In [ ]:
#représentation graphique - heatmap
import seaborn as sns
sns.heatmap(R,vmin=-1,vmax=+1,cmap='Blues')
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<AxesSubplot: >
#changement de dossier
import os
os.chdir("C:/Users/ricco/Desktop/demo")
#chargement des données
import pandas
jobrate = pandas.read_excel("jobrate.xlsx")
jobrate.head()
| Communication_Skills | Problem_Solving | Learning_Ability | Judgement_under_Pressure | Observational_Skills | Willingness_to_Confront_Problems | Interest_in_People | Interpersonal_Sensitivity | Desire_for_Self_Improvement | Appearance | Dependability | Physical_Ability | Integrity | Overall_Rating | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 2 | 6 | 8 | 3 | 8 | 8 | 5 | 3 | 8 | 7 | 9 | 8 | 6 | 7 |
| 1 | 7 | 4 | 7 | 5 | 8 | 8 | 7 | 6 | 8 | 5 | 7 | 6 | 6 | 7 |
| 2 | 5 | 6 | 7 | 5 | 7 | 8 | 6 | 3 | 7 | 7 | 5 | 8 | 7 | 5 |
| 3 | 6 | 7 | 8 | 6 | 9 | 7 | 7 | 7 | 9 | 8 | 8 | 9 | 9 | 7 |
| 4 | 9 | 9 | 9 | 9 | 7 | 7 | 9 | 8 | 8 | 7 | 8 | 8 | 8 | 8 |
#information sur les données
jobrate.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 103 entries, 0 to 102 Data columns (total 14 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 Communication_Skills 103 non-null int64 1 Problem_Solving 103 non-null int64 2 Learning_Ability 103 non-null int64 3 Judgement_under_Pressure 103 non-null int64 4 Observational_Skills 103 non-null int64 5 Willingness_to_Confront_Problems 103 non-null int64 6 Interest_in_People 103 non-null int64 7 Interpersonal_Sensitivity 103 non-null int64 8 Desire_for_Self_Improvement 103 non-null int64 9 Appearance 103 non-null int64 10 Dependability 103 non-null int64 11 Physical_Ability 103 non-null int64 12 Integrity 103 non-null int64 13 Overall_Rating 103 non-null int64 dtypes: int64(14) memory usage: 11.4 KB
#variables actives
X = jobrate[jobrate.columns[:-1]]
print(X.columns)
Index(['Communication_Skills', 'Problem_Solving', 'Learning_Ability',
'Judgement_under_Pressure', 'Observational_Skills',
'Willingness_to_Confront_Problems', 'Interest_in_People',
'Interpersonal_Sensitivity', 'Desire_for_Self_Improvement',
'Appearance', 'Dependability', 'Physical_Ability', 'Integrity'],
dtype='object')
#matrice des corrélations
R = X.corr()
print(R)
Communication_Skills Problem_Solving \
Communication_Skills 1.000000 0.628035
Problem_Solving 0.628035 1.000000
Learning_Ability 0.554550 0.569010
Judgement_under_Pressure 0.553767 0.619508
Observational_Skills 0.538073 0.428397
Willingness_to_Confront_Problems 0.526495 0.501478
Interest_in_People 0.439102 0.397212
Interpersonal_Sensitivity 0.503019 0.439777
Desire_for_Self_Improvement 0.564244 0.409005
Appearance 0.491275 0.387283
Dependability 0.547073 0.454569
Physical_Ability 0.219193 0.320063
Integrity 0.508065 0.384584
Learning_Ability Judgement_under_Pressure \
Communication_Skills 0.554550 0.553767
Problem_Solving 0.569010 0.619508
Learning_Ability 1.000000 0.489166
Judgement_under_Pressure 0.489166 1.000000
Observational_Skills 0.622984 0.373307
Willingness_to_Confront_Problems 0.524514 0.400366
Interest_in_People 0.273500 0.622643
Interpersonal_Sensitivity 0.185492 0.613361
Desire_for_Self_Improvement 0.573672 0.482604
Appearance 0.398800 0.226605
Dependability 0.510967 0.547136
Physical_Ability 0.226865 0.347631
Integrity 0.314219 0.588322
Observational_Skills \
Communication_Skills 0.538073
Problem_Solving 0.428397
Learning_Ability 0.622984
Judgement_under_Pressure 0.373307
Observational_Skills 1.000000
