Importation et inspection des données¶

In [ ]:
#changement de dossier
import os
os.chdir("C:/Users/ricco/Desktop/demo")

#importation des données
import pandas
df = pandas.read_excel("heart_weka_only_male.xls")
df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 209 entries, 0 to 208
Data columns (total 8 columns):
 #   Column           Non-Null Count  Dtype 
---  ------           --------------  ----- 
 0   disease          209 non-null    object
 1   age              209 non-null    int64 
 2   chest_pain       209 non-null    object
 3   restbpress       209 non-null    int64 
 4   blood_sugar      209 non-null    object
 5   restecg          209 non-null    object
 6   max_hrate        209 non-null    int64 
 7   exercice_angina  209 non-null    object
dtypes: int64(3), object(5)
memory usage: 13.2+ KB
In [ ]:
#liste des modalités par variable
for v in df.select_dtypes(include='object'):
    print(df[v].value_counts(),'\n')

disease
negative    117
positive     92
Name: count, dtype: int64 

chest_pain
asympt         102
atyp_angina     65
non_anginal     36
typ_angina       6
Name: count, dtype: int64 

blood_sugar
f    193
t     16
Name: count, dtype: int64 

restecg
normal                   174
st_t_wave_abnormality     30
left_vent_hyper            5
Name: count, dtype: int64 

exercice_angina
no     137
yes     72
Name: count, dtype: int64

La méthode DISMIX¶

Instanciation, entraînement, classement en resubstitution¶

In [ ]:
# Importation de la classe de Calcul
from scientisttools.discriminant_analysis import DISMIX

# Instanciation
mixdisc = DISMIX(n_components=5,
                  target=["disease"],
                  quanti_features_labels=["age","restbpress","max_hrate"],
                  quali_features_labels=["chest_pain","blood_sugar","restecg","exercice_angina"],
                  row_labels=df.index,
                  priors=None)

# Entrainement - Fit
mixdisc.fit(df)
Out[ ]:
DISMIX(n_components=5,
       quali_features_labels=['chest_pain', 'blood_sugar', 'restecg',
                              'exercice_angina'],
       quanti_features_labels=['age', 'restbpress', 'max_hrate'],
       row_labels=RangeIndex(start=0, stop=209, step=1), target=['disease'])
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DISMIX(n_components=5,
       quali_features_labels=['chest_pain', 'blood_sugar', 'restecg',
                              'exercice_angina'],
       quanti_features_labels=['age', 'restbpress', 'max_hrate'],
       row_labels=RangeIndex(start=0, stop=209, step=1), target=['disease'])
In [ ]:
#résultats immédiats - coefficients
mixdisc.coef_
Out[ ]:
negative positive
age -0.048053 0.061111
restbpress 0.039598 -0.050358
max_hrate 0.103109 -0.131127
chest_pain_asympt -0.085376 0.108577
chest_pain_atyp_angina 0.074180 -0.094337
chest_pain_non_anginal 0.058424 -0.074300
chest_pain_typ_angina -0.035248 0.044826
blood_sugar_f 0.007867 -0.010005
blood_sugar_t -0.027323 0.034748
restecg_left_vent_hyper 0.032314 -0.041095
restecg_normal -0.016439 0.020907
restecg_st_t_wave_abnormality 0.026399 -0.033573
exercice_angina_no 0.054955 -0.069889
exercice_angina_yes -0.075806 0.096405
In [ ]:
#intercept
mixdisc.intercept_
Out[ ]:
negative positive
Intercept -0.877854 -1.302011
In [ ]:
#matrice de confusion en resubstitution
from sklearn import metrics
metrics.ConfusionMatrixDisplay.from_predictions(df.disease,mixdisc.predict(df.iloc[:,1:]).predict)
Out[ ]:
<sklearn.metrics._plot.confusion_matrix.ConfusionMatrixDisplay at 0x1a269f3b8e0>

Performances en validation croisée¶

In [ ]:
#outil pour la validation croisée
from sklearn.model_selection import StratifiedKFold
cv_splitter = StratifiedKFold(n_splits=5,shuffle=True,random_state=1)
cv_splitter.get_n_splits(df.iloc[:,1:],df.disease)
Out[ ]:
5
In [ ]:
#vecteurs pour les résultats
import numpy
effectifs = numpy.zeros(5)
acc = numpy.zeros(5)

