EM solution of mixed Gaussian model (mixtures of Gaussians) and Python implementation source code

Today we bring the solution of EM derivation for mixed Gaussian model.

All codes are as follows!

def Ndimensiongaussian (X_vector,u_mean,covariancematrix): #X =numpy.mat (x_vector) x=x_vector D=numpy.shape (X) [0] #U =numpy.mat (U_mean) U=u_mean #CM =numpy.mat (covariancematrix) Cm=covariancematrix y=x-u temp=y.transpose ( ) * CM. I * Y result= (1.0/((2*NUMPY.PI) * * (D/2))) * (1.0/(Numpy.linalg.det (CM) **0.5)) *numpy.exp ( -0.5*temp) return resultdef Cal             Mean (x): D,n=numpy.shape (x) Meanvector=numpy.mat (Numpy.zeros ((d,1))) for D in range (d): for n in range (n): meanvector[d,0] + = X[d,n] meanvector[d,0]/= float (n) return meanvectordef calcovariance (X,MV): D , N=numpy.shape (X) Cov=numpy.mat (Numpy.zeros ((d,d))) for N in range (n): temp=x[:,n]-mv CoV + = Temp*temp . Transpose () CoV/= float (N) return covdef Calenergy (Xn,pik,uk,cov): D,n=numpy.shape (Xn) D_k,k=numpy.shape (U        k) if D!=d_k:print (' dimension not Equal, Break ') return energy=0.0 for N_iter in range (n):      Temp=0   For K_iter in range (k): temp + = pik[0,k_iter] * Ndimensiongaussian (Xn[:,n_iter],uk[:,k_iter],cov[k_iter]) Energy + = Numpy.log (temp) return float (energy) def Sequentialemformixgaussian (inputdata,k): #初始化piK pi_cof=nu Mpy.mat (Numpy.ones ((1,k)) * (1.0/float (K))) X=numpy.mat (Inputdata) X_mean=calmean (X) print (X_mean) X_cov=calcov Ariance (X,x_mean) print (X_cov) #初始化uK, where column K represents the mean vector #X为D维 of the K-Gaussian function, N sample points D,n=numpy.shape (X) print (d,n) UK =numpy.mat (Numpy.zeros ((d,k))) for D_iter in range (D): For K_iter in Range (K): uk[d_iter,k_iter] = X_ mean[d_iter,0] + ( -1) **k_iter + ( -1) **d_iter print (UK) #初始化k个协方差矩阵的列表 list_cov=[] for K_iter in range (k) : List_cov.append (Numpy.mat (Numpy.eye (x[:,0].size))) print (List_cov) list_cov_new=copy.deepcopy (List_cov ) Rznk=numpy.mat (Numpy.zeros ((n,k)) Denominator=numpy.mat (Numpy.zeros ((n,1))) Rznk_new=numpy.mat (Numpy.zeros (N, K)) Nk=0.5*numpy. MAT (Numpy.ones (1,k)) print (Nk) Nk_new=numpy.mat (Numpy.zeros ((1,k))) Uk_new=numpy.mat (Numpy.zeros ((d,k))) p I_cof_new=numpy.mat (Numpy.zeros ((1,k))) for N_iter in range (1,n): #rZnk =pi_k*gaussian (Xn|uk,cov_k)/sum (pi_j* Gaussian (Xn|uj,cov_j)) for K_iter in range (k): rznk_new[n_iter,k_iter] = pi_cof[0,k_iter] * Ndimensionga             Ussian (X[:,n_iter],uk[:,k_iter],list_cov[k_iter]) denominator[n_iter,0] + = Rznk_new[n_iter,k_iter] For K_iter in range (k): Rznk_new[n_iter,k_iter]/= denominator[n_iter,0] Print (' Rznk_new ', rznk_new [N_iter,k_iter], ' \ n ') for K_iter in range (k): nk_new[0,k_iter] = Nk[0,k_iter] + rznk_new[n_it Er,k_iter]-rznk[n_iter,k_iter] Print (' nk_new ', nk_new, ' \ n ') ############# #当前有 (n_iter+1) sample ######### ################## Pi_cof_new[0,k_iter] = nk_new[0,k_iter]/float (n_iter+1) print (' Pi_cof_new ', pi_           Cof_new, ' \ n ') Uk_new[:,k_iter] = Uk[:,k_iter] + ((Rznk_new[n_iter,k_iter]-rznk[n_iter,k_iter])/float (nk_new[0,k_iter)) * (X[:,n_i            Ter]-uk[:,k_iter]) print (' Uk_new ', uk_new, ' \ n ') Temp = X[:,n_iter]-Uk_new[:,k_iter] List_cov_new[k_iter] = List_cov[k_iter] + ((Rznk_new[n_iter,k_iter]-rznk[n_iter,k_iter])/float (Nk_new[0,k_iter])) * (Temp*temp.transpose ()-list_cov[k_iter]) print (' List_cov_new ', list_cov_new, ' \ n ') Rznk=co Py.deepcopy (rznk_new) pi_cof=copy.deepcopy (pi_cof_new) uk_new=copy.deepcopy (UK) List_cov=copy.deepcop Y (list_cov_new) print (Pi_cof,uk_new,list_cov) return pi_cof,uk_new,list_covdef Batchemformixgaussian (InputData,K,M    Axiter): #初始化piK Pi_cof=numpy.mat (Numpy.ones ((1,k)) * (1.0/float (K))) X=numpy.mat (Inputdata) X_mean=calmean (X) Print (X_mean) x_cov=calcovariance (x,x_mean) print (X_cov) #初始化uK, where the K column represents the mean vector #X为D维 of the K-Gaussian function, and N sample points D,n=num Py.shape (X) print (d,n)    Uk=numpy.mat (Numpy.zeros ((d,k))) for D_iter in range (D): For K_iter in Range (K): Uk[d_iter,k_iter ] = x_mean[d_iter,0] + ( -1) **k_iter + ( -1) **d_iter print (UK) #初始化k个协方差矩阵的列表 list_cov=[] for k_iter in RA Nge (K): List_cov.append (Numpy.mat (Numpy.eye (x[:,0].size))) print (List_cov) energy_new=0 Energy_old=ca                Lenergy (X,pi_cof,uk,list_cov) print (energy_old) currentiter=0 while true:currentiter + = 1 List_cov_new=[] Rznk=numpy.mat (Numpy.zeros (n,k)) Denominator=numpy.mat (Numpy.zeros ((n,1))) Nk=nump                Y.mat (Numpy.zeros ((1,k)) Uk_new=numpy.mat (Numpy.zeros ((d,k))) Pi_new=numpy.mat (Numpy.zeros ((1,K))) #rZnk =pi_k*gaussian (Xn|uk,cov_k)/sum (Pi_j*gaussian (Xn|uj,cov_j)) for N_iter in range (n): for k_i ter in range (K): rznk[n_iter,k_iter] = pi_cof[0,k_iter] * Ndimensiongaussian (x[:,n_iter],uk[:,k_iter],list_            Cov[k_iter])    denominator[n_iter,0] + = Rznk[n_iter,k_iter] for K_iter in range (k): Rznk[n_iter,k_iter                ]/= denominator[n_iter,0] #print ' rznk ', Rznk[n_iter,k_iter] #pi_new =sum (RZNK)            For K_iter in range (k): For N_iter in range (n): nk[0,k_iter] + = Rznk[n_iter,k_iter] Pi_new[0,k_iter] = nk[0,k_iter]/(float (N)) #print ' pi_k_new ', pi_new[0,k_iter] #uk_new = (1/sum ( RZNK)) *sum (RZNK*XN) for K_iter in range (k): For N_iter in range (n): Uk_new[:,k_iter]                    + = (1.0/float (Nk[0,k_iter])) *rznk[n_iter,k_iter]*x[:,n_iter] #print ' uk_new ', Uk_new[:,k_iter]                For K_iter in range (k): X_cov_new=numpy.mat (Numpy.zeros ((d,d))) for N_iter in range (n): Temp = X[:,n_iter]-Uk_new[:,k_iter] x_cov_new + = (1.0/float (nk[0,k_iter))) *rznk[n_iter,k_iter] * Tem    P * Temp.transpose ()        #print ' x_cov_new ', x_cov_new list_cov_new.append (x_cov_new) Energy_new=calenergy (x,pi_ne W,uk_new,list_cov) print (' Energy_new ', energy_new) #print pi_new #print uk_new #print List_cov _new if Energy_old>=energy_new or currentiter>maxiter:uk=copy.deepcopy (uk_new) pi_cof= Copy.deepcopy (pi_new) list_cov=copy.deepcopy (list_cov_new) Break Else:uk=copy.dee Pcopy (uk_new) pi_cof=copy.deepcopy (pi_new) list_cov=copy.deepcopy (list_cov_new) Energy_ol D=energy_new return Pi_cof,uk,list_cov

EM solution of mixed Gaussian model (mixtures of Gaussians) and Python implementation source code