School of Computing and Information Systems The University of Melbourne
COMP90049 Introduction to Machine Learning (Semester 1, 2022) Week 6
1. Consider the following dataset:
id apple ibm lemon sun label A 4 0 1 1 fruit B 5 0 5 2 fruit C 2 5 0 0 comp D 1 2 1 7 comp E2031? F1010?
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(a) Treat the problem as an unsupervised machine learning problem (excluding the label attributes) and calculate the clusters according to k-means with k = 2, using the Manhattan distance, and instances A and F as starting seeds (initialized cluster centers).
(b) Perform agglomerative clustering of the above dataset (excluding the id and label attributes), using the Euclidean distance and calculating the group average as the cluster centroid.
2. Revise the concept of unsupervised and supervised evaluation for clustering evaluation
(a) Explain the two main concepts that we use to measures the goodness of a clustering structure
without respect to external information.
(b) Explain the two main concepts that we use to measure the how well do cluster labels match
externally supplied class labels.
3. Consider a Naive Bayes model trained using the following familiar weather dataset:
ID Outl Temp Humi Wind PLAY AshnFN BshhTN CohhFY DrmhFY ErcnFY FrcnTN
Suppose that you made additional observations of days and their features. But you don’t have the label for the PLAY in these days:
ID Outl Temp Humi Wind PLAY GomnT? HsmhF?
How could you incorporate this information into your Naïve Bayes model without manually annotating the labels? If necessary, recompute your model parameters.
4. One of the strategies for Query sampling was query-by-committee (QBC), where a suite of classifiers is trained over a fixed training set, and the instance that results in the highest disagreement amongst the classifiers, is selected for querying. Using the equation below, which captures vote entropy, determine the instance that our active learner would select first.
𝑥∗ = argm𝑎𝑥(−*𝑉(𝑦%)𝑙𝑜𝑔 𝑉(𝑦%)) !” $ &!𝐶’𝐶
Respectively 𝑦! , 𝑉(𝑦! ), 𝑎𝑛𝑑 𝐶 are the possible labels, the number of “votes” that a label receives from the classifiers, and the total number of classifiers.
classifier
Instance 1 Instance 2 Instance 3
𝒚𝟏 𝒚𝟐 𝒚𝟑 𝒚𝟏 𝒚𝟐 𝒚𝟑 𝒚𝟏 𝒚𝟐 𝒚𝟑
𝐶$ 0.2 0.7 0.1 𝐶% 0.1 0.3 0.6 𝐶& 0.8 0.1 0.1 𝐶’ 0.3 0.5 0.2
0.2 0.6 0.05 0.9 0.1 0.8
0.1 0.6 0.1 0.3
0.2 0.21 0.21 0.58 0.05 0.75 0.01 0.24 0.1 0.1 0.28 0.62
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