Willingness_to_Confront_Problems 0.729956
Interest_in_People 0.261634
Interpersonal_Sensitivity 0.165465
Desire_for_Self_Improvement 0.598463
Appearance 0.417708
Dependability 0.562557
Physical_Ability 0.427365
Integrity 0.390568
Willingness_to_Confront_Problems \
Communication_Skills 0.526495
Problem_Solving 0.501478
Learning_Ability 0.524514
Judgement_under_Pressure 0.400366
Observational_Skills 0.729956
Willingness_to_Confront_Problems 1.000000
Interest_in_People 0.223305
Interpersonal_Sensitivity 0.129088
Desire_for_Self_Improvement 0.530721
Appearance 0.482461
Dependability 0.487022
Physical_Ability 0.487234
Integrity 0.326041
Interest_in_People \
Communication_Skills 0.439102
Problem_Solving 0.397212
Learning_Ability 0.273500
Judgement_under_Pressure 0.622643
Observational_Skills 0.261634
Willingness_to_Confront_Problems 0.223305
Interest_in_People 1.000000
Interpersonal_Sensitivity 0.805146
Desire_for_Self_Improvement 0.485749
Appearance 0.267870
Dependability 0.607408
Physical_Ability 0.376810
Integrity 0.745175
Interpersonal_Sensitivity \
Communication_Skills 0.503019
Problem_Solving 0.439777
Learning_Ability 0.185492
Judgement_under_Pressure 0.613361
Observational_Skills 0.165465
Willingness_to_Confront_Problems 0.129088
Interest_in_People 0.805146
Interpersonal_Sensitivity 1.000000
Desire_for_Self_Improvement 0.371262
Appearance 0.260027
Dependability 0.540765
Physical_Ability 0.218213
Integrity 0.691997
Desire_for_Self_Improvement Appearance \
Communication_Skills 0.564244 0.491275
Problem_Solving 0.409005 0.387283
Learning_Ability 0.573672 0.398800
Judgement_under_Pressure 0.482604 0.226605
Observational_Skills 0.598463 0.417708
Willingness_to_Confront_Problems 0.530721 0.482461
Interest_in_People 0.485749 0.267870
Interpersonal_Sensitivity 0.371262 0.260027
Desire_for_Self_Improvement 1.000000 0.447442
Appearance 0.447442 1.000000
Dependability 0.598126 0.508938
Physical_Ability 0.375248 0.382005
Integrity 0.566381 0.413541
Dependability Physical_Ability Integrity
Communication_Skills 0.547073 0.219193 0.508065
Problem_Solving 0.454569 0.320063 0.384584
Learning_Ability 0.510967 0.226865 0.314219
Judgement_under_Pressure 0.547136 0.347631 0.588322
Observational_Skills 0.562557 0.427365 0.390568
Willingness_to_Confront_Problems 0.487022 0.487234 0.326041
Interest_in_People 0.607408 0.376810 0.745175
Interpersonal_Sensitivity 0.540765 0.218213 0.691997
Desire_for_Self_Improvement 0.598126 0.375248 0.566381
Appearance 0.508938 0.382005 0.413541
Dependability 1.000000 0.446120 0.653645
Physical_Ability 0.446120 1.000000 0.380959
Integrity 0.653645 0.380959 1.000000
#représentation graphique - heatmap
import seaborn as sns
sns.heatmap(R,vmin=-1,vmax=+1,cmap='Blues')
<AxesSubplot: >
#ou avec le carré des corrélations
#la valeur min devient 0 dans ce cas
sns.heatmap(R**2,vmin=0,vmax=+1,cmap='Blues')
<AxesSubplot: >
import numpy
D = numpy.sqrt(1-R**2)
print(D.iloc[:3,:3])
Communication_Skills Problem_Solving Learning_Ability Communication_Skills 0.000000 0.778185 0.83215 Problem_Solving 0.778185 0.000000 0.82233 Learning_Ability 0.832150 0.822330 0.00000
#préparation pour la CAH de scipy
#vectoriser la matrice des distances
from scipy.spatial.distance import squareform
VD = squareform(D)
print(VD)
