(a) The K-means algorithm with Euclidean distances is a very popular and widely used method for data clustering. What is the basic assumption on the distribution of the data in this K-means clustering?

(b) Answer the following questions in the context of the K-means algorithm.

What are the inputs? Which parameters are usually specified by the user?

What objective function does the K-means algorithm minimise?

(c) You are given a one-dimensional dataset, D = {0, 1, 1, 2, 3, 4, 4, 4, 5}. Compute the kernel density estimate at x = 2 and x = 4 with the bandwidth of 2 using the following triangle kernel:

K(u) = (1 - lu|)(|u| =

where is the function

(|u| =1₀^{|u|=_otherwise}

Justify your answers.

(d) Why do we want to use "weak" learners such as decision stumps when using the method of boosting?