COMP9318 (21T1) ASSIGNMENT 1 DUE ON 20:59 16 APR, 2021 (FRI) Q1. (40 marks) Consider the following base cuboid Sales with four tuples and the aggregate function SUM: Location T ime Item Quantity Sydney 2005 PS2 1400 Sydney 2006 PS2 1500 Sydney 2006 Wii 500 Melbourne 2005 XBox 360 1700 Location, Time, and Item are dimensions and Quantity is the measure. Suppose the system has built-in support for the value ALL. (1) List the tuples in the complete data cube of R in a tabular form with 4 attributes, i.e., Location, T ime, Item,SUM(Quantity)? (2) Write down an equivalent SQL statement that computes the same result (i.e., the cube). You can only use standard SQL constructs, i.e., no CUBE BY clause. (3) Consider the following ice-berg cube query: SELECT Location, Time, Item, SUM(Quantity) FROM Sales CUBE BY Location, Time, Item HAVING COUNT(*) > 1 Draw the result of the query in a tabular form. (4) Assume that we adopt a MOLAP architecture to store the full data cube of R, with the following mapping functions: fLocation(x) = 1 if x = ‘Sydney’, 2 if x = ‘Melbourne’, 0 if x = ALL. fT ime(x) = 1 if x = 2005, 2 if x = 2006, 0 if x = ALL. 1 2 DUE ON 20:59 16 APR, 2021 (FRI) fItem(x) = 1 if x = ‘PS2’, 2 if x = ‘XBox 360’, 3 if x = ‘Wii’, 0 if x = ALL. If we want to draw the MOLAP cube (i.e., sparse multi-dimensional array) in a tabular form of (ArrayIndex, V alue), then which of the following function is feasible? Why? You also need to draw the MOLAP cube. • f(x) = 9 · fLocation(x) + 3 · fT ime(x) + fItem(x) • f(x) = 16 · fLocation(x) + 4 · fT ime(x) + fItem(x) Q2. (30 marks) Consider the following training examples which are used to construct a decision tree to help predict whether a patient is likely to have a lung cancer. Patient ID Gender Smokes? Chest pain? Cough? Lung Cancer 1 Female Yes Yes Male Yes 2 Male Yes No Male Yes 3 Male No No Female Yes 4 Female No Yes Male No 5 Male Yes Yes Female Yes 6 Male No Yes Male No (1) Use Gini index to construct a decision tree that predicts whether a patient is likely to have a lung cancer. You need to show every step of the construction. (2) Translate your decision tree into decision rules. Q3. (30 marks) Consider binary classification where the class attribute y takes two values: 0 or 1. Let the feature vector for a test instance to be a d-dimention column vector x. A linear classifier with the model paramter w (which is a d-dimension column vector) is the following function: y = { 1 , if wTx > 0 0 , otherwise. We make additional simplifying assumptions: x is a binary vector (i.e., each dimension of x take only two values: 0 or 1). (1) Prove that if the feature vectors are d-dimension, then a Na¨ıve Bayes classifier is a linear classifier in a d + 1-dimension space. You need to explicitly write out the vector w that the Na¨ıve Bayes classifier learns. COMP9318 (21T1) ASSIGNMENT 1 3 (2) It is obvious that the Logistic Regression classifier learned on the same training dataset as the Na¨ıve Bayes is also a linear classifier in the same d + 1-dimension space. Let the parameter w learned by the two classifiers be wLR and wNB, respectively. Briefly explain why learning wNB is much easier than learning wLR. Hint1.log ∏ i x i = ∑ i logx i Submission Please write down your answers in a file named ass1.pdf. You must write down your name and student ID on the first page. You can submit your file by give cs9318 ass1 ass1.pdf Late Penalty. 0 mark if not submit on time (i.e., firm deadline).
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