Vérification des versions¶
In [ ]:
#version de python
import sys
print(sys.version)
3.11.9 | packaged by Anaconda, Inc. | (main, Apr 19 2024, 16:40:41) [MSC v.1916 64 bit (AMD64)]
In [ ]:
#version de pytorch
import torch
print(torch.__version__)
2.2.0
Importation et préparation des données¶
Préparation usuelle des données
In [ ]:
#modifier le dossier de travail
import os
os.chdir("C:/Users/ricco/Desktop/demo")
#importer les données
import pandas
pdTrain = pandas.read_excel("breast_train.xlsx",header=0)
print(pdTrain.info())
<class 'pandas.core.frame.DataFrame'> RangeIndex: 399 entries, 0 to 398 Data columns (total 7 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 ucellsize 399 non-null int64 1 ucellshape 399 non-null int64 2 mgadhesion 399 non-null int64 3 sepics 399 non-null int64 4 normnucl 399 non-null int64 5 mitoses 399 non-null int64 6 classe 399 non-null object dtypes: int64(6), object(1) memory usage: 21.9+ KB None
In [ ]:
#premières lignes
pdTrain.head()
Out[ ]:
| ucellsize | ucellshape | mgadhesion | sepics | normnucl | mitoses | classe | |
|---|---|---|---|---|---|---|---|
| 0 | 1 | 1 | 1 | 2 | 1 | 1 | begnin |
| 1 | 3 | 2 | 1 | 3 | 6 | 1 | begnin |
| 2 | 9 | 7 | 3 | 4 | 7 | 1 | malignant |
| 3 | 10 | 10 | 7 | 10 | 2 | 1 | malignant |
| 4 | 8 | 8 | 4 | 10 | 1 | 1 | malignant |
In [ ]:
#structure avec les descripteurs
XTrain = pdTrain[pdTrain.columns[:-1]]
XTrain.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 399 entries, 0 to 398 Data columns (total 6 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 ucellsize 399 non-null int64 1 ucellshape 399 non-null int64 2 mgadhesion 399 non-null int64 3 sepics 399 non-null int64 4 normnucl 399 non-null int64 5 mitoses 399 non-null int64 dtypes: int64(6) memory usage: 18.8 KB
In [ ]:
#outil pour centrer et réduire les X
#avec StandardScaler
from sklearn.preprocessing import StandardScaler
sts = StandardScaler()
#données centrées et réduites
ZTrain = sts.fit_transform(XTrain)
print(ZTrain.shape)
(399, 6)
In [ ]:
#distribution des classes
pdTrain.classe.value_counts()
Out[ ]:
classe begnin 267 malignant 132 Name: count, dtype: int64
In [ ]:
#recoder la cible en 0 : begnin ; 1 : malignant
yTrain = pdTrain.classe.map({'malignant':1,'begnin':0}).values
#comptage
import numpy
numpy.unique(yTrain,return_counts=True)
Out[ ]:
(array([0, 1], dtype=int64), array([267, 132], dtype=int64))
Rendre les données compatibles avec PyTorch
In [ ]:
#tranformer les variables Z en tensor
tensor_ZTrain = torch.FloatTensor(ZTrain)
#qui est d'un type particulier
print(type(tensor_ZTrain))
<class 'torch.Tensor'>
In [ ]:
#dimensions
print(tensor_ZTrain.shape)
torch.Size([399, 6])
In [ ]:
#valeurs
print(tensor_ZTrain)
tensor([[-0.6800, -0.7377, -0.5984, -0.5140, -0.5897, -0.3145],
[-0.0134, -0.4001, -0.5984, -0.0531, 1.0487, -0.3145],
[ 1.9865, 1.2875, 0.1164, 0.4077, 1.3764, -0.3145],
...,
[-0.6800, -0.7377, -0.5984, -0.5140, -0.5897, -0.3145],
[-0.6800, -0.7377, -0.5984, -0.5140, -0.2620, -0.3145],
[ 0.3200, 0.9500, -0.5984, -0.5140, 0.0657, -0.3145]])
In [ ]:
#idem pour y
tensor_yTrain = torch.FloatTensor(yTrain)
print(tensor_yTrain)
tensor([0., 0., 1., 1., 1., 0., 0., 0., 0., 0., 0., 0., 1., 1., 1., 0., 1., 0.,
0., 0., 0., 1., 1., 0., 0., 1., 1., 1., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 1., 1., 0., 0., 0., 0., 1., 1., 0., 1., 0., 0., 0., 0., 0.,
1., 0., 1., 0., 0., 1., 0., 0., 1., 0., 0., 0., 0., 1., 1., 1., 1., 0.,
1., 0., 1., 1., 0., 0., 0., 1., 1., 0., 0., 1., 0., 0., 0., 1., 0., 0.,
0., 1., 1., 0., 1., 0., 0., 0., 1., 1., 0., 0., 0., 0., 1., 0., 0., 0.,
0., 1., 1., 0., 1., 0., 0., 0., 0., 0., 0., 1., 1., 1., 0., 0., 0., 1.,
0., 0., 0., 1., 0., 1., 0., 1., 0., 1., 0., 0., 0., 0., 0., 0., 1., 0.,
1., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 1., 0.,
1., 0., 1., 1., 0., 1., 1., 0., 0., 0., 1., 0., 0., 0., 0., 1., 0., 0.,
1., 0., 1., 0., 0., 1., 0., 1., 0., 1., 0., 0., 1., 1., 0., 1., 0., 0.,
1., 1., 0., 1., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 1., 1.,
0., 1., 1., 0., 1., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 1., 0.,
1., 0., 0., 0., 0., 1., 0., 0., 0., 1., 1., 0., 0., 1., 1., 0., 0., 0.,
1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 1., 1., 1.,
1., 1., 0., 1., 0., 0., 1., 1., 1., 1., 0., 0., 0., 0., 0., 1., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0.,
1., 1., 0., 0., 0., 0., 0., 1., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0.,
1., 1., 1., 0., 1., 1., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.,
1., 1., 1., 1., 0., 0., 1., 0., 1., 1., 0., 1., 1., 0., 0., 0., 1., 1.,
0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 1., 1., 1., 0., 0., 1., 1., 1.,
0., 0., 1.])
