1. Assume you have 3 documents with the following terms:

·         D1 = “computer”, “web”, “storage”, “options”

·         D2 = “computer”, “game”, “development”

·         D3 = “web”, “development”, “frameworks”

If the query Q is composed of terms “computer” and “development”, what is the relevance of each document to the query using the TF.IDF measure?

2. Explain and write the pseudocode for a Mapper/Reducer that takes as input a large file (possibly split into chucks) of integers and outputs:

a.       The sum of the squares of each integer

b.      The maximum integer

3. Assume you have a database with two relations (i.e. tables): customers and accounts. The schema for customers is composed of the following attributes:

·         customerID (integer)

·         name (string)

·         address (string)

·         phone (string)

The schema for accounts is composed of the following attributes:

·         customerID (integer)

·         accountNumber (integer)

·         balance (float)

Write the following queries using SQL:

A.  Find the customer name with account number 12345.

B.  Find all customer names who have at least one account with balance >$100,000

Write the following queries using Relational Algebra:

C. Find all account numbers with balance <$20,000

D. Calculate the sum of all accounts for customer with ID=432

4. Compute the Jaccard similarities of each pair of the following three sets: {1, 2, 3, 4}, {2, 3, 5, 7}, and {2, 4, 6}.

5. List the first ten 3-shingles in the following sentence: “In this section, we introduce the simplest and most common approach, shingling, as well as an interesting variation.”

6. Fill in the signature matrix using the following input matrix of shingles of documents and the given permutations:

Input Matrix

Permutations: π1=(2,4,3,1) π2=(1,2,4,3) π3=(4,3,2,1)

Signature Matrix

7. Using your answers from problem 3, compute the column/column and signature/signature similarities of the following document pairs: a) 1-2 b) 1-3 c) 2-3

8. Perform a hierarchical clustering of the one-dimensional set of points 1, 4, 9, 16, 25, 36, 49, 64, 81, assuming clusters are represented by their centroid (average), and at each step the clusters with the closest centroids are merged. (show each step)

9. Use the k-means algorithm and Euclidean distance to cluster the following 5 examples into 2 clusters: p1=(2,10), p2=(2,5), p3=(8,4), p4=(5,8), p5=(7,4).

Grocery Data

10. Given the following itemsets:

{A,B,C} {B,C} {A,B,C,D} {A,C,D} {C,D} {B,C} {B,D}

a) What is the support of {A}, {A,C}, {B}, {B,C}, {A,C}, {A,C,B}, {B,C,D}, {A,B,C,D} ?

b) What is the confidence of {A}->C, {B}->C, {A,C}->B, {B,C}->D ?

c) What is the interest of {A}->C, {B}->C, {A,C}->B, {B,C}->D ?

11. Apply the A-Priori Algorithm with support threshold 3 to the itemsets from problem 1.

12. If we use a triangular matrix to count pairs, and n, the number of items, is 20, what pair’s count is in a[100]?

13. Assume you are given the following collection of twelve baskets, each of which containing three of the six items 1 through 6:

{1, 2, 3} {2, 3, 4} {3, 4, 5} {4, 5, 6} {1, 3, 5} {2, 4, 6} {1, 3, 4} {2, 4, 5} {3, 5, 6} {1, 2, 4} {2, 3, 5} {3, 4, 6}

Suppose the support threshold is 4. On the first pass of the PCY Algorithm we use a hash table with 11 buckets, and the set {i, j} is hashed to bucket i×j mod 11.

a) By any method, compute the support for each item and each pair of items. b) Which pairs hash to which buckets? c) Which buckets are frequent? d) Which pairs are counted on the second pass of the PCY Algorithm?

14. For this question, you will need to use the Orange Canvas data mining software. You can find it at:http://orange.biolab.si/

Be sure to read the documentation and especially the following:http://docs.orange.biolab.si/widgets/rst/associate/associationrules.html#association-rules

Then download the file grocery-data.txt (from BlackBoard) and use it with the Orange Canvas software to answer the following questions:

a) Which rule has the most confidence?

b) If we consider rules with any confidence, for what support value do we arrive with only 10 rules?

c) Make a screenshot of the Orange schema (i.e. your workspace) you used to answer questions (a) and (b) and insert it.

