Question

1. Implement the K-means algorithm using these two as a reference.

274 14 Unsupervised Lnn Fig. 14.1 A two-dimensional domain with clusters of examples weight bot

2.Use Matlab’s implementation of kmeans to check your results on the fisheriris dataset (https://www.mathworks.com/help/stats/kmeans.html)

a. The fisheriris dataset is built into Matlab, and you can load it using ‘load fisheriris’.

b. Please note the labels are available for the dataset, so you can check the performance of the kmeans algorithm on the dataset.

Answer 1

k-means clustering  :

Then plot the cluster regions.

Load Fisher's iris data set. Use the petal lengths and widths as predictors.

load fisher iris
X = meas(:,3:4);
plot(X(:,1),X(:,2),'k*','MATH SIZE',5);
title 'Fisher''s Iris Data';
X label Petal Lengths (cm); 
Y label Petal Widths (cm);

Fisher's Iris Data 2.5 1.5 0.5 4 5 6 Petal Lengths (cm)

The larger cluster to be split into a lower variance region and a higher variance region. This might indicate that the larger cluster is two overlapping clusters.

Cluster k=3

k means (X,3);

1.   k-means++ algorithm for centroid initialization
2. squared Euclidean distance
3. Local by setting the 'Replicates' name-value pair argument.

4. means displays a warning stating that the algorithm did not converge, which you should expect since the software only implemented one iteration.

   Plot the cluster regions.

5. gs catter(X Grid(:,1),X Grid(:,2),

6. id x2 Region,... [0,0.75,0.75;0.75,0,0.75;0.75,0.75,0],'..');

7. k*('Marker Size',5);

8. title 'Fisher''s Iris Data'; X label Petal Lengths (cm);

9. Y label Petal Widths (cm);

10. legend('Region 1','Region 2','Region 3','Data','Location','South East')

    Fisher's Iris Data 2.5 米米米 Ho 1.5 Region 1 Region 2 Region 3 0.5 Data 4 6 Petal Lengths (cm)

11. randomly generate the sample data.

12. % For reproducibility X = randn(100,2)*0.75+ones(100,2);

13. randn(100,2)*0.5-ones(100,2)]; plot(X(:,1),X(:,2),'.');

    

    Randomly Generated Data 4 -2 -2 4

14. plot(X(i dx==1,1),X(i dx==1,2),'r.','Marker Size',12)
    hold on
    plot(X(idx==2,1),X(idx==2,2),'b.','Marker Size',12)
    plot(C(:,1),C(:,2),'kx',...
         'Marker Size',15,'Line Width',3) 
    legend('Cluster 1','Cluster 2','Centroid',...
           'Location','NW')
    }