In [ ]:
#dimension
print(tensor_yTrain.shape)
torch.Size([399])
Perceptron simple avec PyTorch¶
Elaboration de la structure¶
Structure du réseau de neurones
In [ ]:
#classe de calcul - Perceptron simple
#héritier de torch.nn.Module
class MyPS(torch.nn.Module):
#constructeur - liste des éléments
#qui composent le réseau
def __init__(self,p):
#appel du constructeur de l'ancêtre
super(MyPS,self).__init__()
#couche d'entrée (p variables) vers sortie (1 neurone)
self.layer1 = torch.nn.Linear(p,1)
#fonction de transfert sigmoïde à la sortie
self.ft1 = torch.nn.Sigmoid()
#structuration des éléments
#calcul de la sortie du réseau
#à partir d'une matrice x en entrée
def forward(self,x):
#application de la combinaison linéaire
comb_lin = self.layer1(x)
#transformation avec la fonction de transfert
proba = self.ft1(comb_lin)
return proba
Choix de la fonction de perte à optimiser
In [ ]:
#fonction critère à optimiser
critere_ps = torch.nn.MSELoss()
Instanciation du modèle
In [ ]:
#instanciation du modele
#.shape[1] pour le nombre de descripteurs => 6
ps = MyPS(tensor_ZTrain.shape[1])
Choix de l'algorithme d'optimisation - Gradient stochastique
In [ ]:
#algorithme d'optimisation
#on lui passe les paramètres à manipuler
optimiseur_ps = torch.optim.Adam(ps.parameters())
Quelques vérifications - Coefficients et sortie du réseau
In [ ]:
#poids synaptiques
#initialisés aléatoirement
print(ps.layer1.weight)
Parameter containing:
tensor([[ 0.2754, -0.3938, -0.3197, -0.2911, 0.2502, -0.3007]],
requires_grad=True)
In [ ]:
#et l'intercept
print(ps.layer1.bias)
Parameter containing: tensor([-0.3651], requires_grad=True)
In [ ]:
#calculer des sorties du réseau avec ces poids initiaux (aléatoires)
#équivalent à yPred = ps(tensor_ZTrain)
#on a des probas d'appartenance ici
yPred = ps.forward(tensor_ZTrain)
#affichage des 10 premières valeurs
print(yPred[:10])
tensor([[0.5065],
[0.5872],
[0.4895],
[0.1170],
[0.1574],
[0.5065],
[0.5270],
[0.5065],
[0.5065],
[0.5294]], grad_fn=<SliceBackward0>)
In [ ]:
#format de yPred - matrice en réalité
print(yPred.shape)
torch.Size([399, 1])
In [ ]:
#pour transformer en vecteur
print(yPred.squeeze()[:10])
tensor([0.5065, 0.5872, 0.4895, 0.1170, 0.1574, 0.5065, 0.5270, 0.5065, 0.5065,
0.5294], grad_fn=<SliceBackward0>)
In [ ]:
#en effet
print(yPred.squeeze().shape)
torch.Size([399])
Valeur de départ de la perte
In [ ]:
#MSE au départ (avec les poids initiaux aléatoires)
MSE1st = critere_ps(yPred.squeeze(),tensor_yTrain)
print(MSE1st)
tensor(0.3336, grad_fn=<MseLossBackward0>)
In [ ]:
#vérification en passant par les vecteurs numpy
#on a bien une fonction de perte MSE
numpy.mean((yPred.squeeze().detach().numpy()-tensor_yTrain.numpy())**2)
Out[ ]:
0.33355263
Entraînement du modèle¶
Bien détailler la structure du code avec les différentes étapes.
In [ ]:
#fonction pour apprentissage avec les paramètres :
#X, y, instance de classe torch, critère à optimiser, algo d'optimisation...
#...et n_epochs nombre de passage sur la base
def train_session(X,y,classifier,criterion,optimizer,n_epochs=10000):
#vecteur pour collecter le loss au fil des itérations
losses = numpy.zeros(n_epochs)
#itérer (boucle) pour optimiser - n_epochs fois sur la base
for iter in range(n_epochs):
#réinitialiser (ràz) le gradient
#nécessaire à chaque passage sinon PyTorch accumule
optimizer.zero_grad()
#calculer la sortie du réseau
yPred = classifier.forward(X) #ou simplement classifier(X)
#calculer la perte
perte = criterion(yPred.squeeze(),y)
#collecter la perte calculée dans le vecteur losses
losses[iter] = perte.item()
#calcul du gradient et retropropagation
perte.backward()
#màj des poids synaptiques
optimizer.step()
#sortie de la boucle
#renvoie le vecteur avec les valeurs de perte à chaque epoch
return losses
On peut lancer l'entraînement du modèle maintenant.
