You are given the dataset minerals.csv which contains data about the height, width, density,

compactness and texture of some mineral stones. You are going to apply cluster analysis on this

dataset.

a$.$ Apply the 'elbow' method to guess to proper number of clusters.

b$.$ Apply $k-$means with the value of $k$ found in part $A$

c$.$ Visualize the results through a scatter plot

d$.$ Visualize the results through a heatmap

e$.$ As known, the generated labels in clustering are symbolic $(0,1,2,$dots$)$ So$,$ for example

labels $1,1,0,0,1,2,2,0$ and labels $0,0,2,2,0,1,1,2$ represent the same clustering.

Write a function which adjusts the labels list, so that the fist appearing label $($in the list$)$

is $0,$ then the next appearing label is $1,$ then $2$ and so on$.$ For example both mentioned

cases would be adjusted as: $0,0,1,1,0,2,2,1$

f$.$ Write a function which takes as input two lists of clustering labels and determines

whether they are identical.