[0.77818523 0.83215007 0.83267178 0.84289804 0.85017808 0.89843705 0.86427518 0.82560814 0.87100447 0.83708488 0.97568158 0.8613188 0.82233043 0.78499017 0.90359063 0.86517037 0.91772702 0.89810686 0.91253221 0.92196106 0.89071177 0.94739634 0.92309005 0.87219097 0.78223456 0.85140174 0.96187211 0.98264578 0.8190852 0.91703795 0.85960042 0.97392625 0.94935047 0.92770778 0.91635538 0.78250602 0.78980271 0.87583841 0.97398669 0.83704371 0.93763126 0.80862658 0.68349431 0.96516709 0.9862157 0.80115068 0.90858111 0.82675831 0.90407921 0.92057396 0.97474855 0.99163318 0.84754664 0.87591723 0.87338953 0.87327121 0.94535553 0.59307603 0.87409835 0.96345514 0.79439041 0.92629042 0.66686892 0.92852812 0.9656013 0.84117373 0.97590127 0.7219 0.89431316 0.80140227 0.92692439 0.82414385 0.86080325 0.92416038 0.91048572 0.8949733 0.75680154 0.9245921 ]
#CAH - Ward
from scipy.cluster.hierarchy import ward
cah = ward(VD)
print(cah)
[[ 6. 7. 0.59307603 2. ] [ 4. 5. 0.68349431 2. ] [12. 13. 0.72571077 3. ] [ 0. 1. 0.77818523 2. ] [ 8. 10. 0.80140227 2. ] [ 3. 16. 0.81925402 3. ] [ 2. 17. 0.85193531 3. ] [14. 19. 0.91093491 5. ] [ 9. 11. 0.92416038 2. ] [20. 21. 0.98022744 7. ] [18. 22. 1.03939101 10. ] [15. 23. 1.23922901 13. ]]
#dendrogramme
import matplotlib.pyplot as plt
from scipy.cluster.hierarchy import dendrogram
plt.title("CAH")
dendrogram(cah,labels=X.columns,orientation='left',color_threshold=0)
plt.show()
#matérialisation de 4 classes
plt.title("CAH - 4 classes")
dendrogram(cah,labels=X.columns,orientation='left',color_threshold=0.95)
plt.show()
#découpage effectif en 4 classes
from scipy.cluster.hierarchy import fcluster
groupes = fcluster(cah,t=0.95,criterion='distance')
print(groupes)
[2 2 3 2 3 3 1 1 3 4 3 4 1]
#comptage
print(numpy.unique(groupes,return_counts=True))
(array([1, 2, 3, 4], dtype=int32), array([3, 3, 5, 2], dtype=int64))
#liste des variables pour le groupe 1
print(X.columns[groupes == 1])
Index(['Interest_in_People', 'Interpersonal_Sensitivity', 'Integrity'], dtype='object')
#affichage des groupes
for g in numpy.unique(groupes):
print(g," : ",X.columns[groupes == g])
1 : Index(['Interest_in_People', 'Interpersonal_Sensitivity', 'Integrity'], dtype='object')
2 : Index(['Communication_Skills', 'Problem_Solving', 'Judgement_under_Pressure'], dtype='object')
3 : Index(['Learning_Ability', 'Observational_Skills',
'Willingness_to_Confront_Problems', 'Desire_for_Self_Improvement',
'Dependability'],
dtype='object')
4 : Index(['Appearance', 'Physical_Ability'], dtype='object')
#corrélation avec chaque variable
print(X.corrwith(jobrate.Overall_Rating))
Communication_Skills 0.680250 Problem_Solving 0.577254 Learning_Ability 0.592385 Judgement_under_Pressure 0.655048 Observational_Skills 0.584425 Willingness_to_Confront_Problems 0.589032 Interest_in_People 0.613343 Interpersonal_Sensitivity 0.577246 Desire_for_Self_Improvement 0.667191 Appearance 0.568722 Dependability 0.769633 Physical_Ability 0.438495 Integrity 0.671647 dtype: float64
#dataset pour le groupe 1
X[X.columns[groupes == 1]].head()
| Interest_in_People | Interpersonal_Sensitivity | Integrity | |
|---|---|---|---|
| 0 | 5 | 3 | 6 |
| 1 | 7 | 6 | 6 |
| 2 | 6 | 3 | 7 |
| 3 | 7 | 7 | 9 |
| 4 | 9 | 8 | 8 |
#corrélations des variables du groupe 1 avec "overall"
print(X[X.columns[groupes == 1]].corrwith(jobrate.Overall_Rating))
Interest_in_People 0.613343 Interpersonal_Sensitivity 0.577246 Integrity 0.671647 dtype: float64
#moyenne des carrés des corrélations avec les groupes
for g in numpy.unique(groupes):
print(g," : ",numpy.mean(X[X.columns[groupes==g]].corrwith(jobrate.Overall_Rating)**2))
1 : 0.38683756104936434 2 : 0.40834988274785666 3 : 0.4153820426907955 4 : 0.25786162385199723