#importation
import os
os.chdir("C:/Users/ricco/Desktop/demo")

import pandas
iris = pandas.read_excel("iris_for_measures_clustering.xlsx")
iris.head()

	SepalLength	SepalWidth	PetalLength	PetalWidth	Species
0	5.1	3.5	1.4	0.2	setosa
1	4.9	3.0	1.4	0.2	setosa
2	4.7	3.2	1.3	0.2	setosa
3	4.6	3.1	1.5	0.2	setosa
4	5.0	3.6	1.4	0.2	setosa

#distribution des "vraies" classes
iris.Species.value_counts()

setosa        50
versicolor    50
virginica     50
Name: Species, dtype: int64

#X - variables actives
X = iris[iris.columns[:-1]]
X.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 150 entries, 0 to 149
Data columns (total 4 columns):
 #   Column       Non-Null Count  Dtype  
---  ------       --------------  -----  
 0   SepalLength  150 non-null    float64
 1   SepalWidth   150 non-null    float64
 2   PetalLength  150 non-null    float64
 3   PetalWidth   150 non-null    float64
dtypes: float64(4)
memory usage: 4.8 KB

#graphiques par paires de variables
import seaborn as sns
sns.pairplot(X,markers=".",height=2)

<seaborn.axisgrid.PairGrid at 0x2430233ddf0>

K-Means avec 3 et 4 clusters

#k-means en 3 classes
from sklearn.cluster import KMeans
k3 = KMeans(n_clusters=3,n_init=10,random_state=0)
k3.fit(X)

#effectifs par classe
import numpy
numpy.unique(k3.labels_,return_counts=True)

(array([0, 1, 2]), array([62, 50, 38], dtype=int64))

#positions des clusters par paires de variables
tempDf = X.copy()
tempDf['clusters'] = k3.labels_
sns.pairplot(tempDf,hue='clusters',palette=["cornflowerblue","orange","green"],markers=".",height=2) #0, 1, 2

<seaborn.axisgrid.PairGrid at 0x24326d78e80>

#croisement avec les classes réelles
tab3 = pandas.crosstab(iris.Species,k3.labels_)
tab3

col_0	0	1	2
Species
setosa	0	50	0
versicolor	48	0	2
virginica	14	0	36

#k-means en 4 classes
k4 = KMeans(n_clusters=4,n_init=10,random_state=0)
k4.fit(X)

#effectifs par classe
import numpy
numpy.unique(k4.labels_,return_counts=True)

(array([0, 1, 2, 3]), array([28, 50, 32, 40], dtype=int64))

#position des clusters par paires de variables
tempDf = X.copy()
tempDf['clusters'] = k4.labels_
sns.pairplot(tempDf,hue='clusters',palette=["cornflowerblue","orange","green","black"],markers=".",height=2) #0, 1, 2, 3

<seaborn.axisgrid.PairGrid at 0x2432bdf0af0>

#croisement avec les "vraies"classes
tab4 = pandas.crosstab(iris.Species,k4.labels_)
tab4

col_0	0	1	2	3
Species
setosa	0	50	0	0
versicolor	27	0	0	23
virginica	1	0	32	17

Mesures externes - Classes réelles vs. clusters

#v de Cramer de Scipy
from scipy.stats.contingency import association
print(association(tab3,method="cramer"))
print(association(tab4,method="cramer"))

0.8633255872551836
0.8861231775065392

#librairie metrics de sklearn
from sklearn import metrics

#information mutuelle
print(metrics.mutual_info_score(iris.Species, k3.labels_))
print(metrics.mutual_info_score(iris.Species, k4.labels_))

0.8255910976103357
0.8880235203213085

#information mutuelle normalisée
print(metrics.normalized_mutual_info_score(iris.Species, k3.labels_))
print(metrics.normalized_mutual_info_score(iris.Species, k4.labels_))

0.7581756800057785
0.7219203867820961

#information mutuelle ajustée
print(metrics.adjusted_mutual_info_score(iris.Species, k3.labels_))
print(metrics.adjusted_mutual_info_score(iris.Species, k4.labels_))

0.7551191675800484
0.7172081944051023

#indice de rand
print(metrics.rand_score(iris.Species, k3.labels_))
print(metrics.rand_score(iris.Species, k4.labels_))

0.8797315436241611
0.8539597315436241

#rand score ajusté
print(metrics.adjusted_rand_score(iris.Species, k3.labels_))
print(metrics.adjusted_rand_score(iris.Species, k4.labels_))

0.7302382722834697
0.6498176853819967

#homogeneity score
print(metrics.homogeneity_score(iris.Species, k3.labels_))
print(metrics.homogeneity_score(iris.Species, k4.labels_))

0.7514854021988339
0.8083138423637095

#completness score
print(metrics.completeness_score(iris.Species, k3.labels_))
print(metrics.completeness_score(iris.Species, k4.labels_))

0.7649861514489816
0.6522113355514313

#v-measure : moyenne harmonique
print(metrics.v_measure_score(iris.Species, k3.labels_))
print(metrics.v_measure_score(iris.Species, k4.labels_))

0.7581756800057786
0.721920386782096

Mesures internes

#inerties intra-classes - à minimiser
print(k3.inertia_)
print(k4.inertia_)

78.85144142614601
57.22847321428571

#inertie totale
XC = X - numpy.mean(X,axis=0) #centrer les données par rapport à la moyenne
CARDIST = numpy.sum(XC**2,axis=1) #carrés des distances à la moyenne
TSS = numpy.sum(CARDIST) #somme des carrés...
print(TSS)

681.3706

#inerties expliquées par les partitions (BSS/TSS) - à maximiser
print((TSS-k3.inertia_)/TSS)
print((TSS-k4.inertia_)/TSS)

0.8842752513446485
0.9160097702861179

#indice de Calinski-Harabasz - à maximiser
print(metrics.calinski_harabasz_score(X,k3.labels_))
print(metrics.calinski_harabasz_score(X,k4.labels_))

561.62775662962
530.7658081872851

#silhouette score (global) - à maximiser
print(metrics.silhouette_score(X,k3.labels_))
print(metrics.silhouette_score(X,k4.labels_))

0.5528190123564102
0.49805050499728815

#grahique silhouette
from yellowbrick.cluster import SilhouetteVisualizer
visualizer = SilhouetteVisualizer(k3,colors=["cornflowerblue","orange","green"]) #0, 1, 2
visualizer.fit(X)

c:\Users\ricco\anaconda3\lib\site-packages\sklearn\base.py:450: UserWarning: X does not have valid feature names, but KMeans was fitted with feature names
  warnings.warn(

SilhouetteVisualizer(ax=<AxesSubplot: >,
                     colors=['cornflowerblue', 'orange', 'green'],
                     estimator=KMeans(n_clusters=3, random_state=0))

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
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#indice de Davies-Bouldin - à minimiser
print(metrics.davies_bouldin_score(X,k3.labels_))
print(metrics.davies_bouldin_score(X,k4.labels_))

0.6619715465007465
0.7803069838811107