In this assignment, you will use Python's sklearn.cluster package and three of its tools called "KMeans", "DBSCAN", and "AgglomerativeClustering" to apply three main clustering methods k$-$means, density$-$based, and hierarchical methods on different toy datasets of Python SKLearn $($see here for more detail $).$ You can watch the video illustrating some of the Python tools that you need for this assignment:

Part $1$: k$-$means clustering $(25$ points$)$:

Load breast cancer dataset $($by calling sklearn.datasets.load$\_$breast$\_$cancer$)$

data $=$ load$\_$breast$\_$cancer$().$data

Since the dataset has $30$ different features, use the following code to reduce the dimensions of the dataset to $2$ features $($as we will later plot the observations using $2$D scatter plots, this is a necessary step!$)$:

from sklearn.decomposition import PCA

pca $=$ PCA$(2)$

df $=$ pca.fit$\_$transform$($data$)$

Create an object of sklearn.cluster.KMeans class with n$\_$clusters $=10.$

kmeans $=$ KMeans$($n$\_$clusters $=10)$

Fit and predict the transformed dataset df:

label $=$ kmeans.fit$\_$predict$($df$)$

Use matplotlib.pyplot to plot all the observations on a $2$D coordinate system. Color observations of each cluster with a different color:

import matplotlib.pyplot as plt

for i in range$(10)$:

plt$.$scatter$($df label $==i,1,$ label $=$ i$)$

plt$.$legend$()$

plt$.$show$()$

Part $2(25$ points$)$: Repeat Part I for digits dataset $($use load$\_$digits$)$ instead$).$ Use density$-$based clustering $($use DBSCAN$($min$\_$samples $=10,$ eps $=1\mathrm{.}5)$ instead of clusters $($:$=10\}.$ Draw the plot for labels $0,1,2,...,22$

Part $3(25$ points$)$: Repeat Part I for iris dataset $($use load$\_$iris$()$ instead$).$ Use hierarchical clustering with $5$ clusters $($use AgglomerativeClustering$($n$\_$clusters $=5)$ instead of KMeans$($n$\_$clusters $=10))$

Part points$)$ Repeat Parts $1$ and $3$ for n$\_$clusters $=20$ and digits dataset.

Deliverables

Submit a zip file containing your Python code and a "report.pdf$"$ depicting all the plots drawn in the four parts and a paragraph comparing the three methods under different circumstances.