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.

In K-Means clustering, the algorithm iteratively updates the ______________ of each cluster until convergence.

Question 2Which statement describes better “the smarter initialization of K-mean clusters? 1 point“Draw a line between the data points to create 2 big clusters.” “After we find our centroids, we calculate the distance between all our data points.”“Pick one random point, as initial point, and for the second point, instead of picking it randomly, we prioritize by assigning the probability of the distance.” “We start by having two centroids as far as possible between each other.”

How is a center point (centroid) picked for each cluster in k-means upon initialization? (select two)1 pointWe can create some random points as centroids of the clusters.We can randomly choose some observations out of the data set and use these observations as the initial means.We select the k points closest to the mean/median of the entire dataset.We can select it through correlation analysis.

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.