In [ ]:
#lancer l'apprentissage
#revenir sur les paramètres passés à la fonction
pertes = train_session(tensor_ZTrain,tensor_yTrain,ps,critere_ps,optimiseur_ps)
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#valeur de la perte au final
print(pertes[-1])
0.03577861934900284
In [ ]:
#courbe de décroissance de la perte
import matplotlib.pyplot as plt
plt.plot(numpy.arange(0,pertes.shape[0]),pertes)
plt.title("Evolution fnct de perte")
plt.xlabel("Epochs")
plt.ylabel("Loss")
plt.show()
In [ ]:
#inspection des coefficients après apprentissage
print(ps.layer1.weight)
Parameter containing: tensor([[1.9119, 2.8555, 0.1655, 1.8033, 1.0651, 0.8123]], requires_grad=True)
In [ ]:
#et de l'intercept
print(ps.layer1.bias)
Parameter containing: tensor([0.2614], requires_grad=True)
Evaluation sur l'échantillon test¶
Préparation des données
In [ ]:
#chargement de l'échantillon test
pdTest = pandas.read_excel("breast_test.xlsx",header=0)
print(pdTest.info())
<class 'pandas.core.frame.DataFrame'> RangeIndex: 300 entries, 0 to 299 Data columns (total 7 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 ucellsize 300 non-null int64 1 ucellshape 300 non-null int64 2 mgadhesion 300 non-null int64 3 sepics 300 non-null int64 4 normnucl 300 non-null int64 5 mitoses 300 non-null int64 6 classe 300 non-null object dtypes: int64(6), object(1) memory usage: 16.5+ KB None
In [ ]:
#données centrées et réduites (avec les moyennes et écarts-type de train)
ZTest = sts.transform(pdTest[pdTest.columns[:-1]])
print(ZTest)
[[-0.67999948 -0.06259939 -0.59835544 -0.97482724 -0.58966111 -0.31445173] [ 2.31985082 0.27492976 1.54605012 -0.05313039 2.3594657 -0.31445173] [-0.67999948 -0.73765769 -0.59835544 -0.51397882 -0.58966111 -0.31445173] ... [ 0.98658402 -0.06259939 1.1886492 0.40771803 1.70410419 1.57699912] [-0.67999948 -0.06259939 -0.59835544 -0.51397882 -0.58966111 -0.31445173] [-0.67999948 -0.73765769 -0.59835544 -0.51397882 -0.58966111 -0.31445173]]
In [ ]:
#mettre au format tensor pour PyTorch
tensor_ZTest = torch.FloatTensor(ZTest)
print(tensor_ZTest)
tensor([[-0.6800, -0.0626, -0.5984, -0.9748, -0.5897, -0.3145],
[ 2.3199, 0.2749, 1.5461, -0.0531, 2.3595, -0.3145],
[-0.6800, -0.7377, -0.5984, -0.5140, -0.5897, -0.3145],
...,
[ 0.9866, -0.0626, 1.1886, 0.4077, 1.7041, 1.5770],
[-0.6800, -0.0626, -0.5984, -0.5140, -0.5897, -0.3145],
[-0.6800, -0.7377, -0.5984, -0.5140, -0.5897, -0.3145]])
In [ ]:
#recoder en 0/1 la cible
yTest = pdTest.classe.map({'malignant':1,'begnin':0}).values
yTest
Out[ ]:
array([0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0,
0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0,
1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,
0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1,
1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0,
0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0,
0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0,
1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0,
0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1,
1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0], dtype=int64)
In [ ]:
#prédiction de la probabilité d'appartenance
#en appliquant le modèle sur les descripteurs standardisés
proba_predTest = ps.forward(tensor_ZTest)
print(proba_predTest)
tensor([[0.0187],
[0.9996],
[0.0063],
[0.0307],
[0.0063],
[0.0063],
[1.0000],
[0.0165],
[0.0063],
[1.0000],
[0.0063],
[0.6162],
[0.0067],
[0.0090],
[1.0000],
[0.0028],
[0.0063],
[0.0063],
[0.9998],
[0.0028],
[1.0000],
[0.0063],
[0.0071],
[0.0165],
[1.0000],
[0.9869],
[0.0751],
[0.0067],
[0.9999],
[0.9370],
[0.0063],
[0.9385],
[0.0063],
[1.0000],
[0.0052],
[0.7079],
[0.9076],
[0.0063],
[0.0067],
[1.0000],
[0.9237],
[0.0063],
[0.0119],
[0.8312],
[1.0000],
[0.0029],
[0.0028],
[1.0000],
[0.0063],
[0.0168],
[0.0063],
[0.5992],
[0.0063],
[0.9999],
[1.0000],
