Question

K-means clustering Assume we have a 2-dimensional space and four points (0, 0), (0, 5), (6, 7), and (7, 0), and we want to cluster the examples into two groups using the k-means algorithm and the Euclidean distance. Part a. Let us assume the algorithm is initialized with means (0, 0) and (7, 0). What are the values of the two means the algorithm converges to? How are data points divided into groups? Part b. Now let us assume the algorithm is initialized from the means (3, 3) and (7, 0). What are the values of the two means the algorithm converges to? How are data points divided into groups? Part c. Let us assume the two runs of the k-means lead to two different clusterings. Write a math expression that would let you compare these different clusterings and pick the best one. Hint: What criterion does the k-means optimize?

          K-means clustering
Assume we have a 2-dimensional space and four points (0, 0), (0, 5), (6, 7), and (7, 0), and we want to cluster the examples into two groups using the k-means algorithm and the Euclidean distance.

Part a. Let us assume the algorithm is initialized with means (0, 0) and (7, 0). What are the values of the two means the algorithm converges to? How are data points divided into groups?

Part b. Now let us assume the algorithm is initialized from the means (3, 3) and (7, 0). What are the values of the two means the algorithm converges to? How are data points divided into groups?

Part c. Let us assume the two runs of the k-means lead to two different clusterings. Write a math expression that would let you compare these different clusterings and pick the best one. Hint: What criterion does the k-means optimize?

Added by Julio R.

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