , Y , Y , Y , Y , Y , N , Y , N , N , N , N , N , N , N , Y , N , N, N, N, N (a) Discretize the data into 8 intervals by equal-width (distance) binning. (10 points) (b) Discretize the data by equal-depth (frequency) binning using a bin depth of 3. (10 points) (c) Discretize the data into two intervals based on entropy-based binning (maximizing information gain), and show the conditional entropy H(class|Age) of the best split (10 points) Hint: You may implement a small program to find out the best split. 2. (30 points) Using the data for Age in Question 2, answer the following: (a) Use min-max normalization to transform the value 40 into the range [0.0, 1.0]. (10 points) (b) Use zero-mean normalization to transform the value 40. (10 points) (c) Use decimal scaling normalization to transform the value 40. (10 points) 3. Apply stratified random sampling on the following data to draw a sample of size 8. The two groups are: a) age<30 and b) age> 30. Note: The number of data points drawn from each group should be proportional to the size of each group. (10 points) Age: 10, 13, 15, 16, 16, 19, 20, 20, 20, 22, 27, 27, 27, 27, 27, 34, 42, 42, 42, 45, 52, 60, 65, 70 4. Consistency is a popular feature subset evaluation measure. Two objects are considered matching objects if their values of all features (except the class) match. For 2 matching objects, an inconsistency occurs if their class values are different. For n matching objects, the number of inconsistencies (i.e., inconsistency counts) are determined by n - max{m0, m1}, where m0+m1=n, and m0 and m1 are the number instances for class 0 and class 1 respectively. Consider the following data with four binary features (F1, F2, F3, and F4) and binary class label C. Perform feature selection using Sequential Backward Selection (SBS) search coupled with inconsistency counts as the subset evaluation measure (smaller inconsistency is better). What will be the selected subset of two features (illustrate your solution by intermediate steps)? (10 points) F1 F2 F3 F4 C 1 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 0 0 1 1 0 5. (10 points) For the same data set above, if Sequential forward Selection (SFS) is used with the same subset evaluation measure, what will be the selected subset of two features (illustrate your solution)? 6. (10 points) Discuss which method, SBS or SFS, is better for the above data and why