[0.0153],
[0.9999],
[0.0071],
[0.0028],
[1.0000],
[0.0028],
[0.1589],
[0.0063],
[0.0090],
[0.0063],
[0.0090],
[0.1429],
[0.9999],
[0.1870],
[0.0063],
[0.0071],
[0.9988],
[0.0063],
[0.0063],
[1.0000],
[0.0063],
[0.9901],
[0.0063],
[1.0000],
[1.0000],
[0.0598],
[0.0153],
[1.0000],
[0.0063],
[0.0063],
[0.0063],
[0.4521],
[0.0067],
[0.9991],
[0.2164],
[0.9923],
[0.0063],
[0.0063],
[0.1274],
[0.9925],
[1.0000],
[0.0063],
[1.0000],
[0.9988],
[0.0063],
[0.0063],
[0.5801],
[0.9997],
[0.0063],
[0.7242],
[0.0063],
[0.0063],
[0.0063],
[0.0063],
[0.0067],
[0.9933],
[0.0063],
[0.9994],
[0.0063],
[0.9927],
[0.0063],
[1.0000],
[0.0063],
[0.0144],
[0.0063],
[1.0000],
[1.0000],
[0.9872],
[0.0144],
[0.9985],
[1.0000],
[0.0144],
[0.0028],
[1.0000],
[0.0865],
[1.0000],
[0.9975],
[0.6464],
[0.0063],
[0.0063],
[0.9999],
[0.0063],
[0.1031],
[0.0063],
[0.0242],
[0.0067],
[0.9183],
[0.0063],
[0.9999],
[1.0000],
[1.0000],
[0.0063],
[0.9813],
[0.1402],
[0.0530],
[1.0000],
[0.0063],
[0.9699],
[0.0236],
[0.0028],
[0.6594],
[0.0071],
[1.0000],
[1.0000],
[1.0000],
[1.0000],
[0.0144],
[0.0189],
[0.0063],
[0.0071],
[0.0028],
[0.3480],
[0.0119],
[0.7270],
[0.0063],
[0.0717],
[0.0144],
[1.0000],
[0.0063],
[0.0063],
[0.0028],
[0.0063],
[0.0063],
[0.0307],
[0.9901],
[1.0000],
[0.9721],
[1.0000],
[0.0076],
[0.0063],
[0.1819],
[0.0063],
[0.0766],
[0.9999],
[1.0000],
[0.0063],
[0.0420],
[0.0472],
[0.1208],
[0.9996],
[0.0420],
[0.0067],
[0.0063],
[0.0067],
[0.0063],
[0.0165],
[1.0000],
[1.0000],
[1.0000],
[0.0090],
[1.0000],
[0.0105],
[1.0000],
[0.0063],
[0.0028],
[0.0029],
[0.0165],
[0.0307],
[0.0028],
[0.2397],
[0.0063],
[0.0063],
[0.9990],
[1.0000],
[0.0063],
[0.9969],
[0.0031],
[0.0063],
[0.9999],
[0.0028],
[1.0000],
[1.0000],
[0.6649],
[0.0667],
[0.0063],
[0.0067],
[0.0063],
[0.0063],
[0.0090],
[0.9999],
[1.0000],
[0.0165],
[0.0028],
[1.0000],
[0.0063],
[0.0420],
[0.0063],
[0.0063],
[0.9930],
[1.0000],
[0.0063],
[0.9993],
[0.0063],
[1.0000],
[0.0063],
[0.0063],
[0.0165],
[1.0000],
[1.0000],
[0.0063],
[0.0063],
[0.0063],
[0.0063],
[0.9933],
[0.0071],
[0.0420],
[0.0063],
[0.0325],
[0.0063],
[0.0063],
[1.0000],
[0.1966],
[0.0063],
[0.0353],
[0.0090],
[0.0063],
[0.0063],
[0.0063],
[0.9995],
[0.0223],
[1.0000],
[0.9987],
[0.3653],
[0.0063],
[0.0063],
[1.0000],
[0.3619],
[0.0063],
[0.9999],
[0.9619],
[0.9708],
[0.9999],
[1.0000],
[0.9225],
[0.6776],
[0.0063],
[0.9915],
[0.1909],
[0.0193],
[1.0000],
[0.0031],
[0.0165],
[0.9975],
[0.0420],
[0.0063]], grad_fn=<SigmoidBackward0>)
In [ ]:
#on a une matrice "torch"
proba_predTest.shape
Out[ ]:
torch.Size([300, 1])
In [ ]:
#que l'on transforme en vecteur numpy
vec_predTest = proba_predTest.detach().squeeze()
vec_predTest.shape
Out[ ]:
torch.Size([300])
In [ ]:
#que l'on peut convertir en classe d'appartenance
#en comparant à la valeur 0.5
classe_predTest = numpy.where(vec_predTest > 0.5,1.0,0.0)
#on a un vecteur numpy ici
print(classe_predTest)
[0. 1. 0. 0. 0. 0. 1. 0. 0. 1. 0. 1. 0. 0. 1. 0. 0. 0. 1. 0. 1. 0. 0. 0. 1. 1. 0. 0. 1. 1. 0. 1. 0. 1. 0. 1. 1. 0. 0. 1. 1. 0. 0. 1. 1. 0. 0. 1. 0. 0. 0. 1. 0. 1. 1. 0. 1. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 1. 0. 0. 1. 0. 1. 0. 1. 1. 0. 0. 1. 0. 0. 0. 0. 0. 1. 0. 1. 0. 0. 0. 1. 1. 0. 1. 1. 0. 0. 1. 1. 0. 1. 0. 0. 0. 0. 0. 1. 0. 1. 0. 1. 0. 1. 0. 0. 0. 1. 1. 1. 0. 1. 1. 0. 0. 1. 0. 1. 1. 1. 0. 0. 1. 0. 0. 0. 0. 0. 1. 0. 1. 1. 1. 0. 1. 0. 0. 1. 0. 1. 0. 0. 1. 0. 1. 1. 1. 1. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 1. 1. 1. 1. 0. 0. 0. 0. 0. 1. 1. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 1. 1. 1. 0. 1. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 1. 0. 1. 0. 0. 1. 0. 1. 1. 1. 0. 0. 0. 0. 0. 0. 1. 1. 0. 0. 1. 0. 0. 0. 0. 1. 1. 0. 1. 0. 1. 0. 0. 0. 1. 1. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 1. 0. 1. 1. 0. 0. 0. 1. 0. 0. 1. 1. 1. 1. 1. 1. 1. 0. 1. 0. 0. 1. 0. 0. 1. 0. 0.]
