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School of Computer Science

Machine Learning and Intelligent Data Analysis

Main Summer Examinations 2021

Machine Learning and Intelligent Data Analysis

Question 1 Dimensionality Reduction

(a)  Explain what is meant by  “dimensionality reduction” and why it is sometimes nec-essary.

(b) Consider the following dataset of four sample points 

Calculate  the  principal  components of this dataset.   Show  all of your  working.

(c) What does principal component analysis (PCA) tell you about the nature of a multi- variate dataset? Explain how it can be used for dimensionality reduction?

(d) What are the limitations of PCA and what other dimensionality reduction technique may be used instead?

(e) You are given a dataset consisting of 100 measurements, each of which is has 10

variables. The eigenvalues of the covariance matrix are shown in the following table:

What can you say about the underlying nature of this dataset?

Question 2 Classification

(a) Consider the Soft Margin Support Vector Machine learnt in Lecture 4e. Consider also that ← = 100 and that we are adopting a linear kernel, i.e., k(x(|）．x(j）) = x(|）≠x(j）. Assume an illustrative binary classification problem with the following training ex- amples:

Which of the Lagrange multipliers below is(are) a plausible solution(s) for this prob- lem? Justify your answer.

(b) Consider a binary classification problem where around 5% of the training examples

are likely to have their labels incorrectly assigned (i.e., assigned as 0 when the true label was 1, and vice-versa). Which value of k for k-Nearest Neighbours is likely to be better suited for this problem:  k = 1 or k = 3? Justify your answer.

(c) Consider a binary classification problem where you wish to predict whether a piece of machinery is likely to contain a defect.  For this problem, 0.5% of the training examples belong to the defective class, whereas 99.5% belong to the non-defective class.  When adopting Na¨ıve Bayes for this problem, the non-defective class may almost always be the predicted class, even when the true class is the defective class. Explain why and propose a method to alleviate this issue.

Question 3 Document Analysis

(a)  In a small universe of five web pages, one has a PageRank of 0.4.  What does this tell us about this page?

(b) Compare and contrast the TF-IDF and word2vec approaches to document vectori-

sation.  You should explain the essential principles of each method, and highlight their respective advantages and disadvantages.

(c) One possible approach to searching a large linked set of documents is to combine a measure of document similarity such as TF-IDF similarity with a measure of a page’s importance such as that provided by PageRank.  Suggest how this could be done.