Q1: Suppose you are given the following pairs. You will simulate the k-means algorithm. Suppose you are given the initial assignment cluster center as C1 and C2 – the first data point A1 is used as the 1st cluster center and A9 as the 2nd cluster center.Point x yA1 3 2A2 3 2A3 1 3A4 4 5A5 2 3A6 7 5A7 6 4A8 9 3A9 8 3A10 8 11.2: Compute the distance matrix (D0) for the data provided in the table at the beginning of the entire question to 4 decimal places. [5]

K means clustering algorithm clusters the data points based on:- Dependent and independent variables The eigen values Distance between the points and a cluster centre None of the above

How does the k-means algorithm determine which data points belong to which cluster?Select one:a.By evaluating the variance of each clusterb.By evaluating the probability that a data point belongs to each clusterc.By comparing the data point to the characteristics of each clusterd.By computing the distance between data points and the centroid of each cluster

The k-means clustering algorithm works by (Select one) A. iteratively improving the position of k centroids in the sample space until an optimal placement is found. B. starting with one point in the sample space, finding more points in the space within a neighborhood ℇ until no more points can be found, and then repeating this process for k-1 points. C. iteratively determining the Gaussian distribution (via its mean and standard deviation) of k clusters until the probabilities of all points in the sample space are maximized. D. pairing each point with another point such that their distance is minimized, and then repeating this process with larger groups of points until there are only k clusters remaining.

Consider the unlabeled data given below: You are now provided with two sets of center points: C1 = (1,2),(2,2),(0,-2) C2 = (0,-2)(4,2)(4.5,0) Would the K-Means algorithm with k = 3 converge to the same clusters when either C1 or C2 were used as the initial center points? If yes, explain your reasoning. If not, explain why not.

The following is ALWAYS TRUE about the k-means algorithm EXCEPTCentroids are recomputed for each newly defined cluster and data points are reassigned based on the proximity to the newly computed centroids.The k-means results to an equal number of data points per cluster.Convergence is reached when the computed centroids do not change or the centroids and the assigned points oscillate back and forth from one iteration to the next.The optimum number of clusters may be determined by examining the within sum of squares for different values of k.