In [ ]:
#calcul de l'accuracy
print(numpy.mean(classe_predTest == yTest))
0.9666666666666667
Perceptron multicouche¶
Définir la nouvelle structure du réseau.
In [ ]:
#perceptron multicouche
class MyPMC(torch.nn.Module):
#constructeur
def __init__(self,p):
#appel du constructeur de l'ancêtre
super(MyPMC,self).__init__()
#couche d'entrée (p variables) vers intermédiaire (2 neurones)
self.layer1 = torch.nn.Linear(p,2)
#fonction de transfert
self.ft1 = torch.nn.Sigmoid()
#couche intermédiaire vers sortie (1 neurone)
self.layer2 = torch.nn.Linear(2,1)
#fonction de transfert sigmoïde
self.ft2 = torch.nn.Sigmoid()
#premier forward
#couche entrée -> couche cachée
def forward_1(self,x):
#application de la combinaison linéaire
comb_lin_1 = self.layer1(x)
#appliquer la fonction sigmoïde
return self.ft1(comb_lin_1)
#second forward
#couche cachée -> couche sortie
def forward_2(self,x_prim):
#puis seconde combinaison linéaire
comb_lin_2 = self.layer2(x_prim)
#appliquer la transformation sigmoïde
return self.ft2(comb_lin_2)
#calcul de la sortie du réseau
#à partir d'une matrice x en entrée
def forward(self,x):
#premier forward
out_1 = self.forward_1(x)
#second forward
out_2 = self.forward_2(out_1)
#return
return out_2
Entraînement du modèle
In [ ]:
#instanciation
pmc = MyPMC(tensor_ZTrain.shape[1])
In [ ]:
#défintion des outils d'apprentissage
#critere - perte quadratique
critere_pmc = torch.nn.MSELoss()
#optimiseur
optimiseur_pmc = torch.optim.Adam(pmc.parameters())
In [ ]:
#lancement de l'entraînement
#en ré-explitant la fonction ci-dessus, seuls les paramètres changent
#dont l'instance de la structure du réseau "pmc"
pertes = train_session(tensor_ZTrain,tensor_yTrain,pmc,critere_pmc,optimiseur_pmc)
In [ ]:
#évolution de la perte vs. epoch
plt.plot(numpy.arange(0,pertes.shape[0]),pertes)
plt.title("Evolution fnct de perte")
plt.xlabel("Epochs")
plt.ylabel("Loss")
plt.show()
Inspection des poids synaptiques (coefficients)
In [ ]:
#poids de entrée -> couche cachée
print(pmc.layer1.weight)
Parameter containing:
tensor([[-1.4811, -6.1619, 0.2026, -1.7708, -1.0070, -0.6883],
[ 0.9091, 3.9800, 0.9036, 1.8425, 2.1994, 1.4802]],
requires_grad=True)
In [ ]:
#intercept corresp.
print(pmc.layer1.bias)
Parameter containing: tensor([-1.1908, 1.2490], requires_grad=True)
In [ ]:
#poids de couche cachée -> couche de sortie
print(pmc.layer2.weight)
Parameter containing: tensor([[-3.6089, 3.8023]], requires_grad=True)
In [ ]:
#intercept corresp.
print(pmc.layer2.bias)
Parameter containing: tensor([-1.0974], requires_grad=True)
Evaluation sur l'échantillon test
In [ ]:
#prédiction proba d'appartenance
proba_pmc = pmc.forward(tensor_ZTest)
print(proba_pmc)
tensor([[0.0125],
[0.9372],
[0.0092],
[0.0108],
[0.0092],
[0.0092],
[0.9373],
[0.0102],
[0.0092],
[0.9373],
[0.0092],
[0.6626],
[0.0092],
[0.0093],
[0.9373],
[0.0091],
[0.0092],
[0.0092],
[0.9373],
[0.0091],
[0.9373],
[0.0092],
[0.0093],
[0.0102],
[0.9373],
[0.9366],
[0.0137],
[0.0092],
[0.9373],
[0.9318],
[0.0092],
[0.9146],
[0.0092],
[0.9373],
[0.0091],
[0.8038],
[0.9300],
[0.0092],
[0.0092],
[0.9373],
[0.8562],
[0.0092],
[0.0093],
[0.6329],
[0.9373],
[0.0091],
[0.0091],
[0.9373],
[0.0092],
[0.0095],
[0.0092],
[0.7078],
[0.0092],
[0.9373],
[0.9373],
[0.0096],
[0.9373],
[0.0093],
[0.0091],
[0.9373],
[0.0091],
[0.0191],
[0.0092],
[0.0093],
[0.0092],
[0.0093],
[0.0219],
[0.9373],
[0.1469],
[0.0092],
[0.0093],
