def generate_images_iterations_ll(Xs,mus,covs, Ks ,myDManager, logl,theta_list,model_theta_list,folder_images_gif):
# os.remove(folder_images_gif) # Remove previous images if existing
"""
WARNING: MEANT FOR ONLY 3 Distributions due to the color RGB
"""
import shutil
ul.create_folder_if_needed(folder_images_gif)
shutil.rmtree(folder_images_gif)
ul.create_folder_if_needed(folder_images_gif)
######## Plot the original data #####
Xdata = np.concatenate(Xs,axis = 1).T
colors = ["r","b","g"]
K_G,K_W,K_vMF = Ks
### FOR EACH ITERATION
for i in range(len(theta_list)): # theta_list
indx = i
gl.init_figure()
ax1 = gl.subplot2grid((1,2), (0,0), rowspan=1, colspan=1)
## Get the relative ll of the Gaussian denoising cluster.
ll = myDManager.pdf_log_K(Xdata,theta_list[indx])
N,K = ll.shape
# print ll.shape
for j in range(N): # For every sample
#TODO: Can this not be done without a for ?
# Normalize the probability of the sample being generated by the clusters
Marginal_xi_probability = gf.sum_logs(ll[j,:])
ll[j,:] = ll[j,:]- Marginal_xi_probability
ax1 = gl.scatter(Xdata[j,0],Xdata[j,1], labels = ['EM Evolution. Kg:'+str(K_G)+ ', Kw:' + str(K_W) + ', K_vMF:' + str(K_vMF), "X1","X2"],
color = (np.exp(ll[j,1]), np.exp(ll[j,0]), np.exp(ll[j,2])) , ### np.exp(ll[j,2])
alpha = 1, nf = 0)
# Only doable if the clusters dont die
for k_c in myDManager.clusterk_to_Dname.keys():
k = myDManager.clusterk_to_thetak[k_c]
distribution_name = myDManager.clusterk_to_Dname[k_c] # G W
if (distribution_name == "Gaussian"):
## Plot the ecolution of the mu
#### Plot the Covariance of the clusters !
mean,w,h,theta = bMA.get_gaussian_ellipse_params( mu = theta_list[indx][k][0], Sigma = theta_list[indx][k][1], Chi2val = 2.4477)
r_ellipse = bMA.get_ellipse_points(mean,w,h,theta)
gl.plot(r_ellipse[:,0], r_ellipse[:,1], ax = ax1, ls = "-.", lw = 3,
AxesStyle = "Normal2",
legend = ["Kg(%i). pi:%0.2f"%(k, float(model_theta_list[indx][0][0,k]))])
elif(distribution_name == "Watson"):
#### Plot the pdf of the distributino !
## Distribution parameters for Watson
kappa = float(theta_list[indx][k][1]); mu = theta_list[-1][k][0]
Nsa = 1000
# Draw 2D samples as transformation of the angle
Xalpha = np.linspace(0, 2*np.pi, Nsa)
Xgrid= np.array([np.cos(Xalpha), np.sin(Xalpha)])
probs = [] # Vector with probabilities
for i in range(Nsa):
probs.append(np.exp(Wad.Watson_pdf_log(Xgrid[:,i],[mu,kappa]) ))
probs = np.array(probs)
# Plot it in polar coordinates
X1_w = (1 + probs) * np.cos(Xalpha)
X2_w = (1 + probs) * np.sin(Xalpha)
gl.plot(X1_w,X2_w,
alpha = 1, lw = 3, ls = "-.", legend = ["Kw(%i). pi:%0.2f"%(k, float(model_theta_list[indx][0][0,k]))])
elif(distribution_name == "vonMisesFisher"):
