Suppose M is a 10 3 matrix (i.e., M R03). Let A be the matrix consisting...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Suppose M is a 10 3 matrix (i.e., M R03). Let A be the matrix consisting of the first and second columns of M and let B be the matrix consisting of the first and third 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 c.) Suppose the k-means algorithm finds 2 clusters for matrix B and produces 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) Create an example (with actual numeric entries) in M where the cluster vectors a and b are the same. State the actual cluster vectors a and b and draw plots to illustrate. (b) Create an example (with actual numeric entries) in M where the clusters found from A differ significantly with the clusters found from B. (Note that just interchanging cluster names in the cluster vectors does not actually alter the points in each cluster.) State the actual cluster vectors a and b and draw plots to illustrate. (c) For the example you gave in part (b), draw a plot of the data in matrix A labeled or colored based on the cluster vector b. Also draw a plot of the data in matrix B with the points labeled or colored on the cluster vector a. (d) For the example you gave in part (b), and looking at the picture you made in part (c), do either of the cluster vectors a or b actually succeed in providing meaningful clusters of the data in matrix M? Explain your reasoning. Suppose M is a 10 3 matrix (i.e., M R03). Let A be the matrix consisting of the first and second columns of M and let B be the matrix consisting of the first and third 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 c.) Suppose the k-means algorithm finds 2 clusters for matrix B and produces 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) Create an example (with actual numeric entries) in M where the cluster vectors a and b are the same. State the actual cluster vectors a and b and draw plots to illustrate. (b) Create an example (with actual numeric entries) in M where the clusters found from A differ significantly with the clusters found from B. (Note that just interchanging cluster names in the cluster vectors does not actually alter the points in each cluster.) State the actual cluster vectors a and b and draw plots to illustrate. (c) For the example you gave in part (b), draw a plot of the data in matrix A labeled or colored based on the cluster vector b. Also draw a plot of the data in matrix B with the points labeled or colored on the cluster vector a. (d) For the example you gave in part (b), and looking at the picture you made in part (c), do either of the cluster vectors a or b actually succeed in providing meaningful clusters of the data in matrix M? Explain your reasoning.
Expert Answer:
Related Book For
Posted Date:
Students also viewed these algorithms questions
-
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
-
QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...
-
Assume that 3-month Treasury bills totaling $23 billion were sold in $10,000 denominations at a discount rate of 5.200%. In addition, the Treasury Department sold 6-month bills totaling $21 billion...
-
In January 2016, Sayers Manufacturing incurred the following costs in manufacturing Detecto, its only product: An analysis of the accounting records showed the following balances in the inventory...
-
A square loop of wire (side a) lies on a table, a distance s from a very long straight wire, which carries a current I, as shown in Fig. 7.17. (a) Find the flux of B through the loop. (b) If someone...
-
Identify five documents cohabitants might execute in order to protect and provide for each other and define their respective rights and responsibilities.
-
Spiller Corp. plans to issue 10%, 15-year, $500,000 par value bonds payable that pay interest semiannually on June 30 and December 31. The bonds are dated December 31, 2008, and are issued on that...
-
ACTUAL $ 750,000 Big Boats, Inc. makes laury speed boats for water sking Actual results and the static budge Sales commissions are computed at 5% of gross sales The expected ROI for this subsidiary...
-
American Dream, is a retail and entertainment complex located in the Meadowlands Sports Complex in Rutherford, NJ. The mega-sized mall opened only a few months prior to the start of COVID in the...
-
Directions: Analyze each of the following arguments in terms of new case, comparison cases, known similarities, and inferred similarity. Then indicate what seems to you the most significant relevant...
-
State the domain, then divide. 4x5 7x7 5 8
-
What are the psychological mechanisms underlying the desire for power, and how do they manifest in interpersonal relationships, organizational dynamics, and political behavior?
-
How do individuals and groups acquire, wield, and contest power within various institutional and interpersonal settings, and what are the ethical implications of different forms of power utilization ?
-
Compare & contrast AD vs AS management policies. State the assumptions of the 4th generation Keynesian model and explain how its endogenous variables are determined. Compare & contrast anticipated vs...
-
How can theories of power inform strategies for promoting social justice, equity, and democratization, and what are the practical implications of these theoretical insights for political activism and...
-
The cost - allocation base used for the fixed overhead rate should be O A. underestimated due to the conservatism principle O B. overestimated due to the conservatism principle OC. the most plausible...
-
Determine the optimal use of Applichem's plant capacity using the Solver in Excel.
-
Solve the following initial value problems: (a) du/dt = 5u, u(0) = -3, (b) du/dt = 2u, u(1) = 3. (c) du/dt = -3m, m(-1) = 1.
-
Decompose the following matrices into a product of elementary matrices. Then interpret each of the factors as a linear transformation. 11 101 -110 011 241 122 12 9 31
-
(a) Prove that the commutator of two upper triangular matrices is upper triangular. (b) Prove that the commutator of two skew symmetric matrices is skew symmetric. (c) Is the commutator of two...
-
Compare the full sets of public service announcements (PSAs) represented by Figures 7.11, 7.12, and 7.13 by visiting http://city.milwaukee.gov/health/Safe-Sleep-Campaign. Which set is most effective?...
-
Ask someone to follow a set of instructions or to fill out a form. As an alternative, you also might test a document youve created for a course. You also may try ordering food from a website, such as...
-
In a pair or in small groups, find three online shopping sites that sell similar types of merchandise (e.g., Backcountry.com, Moosejaw.com, REI.com). Consider the following questions: Who are the...
Study smarter with the SolutionInn App