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quiz3_2008

# quiz3_2008 - 6.034 Quiz 3 Name EMail Circle your TA and...

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6.034 Quiz 3 November 12, 2008 Name EMail Circle your TA and recitation time, if any, so that we can more easily enter your score in our records and return your quiz to you promptly. TAs Sam Glidden Mike Klein Mark Seifter Theopholis T. Yeh Thu Time Instructor 1-2 Bob Berwick 2-3 Bob Berwick 3-4 Bob Berwick Fri Time Instructor 1-2 Howard Shrobe 2-3 Howard Shrobe 3-4 Howard Shrobe Problem number Maximum Score Grader 1 50 2 50 Total 100 There are 13 pages in this quiz, including this one. In addition, tear-off sheets are provided at the end with duplicate drawings, data, and neural net notes . As always, open book, open notes, open just about everything. 1

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Problem 1: Nearest Neightbors and ID Trees (50 points) Taking advantage shifts in MIT's requirements, Johnathan decides to take a geology subject instead of 8.02. He begins by learning how to classify minerals as sedimentary or metamorphic. He decides to take advantage techniques he learned in 6.034. Johnathan has a data set of eight minerals classified as either sedimentary or metamorphic, with the following characteristics: Sample # Mineral Hardness Density Grainsize 1 Sedimentary 3 4 huge 2 Sedimentary 2 3 normal 3 Sedimentary 4 3 huge 4 Sedimentary 4 2 huge 5 Metamorphic 2 5 tiny 6 Metamorphic 3 2 normal 7 Metamorphic 4 5 tiny 8 Metamorphic 5 3 tiny He wants to classify these two minerals: Sample Mineral Hardness Density Grainsize A ? 2 1 huge B ? 4 1 tiny 2
Part A: Nearest Neighbors (25 points) Johnathan decides to try using Nearest Neighbors to classify minerals A and B. To make it easier, he only uses the first two characteristics: hardness and density. Part A1 (17 points) On the following graph, draw the decision boundaries produced by 1-Nearest Neighbor. Ignore Samples A and B. Density 6 5 4 3 2 1 0 M M S S S M M S A B 0 1 2 3 4 5 Hardness 6 3

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Part A2 (8 points) How is Sample A classified by 1-NN?
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