15. Clustering

import matplotlib.pyplot as plt
import numpy as np
import itertools
import seaborn as sns
import pandas as pd
from sklearn import datasets
from sklearn.cluster import KMeans
from sklearn import metrics
import string
import itertools as it

%matplotlib inline

C = 4
N = 200
offset = 2
spacing = 2

# choose the first C uppcase letters using the builtin string class
classes = list(string.ascii_uppercase[:C])
# get the number of grid locations needed
G = int(np.ceil(np.sqrt(C)))
# get the locations for each axis
grid_locs = a = np.linspace(offset,offset+G*spacing,G)
# compute grid (i,j) for each combination of values above & keep C values
means = [(i,j) for i, j in it.product(grid_locs,grid_locs)][:C]
# store in dictionary with class labels
mu = {c: i for c, i in zip(classes,means)}
# random variances
sigma = {c: i*.5 for c, i in zip(classes,np.random.random(4))}

#randomly choose a class for each point, with equal probability
clusters_true = np.random.choice(classes,N)
# draw a randome point according to the means from above for each point
data = [np.random.multivariate_normal(mu[c],.25*np.eye(2)) for c in clusters_true]
# rounding to make display neater later
df = pd.DataFrame(data = data,columns = ['x' + str(i) for i in range(2)]).round(2)

# store in dataFram
df['true_cluster'] = clusters_true

sns.pairplot(data =df, hue='true_cluster')

<seaborn.axisgrid.PairGrid at 0x7ff8cc3089d0>

sns.pairplot(data =df)

<seaborn.axisgrid.PairGrid at 0x7ff8a23fb9d0>

data_cols =['x0','x1']

K = 4
mu = df[data_cols].sample(n=K).values
mu

array([[5.95, 1.66],
       [6.13, 5.64],
       [2.42, 5.99],
       [2.17, 5.71]])

def mu_to_df(mu,i):
    mu_df = pd.DataFrame(mu,columns=['x0','x1'])
    mu_df['iteration'] = str(i)
    mu_df['class'] = ['M'+str(i) for i in range(K)]
    mu_df['type'] = 'mu'
    return mu_df

cmap_pt = sns.color_palette('tab20',8)[1::2]
cmap_mu = sns.color_palette('tab20',8)[0::2]

sns.color_palette('tab20',8)

df[data_cols].head(1)

	x0	x1
0	2.5	1.6

mu[0]

array([5.95, 1.66])

df['1']= pd.concat([((df[data_cols]-mu_i)**2).sum(axis=1) for mu_i in mu],axis=1).idxmin(axis=1)

sfig = sns.scatterplot(data=df, x='x0',y='x1', palette=cmap_pt, hue='1')
mu_df = mu_to_df(mu,1)
sns.scatterplot(data =mu_df,x='x0',y='x1',hue='class',palette=cmap_mu,ax=sfig,legend=False)

<Axes: xlabel='x0', ylabel='x1'>

df.head()

	x0	x1	true_cluster	1
0	2.50	1.60	A	0
1	6.03	2.60	C	0
2	2.30	6.06	B	2
3	7.25	5.80	D	1
4	1.20	2.01	A	3

mu = df.groupby('1')[data_cols].mean().values

sfig = sns.scatterplot(data=df, x='x0',y='x1', palette=cmap_pt, hue='1')
mu_df = mu_to_df(mu,2)
sns.scatterplot(data =mu_df,x='x0',y='x1',hue='class',palette=cmap_mu,ax=sfig,legend=False)

<Axes: xlabel='x0', ylabel='x1'>

Now we can update the assignments again

df['2'] = pd.concat([((df[data_cols]-mu_i)**2).sum(axis=1) for mu_i in mu],axis=1).idxmin(axis=1)

sfig = sns.scatterplot(data=df, x='x0',y='x1', palette=cmap_pt, hue='2')
mu_df = mu_to_df(mu,2)
sns.scatterplot(data =mu_df,x='x0',y='x1',hue='class',palette=cmap_mu,ax=sfig,legend=False)

