Christoph F. Eick

Questions and Topics Review Dec. 6, 20121. Compare AGNES /Hierarchical clustering with K-means; what are the main differences?2 Compute the Silhouette of the following clustering that consists of 2 clusters: {(0,0), (0,1), (2,2)}

{(3,2), (3,3)}. Assume Manhattan Distance is used. • Silhouette: For an individual point, i

– Calculate a = average distance of i to the points in its cluster– Calculate b = min (average distance of i to points in another cluster)– The silhouette coefficient for a point is then given by:

s = (b-a)/max(a,b)

3. APRIORI has been generalized for mining sequential patterns. How is the APRIORI property defined and used in the context of sequence mining?

4. Assume the Apriori-style sequence mining algorithm described at pages 429-435 is used and the algorithm generated 3-sequences listed below (see 2007 Final Exam!):

 Frequent 3-sequences Candidate Generation Candidates that survived pruning

<(1) (2) (3)>

<(1 2 3)>

<(1) (2) (4)>

<(1) (3) (4)>

<(1 2) (3)>

<(2 3) (4)>

<(2) (3) (4)>

<(3) (4 5)>

Christoph F. Eick

Answers1.

a. AGNES creates set of clustering/a dendrogram; K-Means creates a single clusteringb. K-means forms cluster by using an iteration procedure which minimizes an objective functions,

AGNES forms the dendrogram by merging the closest 2 clusters until a single cluster is obtainedc. …

3. If a k-sequence s is frequent than all its (k-1) subsequences are frequentHow used by the algorithm?

d. Frequent k-sequences are computed by combining frequent (k-1)-sequencese. For subset pruning: if a k-sequence s has a (k-1)-subsequence which not frequent, then

s is not frequent.

1 3 2 5 4 60

0.05

0.1

0.15

0.2

Christoph F. Eick

Questions and Topics Review Dec. 6, 20125. The Top 10 Data Mining Algorithms article says about k-means “The greedy-descent nature of k-means on a non-convex cost also implies that the convergence is only to a local optimum, and indeed the algorithm is typically quite sensitive to the initial centroid locations…The local minima problem can be countered to some extent by running the algorithm multiple times with different initial centroids.” Explain why the suggestion in boldface is a potential solution to the local maximum problem. Propose a modification of the k-means algorithm that uses the suggestion!

6. What is the role of slack variables in the Linear/SVM/Non-separable approach (textbook pages 266-270)—what do they measure? What properties of hyperplanes are maximized by the objective function f(w) (on page 268) in the approach?

7. Give the equation system that PAGERANK would use for the webpage structure given on the below. give a sketch of an approach that determines the page rank of the 4 pages from the equation system!

8. What is a data warehouse; how is it different from a traditional database?

9. Example Essay-style Question: Assume you own an online book store which sells books over the internet. How can your business benefit from data mining? Limit your answer to 7-10 sentences!

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kiC

wwL

1

2

2

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Christoph F. Eick

Sample Network Structure N

P1 P2

P3

P4

PR(A) = (1-d) + d (PR(T1)/C(T1) + ... + PR(Tn)/C(Tn))PR(P4)= (1-d) + d*PR(P3)/3

Christoph F. Eick

Questions and Topics Review Dec. 1, 20111. Give an example of a problem that might benefit from feature creation

2. Compute the Silhouette of the following clustering that consists of 2 clusters: {(0,0), (0,1), (2,2)}

{(3,2), (3,3)}. • Silhouette: For an individual point, i

– Calculate a = average distance of i to the points in its cluster– Calculate b = min (average distance of i to points in another cluster)– The silhouette coefficient for a point is then given by:

s = (b-a)/max(a,b)

3. APRIORI has been generalized for mining sequential patterns. How is the APRIORI property defined and used in the context of sequence mining?

•Property: see text book [2]•Use: Combine sequences that a frequent and which agree in all elements except the first element of the first sequence, and the last element of the second sequence.•Prune sequences if not all subsequences that can be obtained by removing a single element are frequent. [3]

3. Assume the Apriori-style sequence mining algorithm described at pages 429-435 is used and the algorithm generated 3-sequences listed below:

 Frequent 3-sequences Candidate Generation Candidates that survived pruning

<(1) (2) (3)>

<(1 2 3)>

<(1) (2) (4)>

<(1) (3) (4)>

<(1 2) (3)>

<(2 3) (4)>

<(2) (3) (4)>

<(3) (4 5)>

Christoph F. Eick

Questions and Topics Review Dec. 1, 2011

3. Assume the Apriori-style sequence mining algorithm described at pages 429-435 is used and the algorithm generated 3-sequences listed below:

 Frequent 3-sequences Candidate Generation Candidates that survived pruning • 3) Association Rule and Sequence Mining [15]• a) Assume the Apriori-style sequence mining algorithm described at pages 429-435 is used and

the algorithm generated 3-sequences listed below:• Candidates that survived pruning:• <(1) (2) (3) (4)>•  • Candidate Generation:• <(1) (2) (3) (4)> survived• <(1 2 3) (4)> pruned, (1 3) (4) is infrequent• <(1) (3) (4 5)> pruned (1) (4 5) is infrequent• <(1 2) (3) (4)> pruned, (1 2) (4) is infrequent• <(2 3) (4 5)> pruned, (2) (4 5) is infrequent• <(2) (3) (4 5)>pruned, (2) (4 5) is infrequent•  •  •  • What if the ans are correct, but this part of description isn’t giving?? Do I need to take any

points off?? Give an extra point if explanation is correct and present; otherwise subtract a point; more than 2 errors: 2 points or less!

• Frequent 3-sequences Candidate Generation Candidates that survived pruning <(1) (2) (3)>• <(1 2 3)>• <(1) (2) (4)>• <(1) (3) (4)>• <(1 2) (3)>• <(2 3) (4)>• <(2) (3) (4)>• <(3) (4 5)>•  • What candidate 4-sequences are generated from this 3-sequence set? Which of the generated

4-sequences survive the pruning step? Use format of Figure 7.6 in the textbook on page 435 to describe your answer! [7]

•  

Christoph F. Eick

5. The Top 10 Data Mining Algorithms article says about k-means “The greedy-descent nature of k-means on a non-convex cost also implies that the convergence is only to a local optimum, and indeed the algorithm is typically quite sensitive to the initial centroid locations…The local minima problem can be countered to some extent by running the algorithm multiple times with different initial centroids.” Explain why the suggestion in boldface is a potential solution to the local maximum problem. Propose a modification of the k-means algorithm that uses the suggestion!

Using k-means with different seeds will find different local maxima of K-mean’s objective function; therefore, running k-means with different initial seeds that are in proximity of different local maxima will produce alternative results.[2]

Run k-means with different seeds multiple times (e.g. 20 times), then compute the SSE of each clustering, return the clustering with the lowest SSE value as the result. [3]