def init_q_with_kmeans(self,data):
'''
Fonction qui initialise notre algorithme EM
Paramètres: data:(np.array(nb_samples,nb_composante)) Les échantillons sur lesquels sera calculé EM
'''
self.q_e_step = np.zeros([data.shape[0],self.k])
km = KMeans(self.k)
km.fit(data)
prediction = km.predict(data)
for i in range(data.shape[0]):
self.q_e_step[i,prediction[i]]=1
def _init_parameters(self,data) :
if self.init == 'random' :
self.mu = data[np.random.choice(data.shape[0], self.k, replace=False)]
self.pi = [1/self.k for j in range(self.k)]
self.q = 1/self.k * np.ones((data.shape[0],self.k))
elif self.init == 'kmeans' :
clf = KMeans(k=self.k, random_seed=self.random_seed, init='kmeans++')
clf.fit(data)
self.mu = clf.centers
self.pi = [np.sum(clf.labels==j)/data.shape[0] for j in range(self.k)]
self.q = np.zeros((data.shape[0],self.k))
for index, label in np.ndenumerate(clf.labels):
self.q[index,int(label)] = 1
self.sigma = np.zeros((self.k,data.shape[1],data.shape[1]))
if self.format_covariance == 'isotropic' :
for j in range(self.k) :
sigma_squared = sum([self.q[i,j]*np.dot(x_i-self.mu[j, :], x_i-self.mu[j, :]) for (i,x_i) in enumerate(data)])/(2*np.sum(self.q[:, j]))
self.sigma[j] = sigma_squared * np.identity(data.shape[1])
elif self.format_covariance == 'general' :
for j in range(self.k) :
mu_j = self.mu[j, :].reshape((-1, 1))
self.sigma[j] = sum([self.q[i,j]*(x_i.reshape((-1,1))-mu_j).dot(x_i.reshape((-1,1)).T-mu_j.T) for (i,x_i) in enumerate(data)])/np.sum(self.q[:, j])