<Axes: xlabel='x0', ylabel='x1'>

df.head()

	x0	x1	true_cluster	1	2
0	2.50	1.60	A	0	0
1	6.03	2.60	C	0	0
2	2.30	6.06	B	2	2
3	7.25	5.80	D	1	1
4	1.20	2.01	A	3	3

i = 2
mu_list = [mu_to_df(mu,1),mu_to_df(mu,i)]
cur_old = str(i-1)
cur_new = str(i)
while sum(df[cur_old] !=df[cur_new]) >0:
    cur_old = cur_new
    i +=1
    cur_new = str(i)
    #     update the means and plot with current generating assignments
    mu = df.groupby(cur_old)[data_cols].mean().values
    mu_df = mu_to_df(mu,i)
    mu_list.append(mu_df)
    fig = plt.figure()
    sfig = sns.scatterplot(data =df,x='x0',y='x1',hue=cur_old,palette=cmap_pt,legend=False)
    sns.scatterplot(data =mu_df,x='x0',y='x1',hue='class',palette=cmap_mu,ax=sfig,legend=False)
    file_num = str(i*2 -1).zfill(2)
    sfig.get_figure().savefig('kmeans' +file_num + '.png')
    #     update the assigments and plot with the associated means
    df[cur_new] = pd.concat([((df[data_cols]-mu_i)**2).sum(axis=1) for mu_i in mu],axis=1).idxmin(axis=1)

    fig = plt.figure()
    sfig = sns.scatterplot(data =df,x='x0',y='x1',hue=cur_new,palette=cmap_pt,legend=False)
    sns.scatterplot(data =mu_df,x='x0',y='x1',hue='class',palette=cmap_mu,ax=sfig,legend=False)
#     plt.plot(mu[:,0],mu[:,1],marker='s',linewidth=0)

    file_num = str(i*2).zfill(2)
    sfig.get_figure().savefig('kmeans' +file_num + '.png')

n_iter = i

df

	x0	x1	true_cluster	1	2	3	4
0	2.50	1.60	A	0	0	3	3
1	6.03	2.60	C	0	0	0	0
2	2.30	6.06	B	2	2	2	2
3	7.25	5.80	D	1	1	1	1
4	1.20	2.01	A	3	3	3	3
...	...	...	...	...	...	...	...
195	2.44	5.25	B	3	2	2	2
196	5.64	2.43	C	0	0	0	0
197	5.01	4.22	D	1	1	1	1
198	1.62	1.73	A	3	3	3	3
199	6.20	6.70	D	1	1	1	1

200 rows × 7 columns

16. Evaluating Clustering Solutions

km4 = KMeans(n_clusters=4)

df['km_clusters'] = km4.fit_predict(df[data_cols])

/opt/hostedtoolcache/Python/3.8.16/x64/lib/python3.8/site-packages/sklearn/cluster/_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning
  warnings.warn(

sns.pairplot(data=df,vars=data_cols,hue='km_clusters',palette=cmap_pt)

<seaborn.axisgrid.PairGrid at 0x7ff89ad2d850>

metrics.silhouette_score(df[data_cols],df['km_clusters'])

0.756216924296399

metrics.silhouette_score(df[data_cols],df['true_cluster'])

0.756216924296399

metrics.silhouette_score(df[data_cols],df['1'])

0.29750816193050483

metrics.silhouette_score(df[data_cols],df['2'])

0.571043759335564

df.head()

	x0	x1	true_cluster	1	2	3	4	km_clusters
0	2.50	1.60	A	0	0	3	3	1
1	6.03	2.60	C	0	0	0	0	3
2	2.30	6.06	B	2	2	2	2	2
3	7.25	5.80	D	1	1	1	1	0
4	1.20	2.01	A	3	3	3	3	1

metrics.adjusted_mutual_info_score(df['true_cluster'],df['km_clusters'])

1.0000000000000002

metrics.adjusted_mutual_info_score(df['true_cluster'],df['1'])

0.6907774497207733

metrics.adjusted_mutual_info_score(df['true_cluster'],df['2'])

0.8029652452987396