Suppose that the data mining task is to cluster points into two clusters, where the points are 2, 3, 4, 10, 11, 12, 20, 25, 30. The distance function is the Euclidian distance. Suppose initially we assign 4 and 12 as the center of each cluster, respectively. Use k-means algorithm to find final clusters and its centroids after convergence.

Suppose that the data mining task is to cluster points into two clusters, where the points are 2, 3, 4, 10, 11, 12, 20, 25, 30. The distance function is the Euclidian distance. Suppose initially we assign 4 and 12 as the center of each cluster, respectively. Use k-means algorithm to find final clusters and its centroids after convergence.

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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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]
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:
The procedure of evaluating the results of a clustering algorithm is known under the termcluster validity. In general terms, there are two approaches to investigate cluster validity Internal and External criteria. Both DB (Davies-Bouldin) and Silhouette Coefficient are internal criteria. Which one is NOT correct about these two criteria? Group of answer choices The minimum DB score is zero, with lower values indicating better clustering. DB is a measure of how similar an object is to its own cluster (cohesion) compared to other clusters (separation). The best value of Silhouette is 1 and the worst value is -1 No answer text provided.
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.
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.
Suppose there are six cities in a state. The distance matrix between each pair of the cities is given below. What is the dendrogram generated by hierarchical clustering with single-linkage? A В D E F A 60 120 185 260 300 60 90 210 258 320 120 185 90 140 179 200 210 132 140 179 125 E 260 258 125 135 300 320 200 132 135 Based on the resulting dendrogram, if we want to create 4 clusters, they are Cluster Number Items 1
Given an unlabeled dataset {x(1), ... , x(m)}. The K-mean algorithm has been run with 40 different random initializations, and 40 different clusterings of the data have been obtained. Describe how we should use Ex(1) – µ01² to choose the best m clustering.
Suppose that you need to group some data into clusters, and you run K-means 100 times, starting each time from a different random initialisation. You get 100 different clusterings of the data. Which one should you choose? Simply pick one at random. Choose the one that minimises the mean distance of points from the centroid of their allocated cluster. Label the clusters 1, 2, ..., Choose the clustering you get from the 100th run. k each time, and assign each point to the cluster it ends up in most often.
Apply the Fuzzy C Mean Clustering on the given data points. Consider the number of clusters is 2. Determine the number of data points in each cluster separately whose membership value is greater than 0.5. Given Data points A(3, 3) B( 4, 3) C (2, 2 ) D( 4 ,2 ) E(3, 2)
Consider a set of data points {(-10, 13), (-6, 9), (-6, 17), (-2, 13), (-3, 0)}. Add last two digits of your registration with each given value such as. If last two digit of your registration number is 14 then First point will be (-10+14, 13+14) = (4, 27). Use the k-means clustering procedure with k = 2 to groups these data points. Start with the three initial cluster centers: (-6,9), (-2,13), (10,15). Show your working for 2 iterations. Use D=√(xi-yi)*2 for distance calculation.
Let D be a dataset of two-dimensional points to be partitioned into 5 clusters. After applying two different centroid-based partitioning algorithms, two different partitions of 5 clusters are obtained, P1 and P2 (that is, P1 consists of 5 clusters and P2 consists of 5 clusters). Let E, and E2 be the within-cluster sum of squares of P1 and P2, respectively. If E1 = 25.52 and E2 = 56.80, which one would you consider being of a better quality, P1 or P2? Enter 1 if P1 is your choice, 2 if it is P2.