[0.9373],
[0.0092],
[0.0092],
[0.9373],
[0.0092],
[0.9366],
[0.0092],
[0.9373],
[0.9373],
[0.0150],
[0.0096],
[0.9373],
[0.0092],
[0.0092],
[0.0092],
[0.4909],
[0.0092],
[0.9373],
[0.0159],
[0.9368],
[0.0092],
[0.0092],
[0.0134],
[0.9347],
[0.9373],
[0.0092],
[0.9373],
[0.9373],
[0.0092],
[0.0092],
[0.8155],
[0.9370],
[0.0092],
[0.8813],
[0.0092],
[0.0092],
[0.0092],
[0.0092],
[0.0092],
[0.9372],
[0.0092],
[0.9373],
[0.0092],
[0.9370],
[0.0092],
[0.9373],
[0.0092],
[0.0095],
[0.0092],
[0.9373],
[0.9373],
[0.9364],
[0.0095],
[0.9373],
[0.9373],
[0.0095],
[0.0091],
[0.9373],
[0.0748],
[0.9373],
[0.9365],
[0.5102],
[0.0092],
[0.0092],
[0.9372],
[0.0092],
[0.1221],
[0.0092],
[0.0109],
[0.0092],
[0.9317],
[0.0092],
[0.9373],
[0.9373],
[0.9373],
[0.0092],
[0.9261],
[0.2326],
[0.0135],
[0.9373],
[0.0092],
[0.9337],
[0.0095],
[0.0091],
[0.7144],
[0.0093],
[0.9373],
[0.9373],
[0.9373],
[0.9373],
[0.0095],
[0.0098],
[0.0092],
[0.0093],
[0.0091],
[0.4352],
[0.0093],
[0.7726],
[0.0092],
[0.0119],
[0.0095],
[0.9373],
[0.0092],
[0.0092],
[0.0091],
[0.0092],
[0.0092],
[0.0108],
[0.9361],
[0.9373],
[0.9360],
[0.9373],
[0.0094],
[0.0092],
[0.0654],
[0.0092],
[0.0249],
[0.9373],
[0.9373],
[0.0092],
[0.0182],
[0.0159],
[0.0167],
[0.9373],
[0.0182],
[0.0092],
[0.0092],
[0.0092],
[0.0092],
[0.0102],
[0.9373],
[0.9373],
[0.9373],
[0.0093],
[0.9373],
[0.0094],
[0.9373],
[0.0092],
[0.0091],
[0.0091],
[0.0102],
[0.0108],
[0.0091],
[0.1325],
[0.0092],
[0.0092],
[0.9373],
[0.9373],
[0.0092],
[0.9371],
[0.0091],
[0.0092],
[0.9373],
[0.0091],
[0.9373],
[0.9373],
[0.9006],
[0.0134],
[0.0092],
[0.0092],
[0.0092],
[0.0092],
[0.0093],
[0.9373],
[0.9373],
[0.0102],
[0.0091],
[0.9373],
[0.0092],
[0.0182],
[0.0092],
[0.0092],
[0.9371],
[0.9373],
[0.0092],
[0.9372],
[0.0092],
[0.9373],
[0.0092],
[0.0092],
[0.0102],
[0.9373],
[0.9373],
[0.0092],
[0.0092],
[0.0092],
[0.0092],
[0.9366],
[0.0093],
[0.0182],
[0.0092],
[0.0101],
[0.0092],
[0.0092],
[0.9373],
[0.2718],
[0.0092],
[0.0150],
[0.0093],
[0.0092],
[0.0092],
[0.0092],
[0.9372],
[0.0094],
[0.9373],
[0.9373],
[0.1605],
[0.0092],
[0.0092],
[0.9373],
[0.6371],
[0.0092],
[0.9373],
[0.9279],
[0.9366],
[0.9373],
[0.9373],
[0.9284],
[0.8799],
[0.0092],
[0.9371],
[0.0742],
[0.0107],
[0.9373],
[0.0091],
[0.0102],
[0.9365],
[0.0182],
[0.0092]], grad_fn=<SigmoidBackward0>)
In [ ]:
#conversion en classe d'appartenance
classe_pmc = numpy.where(proba_pmc.detach().squeeze() > 0.5,1.0,0.0)
print(classe_pmc)
[0. 1. 0. 0. 0. 0. 1. 0. 0. 1. 0. 1. 0. 0. 1. 0. 0. 0. 1. 0. 1. 0. 0. 0. 1. 1. 0. 0. 1. 1. 0. 1. 0. 1. 0. 1. 1. 0. 0. 1. 1. 0. 0. 1. 1. 0. 0. 1. 0. 0. 0. 1. 0. 1. 1. 0. 1. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 1. 0. 0. 1. 0. 1. 0. 1. 1. 0. 0. 1. 0. 0. 0. 0. 0. 1. 0. 1. 0. 0. 0. 1. 1. 0. 1. 1. 0. 0. 1. 1. 0. 1. 0. 0. 0. 0. 0. 1. 0. 1. 0. 1. 0. 1. 0. 0. 0. 1. 1. 1. 0. 1. 1. 0. 0. 1. 0. 1. 1. 1. 0. 0. 1. 0. 0. 0. 0. 0. 1. 0. 1. 1. 1. 0. 1. 0. 0. 1. 0. 1. 0. 0. 1. 0. 1. 1. 1. 1. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 1. 1. 1. 1. 0. 0. 0. 0. 0. 1. 1. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 1. 1. 1. 0. 1. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 1. 0. 1. 0. 0. 1. 0. 1. 1. 1. 0. 0. 0. 0. 0. 0. 1. 1. 0. 0. 1. 0. 0. 0. 0. 1. 1. 0. 1. 0. 1. 0. 0. 0. 1. 1. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 1. 0. 1. 1. 0. 0. 0. 1. 1. 0. 1. 1. 1. 1. 1. 1. 1. 0. 1. 0. 0. 1. 0. 0. 1. 0. 0.]
