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日期:2022-05-31 08:17

BUCI057H7 page 2 of 9


Question 1 (10 marks)

Provost & Fawcett have defined Data Science in terms of 9 computational problems.

Define the Similarity problem in general and propose examples on multi-dimensional data.

Your answer:


BUCI057H7 page 3 of 9


Question 2 (10 marks)

Spectral analysis can be used to reduce data dimensionality. Explain why dimensionality reduction is

desirable and how Spectral analysis can achieve it.

Your answer:


BUCI057H7 page 4 of 9


Question 3 (10 marks)

Over D = {a, b, c, d, e}, frequency of observations gives us the following distribution:

P = Pr[X=xi] = [3/8, 3/16, 1/8, 1/8, 3/16].

To simplify calculations, however, we decide to adopt the “simpler” distribution

Q = Pr[X=xi] = [1/2, 1/8, 1/8, 1/8, 1/8].

Compute the Kullback-Leibler divergence between P and Q, defined as


To simplify calculations, assume that log23 (logarithm in base 2 of 3) equals 1.585 and show the

process by which you calculated the divergence.

Your answer:


BUCI057H7 page 5 of 9


Question 4 (10 marks)

Define the decision trees employed in the Supervised Segmentation task and describe in words how

the CART algorithm can recursively build a decision tree for a given dataset of labeled Yes/No

examples.

Your answer:


BUCI057H7 page 6 of 9


Question 5 (10 marks)

Sports Rating & Ranking: if a function S(i) measures the strength of a team/player i attending a

tournament, how could we predict the outcome of a match between, say, team i and team j?

What method would you use, among those seen in class, to extract function S(i) from a dataset of past

results?

Your answer:


BUCI057H7 page 7 of 9


Question 6 (10 marks)

Define the Kernel method for creating a feature space and discuss why it is used in combination with

Support Vector Machines to classify data.

Your answer:


BUCI057H7 page 8 of 9


Question 7 (10 marks)

Define the Degree sequence of networks, explain why the sum of degrees is always even and discuss

its usage in network analysis.

Your answer:


BUCI057H7 page 9 of 9


Question 8 (10 marks)

Ranking in Networks: what is the model of i) importance and ii) human navigation of Web pages that

underpins PageRank?


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