(Solved) : 3 Suppose M 10 X 3 Matrix Let Matrix Consisting Second Third Columns M Let B Matrix Consis Q44132639 . . .
3. Suppose M is an 10 x 3 matrix. Let A be the matrix consisting of the second and third columns of M and let B be the matrix consisting of the first and second columns of M. • Suppose the k-means algorithm finds 2 clusters for matrix A and produces a cluster vector a. (Note: a cluster vector is a vector that contains the pointers ci). • Suppose the k-means algorithm finds 2 clusters for matrix B and produces a cluster vector b. • Suppose that in both cases, the k-means algorithm actually succeeds in optimizing the objective function. The examples that you create below should be drawn by hand without using R. Choose examples so that it is easy for a human to determine unique clusters. (a) Give an example (with actual numeric entries) in M where the cluster vectors a and b are the same. State the actual cluster vectors and draw plots to illustrate. (b) Give an example (with actual numeric entries) in M where the cluster vectors a and b differ in just one entry. State the actual cluster vectors and draw plots to illustrate. (c) Give an example (with actual numeric entries) in M where the clusters found from A differ significantly than the clusters found from B. (Note that just interchanging cluster names 1 and 2 in the cluster vectors does not actually alter the points in each cluster.) State the actual cluster vectors and draw plots to illustrate. (d) For the example you gave in part (c), draw a plot of the data in A labeled or colored based on the cluster vector b. Also draw a plot of the data in B with the the points labeled or colored based on the cluster vector a. (e) For the example you gave in part (c), and looking at the picture you made in part (d), do either of the cluster vectors a or b actually succeed in providing meaningful clusters of the data? Explain Show transcribed image text 3. Suppose M is an 10 x 3 matrix. Let A be the matrix consisting of the second and third columns of M and let B be the matrix consisting of the first and second columns of M. • Suppose the k-means algorithm finds 2 clusters for matrix A and produces a cluster vector a. (Note: a cluster vector is a vector that contains the pointers ci). • Suppose the k-means algorithm finds 2 clusters for matrix B and produces a cluster vector b. • Suppose that in both cases, the k-means algorithm actually succeeds in optimizing the objective function. The examples that you create below should be drawn by hand without using R. Choose examples so that it is easy for a human to determine unique clusters. (a) Give an example (with actual numeric entries) in M where the cluster vectors a and b are the same. State the actual cluster vectors and draw plots to illustrate. (b) Give an example (with actual numeric entries) in M where the cluster vectors a and b differ in just one entry. State the actual cluster vectors and draw plots to illustrate. (c) Give an example (with actual numeric entries) in M where the clusters found from A differ significantly than the clusters found from B. (Note that just interchanging cluster names 1 and 2 in the cluster vectors does not actually alter the points in each cluster.) State the actual cluster vectors and draw plots to illustrate. (d) For the example you gave in part (c), draw a plot of the data in A labeled or colored based on the cluster vector b. Also draw a plot of the data in B with the the points labeled or colored based on the cluster vector a. (e) For the example you gave in part (c), and looking at the picture you made in part (d), do either of the cluster vectors a or b actually succeed in providing meaningful clusters of the data? Explain
Expert Answer
Answer to 3. Suppose M is an 10 x 3 matrix. Let A be the matrix consisting of the second and third columns of M and let B be the m…
OR