. [10 points] K-Means
(a) Mention if K-Means is a supervised or an un-supervised method.
Your answer:
(b) Assume that you are trying to cluster data points xi for i ∈ {1, 2 . . . D} into K clusters each with center µk where k ∈ {1, 2, . . . K }. The objective function for doing this clustering involves minimizig the euclidean distance between the points and the cluster centers. It is given by
Min min E E ½ rik II xi – ukII2/2
K
How do you ensure hard assignment of one data point to one and only one cluster at a given time? Note: By hard assignment we mean that your are 100 % sure that a point either belongs or not belongs to a cluster.
Your answer:
(c) What changes must you do in your answer of part b, to make the hard assingment into a soft assignment? Note: By soft assignment we mean that your are sure that a point either belongs or not belongs to a cluster with some probability.
Your answer:
(d) Looking at the following plot, what is the best choice for number of clusters?
5000
Your answer:
(e) Would K-Means be an effecient algorithm to cluster the following data? Explain your answer in a couple of lines.
