Question 1 - Unsupervised learning concepts [25 marks] a. Two main types of unsupervised learning are association analysis and cluster analysis. For each of the two types, give an example application in the education domain; describe the application and how unsupervised learning techniques are employed in the application. [5] b. Principal component analysis ( PCA) is applied to a dataset of 4 features to produce 4 principal components called PC0, PC1, PC2, and PC3. [5] i. What is the total amount of explained variance ratios of all the principal components? ii. Compare the amounts of explained variance ratios of the 4 principal components. iii. A student calculates some cumulative explained variance ratios by hand, and gets the following results. Comment on the correctness of the calculated results with justification. c. The following dataset contains 7 transactions of 6 items: apple, bread, carrot, donut, egg, and fish. Calculate (i) support(\{apple\}), (ii) support(\{donut\}), (iii) support(\{apple }{ donut } ), and (iv) confidence(\{apple }{ donut } ). (Note that this dataset is also used in some later questions.) [5] - T0: apple, bread, egg, fish - T1: apple, bread, carrot, donut, egg - T2: bread, egg - T3: bread, donut, egg - T4: apple, bread, egg - T5: apple, bread, egg, fish - T6: apple, carrot, donut, egg d. Recommender systems use different types of techniques, which employ different data. [5] i. Which type of technique mainly uses product description data? ii. Which type of technique mainly uses recent product sales data? iii. Which type of technique mainly uses historical user purchase data? iv. Which type of technique has the most privacy concerns? Briefly justify your answer. e. Four vectors are given below. [5] i. Compute the cosine similarity among the four vectors, and show the resulting cosine similarity values in 4 decimal places and in a 44 table. You may do it either by hand or by code, and need not show the intermediate work. ii. From the table, determine the vector that is most similar to vector \#1. iii. From the table, determine the vector that is most similar to vector \#2