In [ ]:
#accuracy
print(numpy.mean(classe_predTest == yTest))
0.9666666666666667
Représentation intermédiaire de la couche cachée
In [ ]:
#obtenir la sortie de la couche cachée
#renvoyée par forward_1
hidden = pmc.forward_1(tensor_ZTrain)
print(hidden)
tensor([[9.9743e-01, 3.8527e-03],
[6.0534e-01, 6.9992e-01],
[8.8778e-07, 9.9999e-01],
[5.4958e-11, 1.0000e+00],
[1.0575e-08, 1.0000e+00],
[9.9743e-01, 3.8527e-03],
[9.9643e-01, 7.8887e-03],
[9.9743e-01, 3.8527e-03],
[9.9743e-01, 3.8527e-03],
[9.9579e-01, 5.2092e-03],
[9.9743e-01, 3.8527e-03],
[9.9743e-01, 3.8527e-03],
[1.1559e-03, 9.6520e-01],
[5.9068e-11, 1.0000e+00],
[2.1572e-04, 9.9997e-01],
[9.9743e-01, 3.8527e-03],
[1.7370e-03, 9.9939e-01],
[8.8871e-01, 5.9714e-02],
[1.3007e-01, 9.9032e-01],
[1.3884e-05, 1.0000e+00],
[8.5830e-01, 5.3738e-02],
[9.4992e-11, 1.0000e+00],
[1.4907e-05, 9.9999e-01],
[9.9743e-01, 3.8527e-03],
[9.8117e-01, 2.0059e-02],
[2.5587e-11, 1.0000e+00],
[2.5667e-12, 1.0000e+00],
[1.0692e-09, 1.0000e+00],
[9.9743e-01, 3.8527e-03],
[9.9886e-01, 1.6518e-03],
[9.9743e-01, 3.8527e-03],
[9.9886e-01, 1.6518e-03],
[4.2081e-03, 9.9446e-01],
[9.9743e-01, 3.8527e-03],
[8.5830e-01, 5.3738e-02],
[9.7352e-01, 5.0215e-02],
[4.3081e-01, 1.7872e-01],
[9.9643e-01, 7.8887e-03],
[9.9886e-01, 1.6518e-03],
[3.1143e-04, 9.9760e-01],
[4.0208e-08, 9.9993e-01],
[9.9313e-01, 7.0398e-03],
[9.9743e-01, 3.8527e-03],
[7.8711e-01, 7.1399e-02],
[9.9743e-01, 3.8527e-03],
[1.8419e-06, 9.9999e-01],
[1.4090e-04, 9.9957e-01],
[5.2251e-02, 6.8551e-01],
[4.9220e-01, 6.3312e-01],
[9.9777e-01, 7.3242e-03],
[9.9743e-01, 3.8527e-03],
[9.9886e-01, 1.6518e-03],
[9.9743e-01, 3.8527e-03],
[9.7979e-01, 1.4604e-02],
[9.7158e-11, 1.0000e+00],
[2.4531e-06, 9.9988e-01],
[3.8992e-04, 9.9891e-01],
[8.5830e-01, 5.3738e-02],
[9.9886e-01, 1.6518e-03],
[1.5395e-05, 9.9982e-01],
[9.8117e-01, 2.0059e-02],
[9.9886e-01, 1.6518e-03],
[5.1304e-03, 9.9315e-01],
[9.5543e-01, 3.3484e-02],
[9.5811e-01, 5.3906e-02],
[9.7979e-01, 1.4604e-02],
[9.9777e-01, 7.3242e-03],
[9.9311e-01, 3.2516e-02],
[1.0316e-01, 9.8120e-01],
[1.6145e-11, 1.0000e+00],
[2.6477e-03, 9.9993e-01],
[9.9777e-01, 7.3242e-03],
[2.5092e-09, 1.0000e+00],
[9.9743e-01, 3.8527e-03],
[2.4155e-11, 1.0000e+00],
[3.5294e-06, 1.0000e+00],
[9.9743e-01, 3.8527e-03],
[9.9643e-01, 7.8887e-03],
[9.9743e-01, 3.8527e-03],
[1.5660e-04, 9.9999e-01],
[5.6243e-08, 9.9999e-01],
[9.9743e-01, 3.8527e-03],
[9.9743e-01, 3.8527e-03],
[1.0670e-03, 9.9988e-01],
[9.9743e-01, 3.8527e-03],
[9.9743e-01, 3.8527e-03],
[9.9743e-01, 3.8527e-03],
[1.8448e-12, 1.0000e+00],
[9.9743e-01, 3.8527e-03],
[9.9743e-01, 3.8527e-03],
[2.7865e-03, 9.9647e-01],
[2.9886e-07, 1.0000e+00],
[1.1033e-10, 1.0000e+00],
[9.9743e-01, 3.8527e-03],
[1.4845e-04, 9.9648e-01],
[9.9743e-01, 3.8527e-03],
[9.9579e-01, 5.2092e-03],
[9.9743e-01, 3.8527e-03],
[9.9901e-01, 3.1464e-03],
[2.4951e-10, 1.0000e+00],
[8.5830e-01, 5.3738e-02],
[9.9743e-01, 3.8527e-03],
[9.7979e-01, 1.4604e-02],
[9.9886e-01, 1.6518e-03],
[6.3078e-05, 1.0000e+00],
[9.4788e-01, 5.9701e-01],
[9.9743e-01, 3.8527e-03],
[9.9743e-01, 3.8527e-03],
[8.5830e-01, 5.3738e-02],
[2.0504e-09, 1.0000e+00],
[1.8329e-08, 1.0000e+00],
[9.9743e-01, 3.8527e-03],
[2.3245e-01, 9.9890e-01],
[9.9743e-01, 3.8527e-03],
[9.9743e-01, 3.8527e-03],
