2. There are 6 different datasets noted as A,B,C,D,E,F. Each dataset is clustered using two different methods, and one of them is K-means. All results are shown in Figure 2. Please determine which results more likely to be generated by K-means method. (Hint: check the state when K-means converges; Centers for each cluster have been noted as X; Since x and y axis are scaled proportionally, you can determine the distance to centers geometrically). The distance measure used here is the Euclidean distance. A1 C1 Application of k-means E1 A2 C2 E2 B1 D1 F1 Figure 2: Clustered Results for 6 datasets Dataset A (write A1 or A2, same in the following question); Dataset B Dataset C Dataset D Dataset E Dataset F B2 D2 F2

2. There are 6 different datasets noted as A,B,C,D,E,F. Each dataset is clustered using two different methods, and one of them is K-means. All results are shown in Figure 2. Please determine which results more likely to be generated by K-means method. (Hint: check the state when K-means converges; Centers for each cluster have been noted as X; Since x and y axis are scaled proportionally, you can determine the distance to centers geometrically). The distance measure used here is the Euclidean distance. A1 C1 Application of k-means E1 A2 C2 E2 B1 D1 F1 Figure 2: Clustered Results for 6 datasets Dataset A (write A1 or A2, same in the following question); Dataset B Dataset C Dataset D Dataset E Dataset F B2 D2 F2

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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Use the mtcars dataset, provided by base R to plot 3 scatter plots in the same graph. The three pairs of data are (mpg, drat), (mpg, wt), (mpg, qsec). You can start with the main plot using plot function (mpg, drat, ...), then add/superimpose the other two plots by points() as follows: 1 plot(mpg, drat, ...) points(mpg, wt, ...) points(mpg, qsec, ...) Make sure the final graph will contain all the data points - you need to set the two arguments xlim and ylim in the plot() function. Use color argument for each pair of data.
2. In this problem, you will perform K-means clustering manually, with K = 2, on a small example with n = 6 observations and p = 2 features. The observations are as follows. (a) Plot the observations. (b) Randomly assign a cluster label to each observation. You can use the np.random.choice() function to do this. Report the cluster labels for each observation.
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
4. The data-set X given below contains results of a vaccine trial. The data set contains a measure of various antibodies developed for both the real vaccine shot and placebo shot for six individuals. Perform k- means clustering for 2 iterations and tabulate mean values and the distortion measures in each iterations. (1.4889 2.0347 1.7269 -4.1116 -6.1471 -6.0689) X = 0.6966 1.2939 0.2127 -5.8095 -7.9443 -3.5616/ Assume that there are two clusters and the initial guess of each cluster means are (-2.5) and -2.5 (0.50 0.50
Apply k-means to cluster 6 data points (1, 3), (2, 2), (2, 5), (3, 2), (4, 2), and (4, 3) to 2 clusters. Use the initial centroids (2, 2) and (2, 5). Show your work of computing the distances (Euclidean distance) and centroid updates in each iteration of k-means.
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.
Using scilab, use the Matrix A of the state-space representation and generate a Routh table of the given matrix. The function should look like: function [routhtable] = RouthHurwitz (A) Hint: You can use the routh t command. R(s) 1000 5³+ 105² +31s + 1030 C(s)
Classify the 1’s, 2’s, 3’s for the zip code data in R. (a) Use the k-nearest neighbor classiﬁcation with k = 1, 3, 5, 7, 15. Report both the training and test errors for each choice. (b) Implement the LDA method and report its training and testing errors. Note: Before carrying out the LDA analysis, consider deleting variable 16 ﬁrst from the data, since it takes constant values and may cause the singularity of the covariance matrix. In general, a constant variable does not have a discriminating power to separate two classes.
■ Write out the truth tables for a. p^ (pv q) b. (qr) (pvq) ^
For the multivariate GMM algorithm, the initial means for the Gaussian components are selected randomly by picking one of the data items to be the mean of a category. Now, set the initial clusters to be the same class for the Iris dataset in your implementation and show the resulting clustering.
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.
Find as many situations as you can where the result of K-means clustering is affected by the initial position of the centres. Find the fewest number of points and clusters when K-means clustering does not work.