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\lecture{Machine Learning}{HW02: Nearest neighbor classifier}{CS 689, Spring 2015}

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Hand in via moodle at: \url{https://moodle.umass.edu/course/view.php?id=20836}.
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\bee
\i Give an example of a low dimensional (approx. 20 dimensions), medium dimensional (approx. 1000 dimensions) and high dimensional (approx. 100000 dimensions) problem that you care about. 
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\i What does the decision boundary of 1 nearest neighbor classifier for 2 points (one positive, one negative) look like?
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\i Clustering was introduced as a way to speed up k nearest neighbor (kNN) classification. Is it possible that clustering can lead to a better classifier? Briefly explain why.
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\i Give two examples of data where the Euclidean distance is not the right metric.

\i Does the accuracy of a kNN classifier using the Euclidean distance change if you (a) translate the data (b) scale the data (i.e., multiply the all the points by a constant), or (c) rotate the data? Explain. Answer the same for a kNN classifier using Manhattan distance\footnote{\url{http://en.wikipedia.org/wiki/Taxicab_geometry}}.  
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