Description

1. For the following dataset:
apple ibm lemon sun CLASS
TRAINING IN STAN CES
4 0 1 1 FRUIT
5 0 5 2 FRUIT
2 5 0 0 COMPUTER
1 2 1 7 COMPUTER
TEST INST ANCE S
2 0 3 1 ?
1 2 1 0 ?
(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 there . 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 1, calculate the marginal probability of ‘positive’ results in a Mammogram Screening Test.
4. Based on the results in question 1, calculate P(Cancer = ‘Yes’ | Test = ‘Positive’), using the Bayes Rule.