#évaluation en validation croisée
for i,(train_index,test_index) in enumerate(cv_splitter.split(df.iloc[:,1:],df.disease)):
    #sous-data frame
    dfTrain = df.iloc[train_index,:]
    dfTest = df.iloc[test_index,:]
    #apprentissage
    dmx = DISMIX(n_components=5,
                  target=["disease"],
                  quanti_features_labels=["age","restbpress","max_hrate"],
                  quali_features_labels=["chest_pain","blood_sugar","restecg","exercice_angina"],
                  row_labels=dfTrain.index,
                  priors=None)
    dmx.fit(dfTrain)
    #évaluation
    effectifs[i] = dfTest.shape[0]
    acc[i] = metrics.accuracy_score(dfTest.disease,dmx.predict(dfTest.iloc[:,1:]).predict)

#affichage
print(effectifs)
print(acc)

[42. 42. 42. 42. 41.]
[0.73809524 0.88095238 0.73809524 0.85714286 0.65853659]
In [ ]:
#et donc - accuracy en validation croisée
numpy.sum(effectifs*acc)/numpy.sum(effectifs)
Out[ ]:
0.7751196172248804

Décryptage de la méthode DISMIX¶

Analyse factorielle des données mixtes¶

In [ ]:
#FAMD derrière discmix
mixdisc.famd_model_
Out[ ]:
FAMD(n_components=5,
     quali_labels=['chest_pain', 'blood_sugar', 'restecg', 'exercice_angina'],
     quanti_labels=['age', 'restbpress', 'max_hrate'],
     row_labels=RangeIndex(start=0, stop=209, step=1))
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FAMD(n_components=5,
     quali_labels=['chest_pain', 'blood_sugar', 'restecg', 'exercice_angina'],
     quanti_labels=['age', 'restbpress', 'max_hrate'],
     row_labels=RangeIndex(start=0, stop=209, step=1))
In [ ]:
#variance restituée
from scientisttools.pyplot import plot_eigenvalues
plot_eigenvalues(mixdisc.famd_model_,choice="eigenvalue")
In [ ]:
#coordonnées factorielles des individus
coord = pandas.DataFrame(mixdisc.famd_model_.row_coord_,columns=['Z'+str(i) for i in range(1,6)])
coord.head(12)
Out[ ]:
Z1 Z2 Z3 Z4 Z5
0 -1.069698 0.966425 0.071447 0.170056 1.060476
1 0.876019 0.898690 -0.368467 -0.498966 0.337081
2 -0.648692 -3.072876 0.430116 -0.108650 -0.572960
3 -0.854773 -1.004573 -0.671663 0.468576 -1.950425
4 0.291900 0.342568 -0.166640 -0.265184 -0.159744
5 0.237483 0.289115 -0.149369 -0.259315 -0.183182
6 2.245878 -5.020715 -1.533806 -0.186040 4.486253
7 2.314921 -0.384783 0.439483 0.991553 -0.881329
8 0.747094 0.101416 -0.333469 -0.512404 -0.212075
9 2.890754 0.204545 0.762626 1.649473 -0.808793
10 -0.629731 -0.992587 -0.062308 1.424108 -2.229672
11 0.290273 0.477398 -0.734068 -1.250931 0.254886
In [ ]:
#rajouter la cible au dataset
coord['disease'] = df.disease

#pairplot
import seaborn as sns
sns.pairplot(data=coord,hue='disease')
Out[ ]:
<seaborn.axisgrid.PairGrid at 0x1a27f61db40>

Analyse discriminante linéaire¶

In [ ]:
#analyse discriminante
mixdisc.lda_model_
Out[ ]:
LDA(features_labels=Index(['Z1', 'Z2', 'Z3', 'Z4', 'Z5'], dtype='object'),
    row_labels=RangeIndex(start=0, stop=209, step=1), target=['disease'])
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LDA(features_labels=Index(['Z1', 'Z2', 'Z3', 'Z4', 'Z5'], dtype='object'),
    row_labels=RangeIndex(start=0, stop=209, step=1), target=['disease'])
In [ ]:
#coefficients de l'hyperplan séparateur
mixdisc.lda_coef_
Out[ ]:
negative positive
Z1 -0.561837 0.714510
Z2 -0.199247 0.253390
Z3 -0.019332 0.024585
Z4 0.467886 -0.595030
Z5 -0.143060 0.181935
In [ ]:
#intercept
mixdisc.lda_intercept_
Out[ ]:
negative positive
Intercept -0.877854 -1.302011