School of Computing and Information Systems The University of Melbourne
COMP90049 Introduction to Machine Learning (Semester 1, 2022) Week 3
1. For the following dataset:
id apple ibm lemon sun CLASS TRAINING INSTANCES
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0 COMPUTER 7 COMPUTER
TEST INSTANCES
(i). Using the Euclidean distance measure, classify the test instances using the 1-NN method.
(ii). Using the Manhattan distance measure, classify the test instances using the 3-NN method, for the three weightings we discussed in the lectures: majority class, inverse distance, inverse linear distance.
(iii). Can we do weighted k-NN using cosine similarity?
2. Approximately 1% of women aged between 40 and 50 have breast cancer. 80% of mammogram screening tests detect breast cancer when it is there. 90% of mammograms DO NOT show breast cancer when it is NOT there1. Based on this information, complete the following table.
Cancer Probability
No 99% Yes 1%
Cancer Test Probability
Yes Positive 80% Yes Negative ? No Positive ? No Negative 90%
3. Based on the results in question 2, calculate the marginal probability of ¡®positive¡¯ results in a Mammogram Screening Test.
4. Based on the results in question 2, calculate P(Cancer = ¡®Yes¡¯ | Test = ¡®Positive¡¯), using the Bayes Rule.
1 Remember these numbers are not accurate and simplified to ease the calculations in this question.
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