### multi-dimensional data

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Question 1.a (10 marks)
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Provost & Fawcett have defined Data Science in terms of 9 computational problems.

How would you introduce Regression to someone who already knows Classification?

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Your answer:
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Question 1.b (15 marks)
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Explain the geometry that causes the so-called “curse of dimensionality.”

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Your answer:
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Question 2.a (10 marks)
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Over D = {a, b, c, d, e} compute the entropy of the convex frequency distribution:

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Pr[X=xi] = [3/8, 3/16, 1/8, 1/8, 3/16].
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To simplify calculations, assume the approximation that log2(3) (log in base 2 of 3) equals 1.585.

What is the maximum entropy ever attainable over D?

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Your answer:
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Question 2.b (15 marks)
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Describe in your words was is meant by a Decision Tree and describe how to extract one from a given annotated (X, y) dataset (where y is the annotated/dependent variable).

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Your answer:
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Question 3.a (10 marks)
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What is the goal of Singular-Value Decomposition (SVD)?

How do we obtain the dimension of the matrices that will be generated as the result of its application?

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Your answer:
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Question 3.b (15 marks)
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Kernelization: for a given activity data matrix D, define the Kernel matrix K(n x n) and describe why it can be used instead of the original D in the analysis of the properties of the dataset.

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Your answer:
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Question 4.a (10 marks)
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In the analysis of activity matrices, why are the results of Singular-Value Decomposition not generally interpretable?

Why then are the results of Non-negative Matrix Factorization (NMF) interpretable?

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Your answer:
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Question 4.b (15 marks)
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Support Vector Machines: consider the figure below that shows data from two classes. Explain the lines.

Are the classes represented in the figure above linearly separable? Propose a general (no need to determine the exact parameters) kernel function that would be appropriate for this case.

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Your answer:
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Question 5.a (10 marks)
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Describe a graph representation for the International Trade Network.

Define the clustering coefficient and give an example interpretation for it either in the context of international commerce or in another network of your liking (which you define in your answer).

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Your answer:
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Question 5.b (15 marks)
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In networks, what interesting features are captured by the Closeness and Betweenness centrality measures?

Can you describe a practical example where centrality measures as these could reveal some interesting property?

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Your answer:
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