[9.9743e-01, 3.8527e-03],
[9.9743e-01, 3.8527e-03],
[9.9814e-01, 2.2351e-03],
[9.9743e-01, 3.8527e-03],
[3.8827e-09, 1.0000e+00],
[1.3917e-02, 7.9466e-01],
[1.8448e-12, 1.0000e+00],
[9.3678e-01, 1.2654e-01],
[8.6688e-01, 7.2733e-02],
[9.9743e-01, 3.8527e-03],
[1.2383e-01, 6.9659e-01],
[9.9743e-01, 3.8527e-03],
[7.5396e-01, 8.5081e-01],
[9.9743e-01, 3.8527e-03],
[1.3128e-10, 1.0000e+00],
[9.9743e-01, 3.8527e-03],
[9.5502e-02, 7.4431e-01],
[9.9743e-01, 3.8527e-03],
[6.9585e-05, 9.9997e-01],
[9.9743e-01, 3.8527e-03],
[1.1055e-05, 9.9998e-01],
[9.9886e-01, 1.6518e-03],
[9.9743e-01, 3.8527e-03],
[7.8349e-01, 3.1409e-01],
[9.9743e-01, 3.8527e-03],
[9.9780e-01, 6.9446e-03],
[9.3485e-01, 5.2395e-01],
[8.8307e-04, 9.8842e-01],
[9.9743e-01, 3.8527e-03],
[1.0994e-02, 8.9741e-01],
[9.9743e-01, 3.8527e-03],
[9.7979e-01, 1.4604e-02],
[2.9762e-05, 9.9999e-01],
[9.9743e-01, 3.8527e-03],
[9.9743e-01, 3.8527e-03],
[9.9886e-01, 1.6518e-03],
[9.9743e-01, 3.8527e-03],
[9.9743e-01, 3.8527e-03],
[9.9743e-01, 3.8527e-03],
[4.3081e-01, 1.7872e-01],
[7.2814e-01, 1.1719e-01],
[9.9743e-01, 3.8527e-03],
[3.6993e-03, 9.9986e-01],
[9.9743e-01, 3.8527e-03],
[9.9743e-01, 3.8527e-03],
[3.8542e-04, 9.9996e-01],
[9.9743e-01, 3.8527e-03],
[1.4371e-11, 1.0000e+00],
[4.3835e-03, 8.5417e-01],
[2.0905e-11, 1.0000e+00],
[2.0697e-07, 1.0000e+00],
[9.9596e-01, 4.3470e-02],
[1.5809e-03, 9.9922e-01],
[2.1112e-07, 1.0000e+00],
[9.9743e-01, 3.8527e-03],
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In [ ]:
#sous la forme d'un data frame pandas
p_hidden = pandas.DataFrame(hidden.detach().numpy(),columns=['F1','F2'])
p_hidden.head()
Out[ ]:
| F1 | F2 | |
|---|---|---|
| 0 | 9.974290e-01 | 0.003853 |
| 1 | 6.053422e-01 | 0.699923 |
| 2 | 8.877845e-07 | 0.999991 |
| 3 | 5.495754e-11 | 1.000000 |
| 4 | 1.057500e-08 | 0.999999 |
In [ ]:
#associer la classe d'apparenance au data frame
p_hidden['classe'] = pdTrain.classe
p_hidden.head()
Out[ ]:
| F1 | F2 | classe | |
|---|---|---|---|
| 0 | 9.974290e-01 | 0.003853 | begnin |
| 1 | 6.053422e-01 | 0.699923 | begnin |
| 2 | 8.877845e-07 | 0.999991 | malignant |
| 3 | 5.495754e-11 | 1.000000 | malignant |
| 4 | 1.057500e-08 | 0.999999 | malignant |
In [ ]:
#affichage des points dans le plan "factoriel"
import seaborn as sns
sns.scatterplot(data=p_hidden,x='F1',y='F2',hue='classe')
Out[ ]:
<Axes: xlabel='F1', ylabel='F2'>
In [ ]:
#rappel de la droite de séparation : couche cachée -> sortie
print(f"Coefficients : {pmc.layer2.weight}")
print(f"Intercept : {pmc.layer2.bias}")
Coefficients : Parameter containing: tensor([[-3.6089, 3.8023]], requires_grad=True) Intercept : Parameter containing: tensor([-1.0974], requires_grad=True)
In [ ]:
#récupération des coefficients et de l'intercept
coef = pmc.layer2.weight.detach().numpy()[0]
intercept = pmc.layer2.bias.detach().numpy()
print(coef)
print(intercept)
[-3.60885 3.8022952] [-1.0974166]
In [ ]:
#coordoonées de F2 quand F1 = 0
f2_0 = -intercept/coef[1]
print(f2_0)
[0.28861952]
In [ ]:
#coordoonées de F2 quand F1 = 1
f2_1 = (-intercept - coef[0] * 1)/coef[1]
print(f2_1)
[1.2377436]
In [ ]:
#droite de séparation dans l'espace intermédiaire
plt.plot(numpy.array([0,1]),numpy.array([f2_0,f2_1]),'k-')
sns.scatterplot(data=p_hidden,x='F1',y='F2',hue='classe')
plt.show()
