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@ -14,10 +14,14 @@
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\section{Quantification}
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\subsection{Quantification uniforme}
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\inputminted{python}{../algo_code/quantif.py}
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\newpage
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\subsection{Algorithme de Llyod-max}
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\inputminted{python}{../algo_code/llyod_max.py}
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\newpage
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\subsection{Algorithme LBG}
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en 2D , ne pas essayer de tracer les cellule de voronoi
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\inputminted{python}{../algo_code/LBG.py}
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\section{Codeur prédictif}
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Construire un schéma de prédiction en boucle fermée à fenêtre glissante dasn lequel $M$et $p$ sont paramétrisable. On utilisera un quantificateur à zone morte de pas $\Delta$ paramétrisable.
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\section{KLT}
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@ -2,9 +2,8 @@
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# -*- coding: utf-8 -*-
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import numpy as np
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import matplotlib.pyplot as plt
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from scipy.spatial import Voronoi, voronoi_plot_2d
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#
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#initialisations clusters
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M = 20;
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N =100; #point par cluster
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K = N*M
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@ -17,15 +16,12 @@ for m in range(M):
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X[m*N:(m+1)*N] = xi
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plt.plot(xi[:,0],xi[:,1],'+')
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plt.plot(means[:,0],means[:,1],'ob')
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mean= np.mean(X,axis=0)
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Y0 = np.random.multivariate_normal(mean, 10*cov, M)
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plt.show()
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print(Y0)
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Y0= means
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Y0= means #triche
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plt.plot(Y0[:,0],Y0[:,1],'ok')
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plt.show()
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def LBG(X,Y0,eps=1e-5,maxiter=1000):
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Y = Y0.copy()
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old_dist = np.inf
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@ -41,17 +37,15 @@ def LBG(X,Y0,eps=1e-5,maxiter=1000):
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dist += sum((X[k]-quant_min)**2)
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for j in range(len(Y)):
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Y[j,:] = np.mean(X[cluster_index==j],axis=0)
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print(Y)
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if dist-old_dist < eps:
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break
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else:
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old_dist = dist
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return Y
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Y = LBG(X,Y0)
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vor = Voronoi(Y)
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vor = Voronoi(Y)# black magic
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voronoi_plot_2d(vor,show_vertices=False)
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print(Y)
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plt.plot(X[:,0],X[:,1],'+')
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plt.plot(Y[:,0],Y[:,1],'ob')
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plt.plot(Y0[:,0],Y0[:,1],'ok')
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plt.show()
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plt.show()
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@ -5,8 +5,7 @@ from scipy.stats import norm
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import matplotlib.pyplot as plt
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def ddp(x):
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mean = 0,
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sigma = 1
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mean = 0; sigma = 1
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return norm.pdf(x,mean,sigma)
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def quant(centroids, X):
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@ -34,7 +33,6 @@ def llyodMax(X,M,maxiter=1000,eps=1e-6):
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/integrate.quad(lambda x: ddp(x),bornes[i],bornes[i+1])[0]
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bornes[1:-1] = (centroids[:-1]+centroids[1:])/2
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err = np.linalg.norm(centroids-old_centroids)
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print(err)
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if err < eps :
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break
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return centroids
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X = np.random.normal(0,1,1000)
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centroids = llyodMax(X,M)
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bornes = (centroids[:-1]+centroids[1:])/2
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bornes = np.insert(bornes,0,-np.inf)
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bornes = np.append(bornes,np.inf)
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print(centroids, bornes)
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bornes = np.insert(bornes,0,-np.inf); bornes = np.append(bornes,np.inf)
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plt.figure()
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plt.plot(X)
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plt.plot(quant(bornes,X))
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