15. Given the data set below, apply the k-Nearest Neighbor algorithm to classify the test data for k=1 and k=3. Use the Euclidean distance metric.

·          

16. Compute the confusion matrix, accuracy, precision, recall, and F1 measures given your answers to problem 1 

17. Assume you have the data set given below, which provides hypothetical examples of instances when people did or did not get hired for a job. It consists of three categorical attributes and a label that indicates “hired” or “not hired”. Using this data, induce a decision tree using information gain for splitting the nodes, showing the calculations at each step.

18. Download and install the WEKA data mining toolkit. It is available through this link:http://www.cs.waikato.ac.nz/ml/weka/downloading.html Then use the Explorer GUI interface and open the “credit-g.arff” data set that is included in WEKA (data directory). This is a data set from Germany describing credit-worthiness (good or bad) of customers based on 20 different attributes. Go to the classify tab, select “Percentage Split” and enter 50%. Then run each of the following classification algorithms:

·         trees.J48

·         trees.SimpleCart

·         trees.RandomForests

·         meta.AdaBoostM1

a) For each algorithm, report the accuracy, precision, and recall values with default parameters

b) Adjust the parameters of each algorithm to maximize the accuracy. Report the algorithm and parameter settings that maximized the accuracy measure and provide the maximum accuracy value.

19  . Given the graph below, compute the rank of nodes A, B, and C by setting up the flow equations with the constraint that the sum of ranks is 1, and then solving the equations for the rank values. Make sure to show/explain the steps.

20. Given the following adjacency matrix, use the power iteration method to find the approximate rank vector. Do 3 iterations and show your work.

21. Assume you have the adjacency matrix given in problem 2. Use the PageRank equation with  to compute the rank vector using the power iteration method. Do 3 iterations and show your work.

22. Assume you have the following set of preferences of people over seats at a table: {“John”, {Seat1, Seat2, Seat 3}, “Mary”,{Seat2, Seat4}, “Bob”, {Seat1, Seat3, Seat4}, “Alice”, {Seat3, Seat5}, “Cindy”, {Seat1, Seat2, Seat3}}

What is the competitive ratio of the greedy algorithm vs. the optimal seating arrangement?

Explain in your own words, why is it hard to measure the ClickThrough Rate?

23. Consider the following scenario: There are three advertisers A, B, and C A bids on query x, B bids on x and y, and C bids on x, y, and z All have budgets of $3.

Given the following query stream: x x x y y y z z z

a) What are the sequences of choices for both the greedy algorithm assuming the worst case scenario and the BALANCE algorithm?

b) What are the competitive ratios for both algorithms in this scenario?

24. Three computers, A, B, and C, have the numerical features listed below:

We may imagine these values as defining a vector for each computer; for instance, A’s vector is [3.06, 500, 6]. We can compute the cosine distance between any two of the vectors, but if we do not scale the components, then the disk size will dominate and make differences in the other components essentially invisible. Let us use 1 as the scale factor for processor speed, α for the disk size, and β for the main memory size. (a) In terms of α and β, compute the cosines of the angles between the vectors for each pair of the three computers. (b) What are the angles between the vectors if α = β = 1? (c) What are the angles between the vectors if α = 0.01 and β = 0.5?

·         2. A certain user has rated the three computers of Problem 1 as follows: A: 4 stars, B: 2 stars, C: 5 stars. (a) Normalize the ratings for this user. (b) Compute a user profile for the user, with components forprocessor speed, disk size, and main memory size, based on the data of Problem 1.

25. Given the following utility matrix, representing the ratings, on a 1–5 star scale, of eight items, a through h, by three users A, B, and C:

·          

·         Compute the following from the data of this matrix. (a) Normalize the matrix by subtracting from each nonblank entry the average value for its user. (b) Using the normalized matrix from Part (a), compute the cosine distance between each pair of users

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