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2. Given the following data points in 1D (shown in red): x₁ = 2, x₂ = 4,x3 = 5, X4 = 8, x5 = 10, x6 = 12, answer the following questions. 0 2 6 10 = 12 14 4 and C2₂ (a) Start from initial cluster centers c₁ = 10, perform k-means clustering algorithm for k = 2 on the red points. Show your steps for all iterations: (i) the cluster assignments y₁, ···‚ Y6; (ii) the updated cluster centers at the end of that iteration. (b) How many iterations does it take for k-means algorithm to converge (i.e., number of iterations includes all iterations you perform to find convergence)? What is the reconstruction error (i.e., distortion measure J, equation 9.1 of the Bishop's textbook) at the end of that iteration? (c) Use the clustering assignments to classify the red data points into two classes, the one with the smaller mean as C1 and the other as C2. Then, write down the label of the new data point x = 6.9 (shown by the cyan point in the figure) with k-nearest neighbor estimator when k = 1. Briefly explain the reason.

2. Given the following data points in 1D (shown in red): x₁ = 2, x₂ = 4,x3 = 5, X4 = 8, x5 = 10, x6 = 12, answer the following questions. 0 2 6 10 = 12 14 4 and C2₂ (a) Start from initial cluster centers c₁ = 10, perform k-means clustering algorithm for k = 2 on the red points. Show your steps for all iterations: (i) the cluster assignments y₁, ···‚ Y6; (ii) the updated cluster centers at the end of that iteration. (b) How many iterations does it take for k-means algorithm to converge (i.e., number of iterations includes all iterations you perform to find convergence)? What is the reconstruction error (i.e., distortion measure J, equation 9.1 of the Bishop's textbook) at the end of that iteration? (c) Use the clustering assignments to classify the red data points into two classes, the one with the smaller mean as C1 and the other as C2. Then, write down the label of the new data point x = 6.9 (shown by the cyan point in the figure) with k-nearest neighbor estimator when k = 1. Briefly explain the reason.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Name+Email ID 2. Given the following data points in 1D (shown in red): x₁ = 2, x2 = 4, x3 = 5, x4 = 8, x5 = 10, x6 = 12, answer the following questions. 0 2 4 6 8 10 12 14 4 and C₂ = (a) Start from initial cluster centers c₁ 10, perform k-means clustering algorithm for k = 2 on the red points. Show your steps for all iterations: (i) the cluster assignments Y₁, ···, Y6; (ii) the updated cluster centers at the end of that iteration. (b) How many iterations does it take for k-means algorithm to converge (i.e., number of iterations includes all iterations you perform to find convergence)? What is the reconstruction error (i.e., distortion measure J, equation 9.1 of the Bishop's textbook) at the end of that iteration? Page 2 (c) Use the clustering assignments to classify the red data points into two classes, the one with the smaller mean as C1 and the other as C2. Then, write down the label of the new data point x = 6.9 (shown by the cyan point in the figure) with k-nearest neighbor estimator when k = 1. Briefly explain the reason. (d) Write down the label of the new data point x with k-nearest neighbor estimator when k = 5. Briefly explain the reason.
Transcribed Image Text:Name+Email ID 2. Given the following data points in 1D (shown in red): x₁ = 2, x2 = 4, x3 = 5, x4 = 8, x5 = 10, x6 = 12, answer the following questions. 0 2 4 6 8 10 12 14 4 and C₂ = (a) Start from initial cluster centers c₁ 10, perform k-means clustering algorithm for k = 2 on the red points. Show your steps for all iterations: (i) the cluster assignments Y₁, ···, Y6; (ii) the updated cluster centers at the end of that iteration. (b) How many iterations does it take for k-means algorithm to converge (i.e., number of iterations includes all iterations you perform to find convergence)? What is the reconstruction error (i.e., distortion measure J, equation 9.1 of the Bishop's textbook) at the end of that iteration? Page 2 (c) Use the clustering assignments to classify the red data points into two classes, the one with the smaller mean as C1 and the other as C2. Then, write down the label of the new data point x = 6.9 (shown by the cyan point in the figure) with k-nearest neighbor estimator when k = 1. Briefly explain the reason. (d) Write down the label of the new data point x with k-nearest neighbor estimator when k = 5. Briefly explain the reason.
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