4. Apply the K-means algorithm to cluster the points in one dimension 10, 20, 22, 26, 32, 40, 54 into 2 clusters where the initial centers are 16 and 30. Tabulate your results in a table like the one below but give justification for each entry. Iterate until you have 2 consecutive iterations where the means do not change. Cluster 2 Points Mean Midpoint Cluster 1 Iter. # Points Mean

4. Apply the K-means algorithm to cluster the points in one dimension 10, 20, 22, 26, 32, 40, 54 into 2 clusters where the initial centers are 16 and 30. Tabulate your results in a table like the one below but give justification for each entry. Iterate until you have 2 consecutive iterations where the means do not change. Cluster 2 Points Mean Midpoint Cluster 1 Iter. # Points Mean

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Given a set of three points, -2, 0, and 9, we want to use k- Means Clustering with k = 2 to cluster them into two clusters. If the initial cluster centers are C1 = -4.0 and C2 = 2.0, What will be the center of C1 after completing first iteration of k means clustering algorithm? Answer:
Correct answer will be upvoted else downvoted. You are given two integer clusters an and b of length n. You can switch all things considered one subarray (constant subsegment) of the cluster a. Your errand is to opposite such a subarray that the total ∑i=1nai⋅bi is amplified. Input :The principal line contains one integer n (1≤n≤5000). The subsequent line contains n integers a1,a2,… ,an (1≤ai≤107). The third line contains n integers b1,b2,… ,bn (1≤bi≤107). Output :Print single integer — greatest conceivable total subsequent to switching all things considered one subarray (persistent subsegment) of a.
We are going to use K-means algorithm to cluster 6 data points from dataset D = {0, 1, 2, 3, 4, 2022} in R1 into 2 clusters. Before the first iteration, the cluster centers are randomly initialized at c1 = 0.235 and c2 = 1.984. Next, we simulate the first iteration (for part (a) and (b)) of K-means with manual computation. (a) Compute the cluster assignment for each of the 6 data points given, using the Euclidean distance. [5 pts] (b) Compute the updated cluster center c1 and c2. [5 pts] (c) How many iterations are needed to finish the K-means algorithm for this problem? [10 pts]
Assume, you want to cluster 8 observations into 3 clusters using K-Means clustering algorithm. After the first iteration clusters C1, C2, C3 have the following observations: C1: {(2,3), (4,3), (6,6)} C2: {(0,4), (4,0)} C3: {(5,5),(7,7), (9,9)} What will be the Euclidean distance for observation (9, 9) from cluster centroid C1 in the second iteration?
K-means clustering is run on some data, for a few different values of K. Shown is the plot obtained for the inertia (a measure of average distance of points from the centroid of their allocated cluster), versus the number of clusters. What is the implied natural number of clusters to use? Inertia O 2000 1750 1500 1250 1000 750 500 250 T 9 3 1 -2 3 4 5 6 Number of clusters 7 .8 9
Suppose we cluster a set of N data points using two different using the k-means clusteringalgorithm runs but with different number of initial clusters centres.Run 1: 4 initial cluster centres - (a,b), (c,d), (e,f) and (g,h).Run 2: 2 initial cluster centres - (a,b), (c,d)Run 3: 3 initial cluster centres - ((a,b), (c,d), (e,f).Would the clusters created using Run 3 be similar to the 2 or 4 initial cluster runs? Explainyour answer briefly
Suppose we cluster a set of N data points using two different using the k-means clusteringalgorithm runs but with different number of initial clusters centres.Run 1: 4 initial cluster centres - (a,b), (c,d), (e,f) and (g,h). Run 2: 2 initial cluster centres - (a,b), (c,d) Run 3: 3 initial cluster centres - ((a,b), (c,d), (e,f). Would the clusters created using Run 3 be similar to the 2 or 4 initial cluster runs? Explainyour answer briefly.
Consider a set of data points {(7, 30, 27), (11, 26, 22), (11, 34, 26), (15, 30, 27), (14, 17, 22), (27, 32, 30)}. Use the k-means clustering procedure with k = 3 to group these data points. Start with the three initial cluster centers: (-6, 9, 5), (-2, 13, 10), (10, 15, 13). Show your working for 2 iterations. Use D = √(xi-yi)2 for distance calculation.
Question 1 In the previous example, the K-Means algorithm was able to accurately find the three initial clusters. However, changing the starting centers for K-Means can change the final clusters that K-Means gives us. Change the initial centers to the points [0, 1] , [1, 1] , and [2, 2] ; and fit a cluster.KMeans object called kmeans_q1 on the toy dataset from the previous example. Keep the random_state parameter as 42 and the n_clusters parameter as 3. Hint: You will need to change the init and n_init parameters in cluster.KMeans . 1: kmeans_q1 = ]: grader.check("q1")
Consider a set of data points {(-10,13), (-6,9), (-6,17), (-2,13), (-3,0)}. Use the k-means clustering procedure with k = 3 to groups these data points. Start with the three initial cluster centers: (-6,9), (-2,13), (10,15). Show your working for 3 iterations. Use D= for distance calculation.
Use Bellman-Ford algorithm to find the shortest path from s to every other vertex. The given order of the edges is (8, r), (r, q), (p, q), (p, t), (t, s), (t, r), (t, q), (r, p). Draw the table to indicate the updates, i.e., distance and predecessor, during each iteration. r 3 b 4 9
True or False: When we use k means clustering method to find the best clusters for the chosen k, sometimes we can get stuck at the local minimum, the solution to this issue is to try multiple different initial centroids and use the result with the smallest total within cluster variance for the chosen k.