#### Plot the pdf of the distributino !
## Distribution parameters for Watson
kappa = float(theta_list[indx][k][1]); mu = theta_list[indx][k][0]
Nsa = 1000
# Draw 2D samples as transformation of the angle
Xalpha = np.linspace(0, 2*np.pi, Nsa)
Xgrid= np.array([np.cos(Xalpha), np.sin(Xalpha)])
probs = [] # Vector with probabilities
for i in range(Nsa):
probs.append(np.exp(vMFd.vonMisesFisher_pdf_log(Xgrid[:,i],[mu,kappa]) ))
probs = np.array(probs)
probs = probs.reshape((probs.size,1)).T
# Plot it in polar coordinates
X1_w = (1 + probs) * np.cos(Xalpha)
X2_w = (1 + probs) * np.sin(Xalpha)
# print X1_w.shape, X2_w.shape
gl.plot(X1_w,X2_w,
alpha = 1, lw = 3, ls = "-.", legend = ["Kvmf(%i). pi:%0.2f"%(k, float(model_theta_list[indx][0][0,k]))])
gl.set_zoom(xlim = [-6,6], ylim = [-6,6], ax = ax1)
ax2 = gl.subplot2grid((1,2), (0,1), rowspan=1, colspan=1)
if (indx == 0):
gl.add_text(positionXY = [0.1,.5], text = r' Initilization Incomplete LogLike: %.2f'%(logl[0]),fontsize = 15)
pass
elif (indx >= 1):
gl.plot(range(1,np.array(logl).flatten()[1:].size +1),np.array(logl).flatten()[1:(indx+1)], ax = ax2,
legend = ["Iteration %i, Incom LL: %.2f"%(indx, logl[indx])], labels = ["Convergence of LL with generated data","Iterations","LL"], lw = 2)
gl.scatter(1, logl[1], lw = 2)
pt = 0.05
gl.set_zoom(xlim = [0,len(logl)], ylim = [logl[1] - (logl[-1]-logl[1])*pt,logl[-1] + (logl[-1]-logl[1])*pt], ax = ax2)
gl.subplots_adjust(left=.09, bottom=.10, right=.90, top=.95, wspace=.2, hspace=0.01)
gl.savefig(folder_images_gif +'gif_'+ str(indx) + '.png',
dpi = 100, sizeInches = [16, 8], close = "yes",bbox_inches = None)
gl.close("all")
def plot_2D_clusters(myDManager, clusters_relation, theta, model_theta, ax):
"""
This function plots the 2D clusters in the axes provided
"""
if(clusters_relation == "MarkovChain1"):
model_theta[0] = HMMlf.get_stationary_pi(model_theta[0], model_theta[1])
# Only doable if the clusters dont die
for k_c in myDManager.clusterk_to_Dname.keys():
k = myDManager.clusterk_to_thetak[k_c]
distribution_name = myDManager.clusterk_to_Dname[k_c] # G W
if (distribution_name == "Gaussian" ):
## Plot the ecolution of the mu
#### Plot the Covariance of the clusters !
mean,w,h, angle_theta = bMA.get_gaussian_ellipse_params( mu = theta[k][0], Sigma = theta[k][1], Chi2val = 2.4477)
r_ellipse = bMA.get_ellipse_points(mean,w,h,angle_theta)
gl.plot(r_ellipse[:,0], r_ellipse[:,1], ax = ax, ls = "-.", lw = 3,
AxesStyle = "Normal2",
legend = ["Kg(%i). pi:%0.2f"%(k, float(model_theta[0][0,k]))])
if (distribution_name == "Gaussian2" ):
## Plot the ecolution of the mu
#### Plot the Covariance of the clusters !
mean,w,h,angle_theta = bMA.get_gaussian_ellipse_params( mu = theta[k][0], Sigma = theta[k][1], Chi2val = 2.4477)
r_ellipse = bMA.get_ellipse_points(mean,w,h,angle_theta)
gl.plot(r_ellipse[:,0], r_ellipse[:,1], ax = ax, ls = "-.", lw = 3,
AxesStyle = "Normal2",
legend = ["Kgd(%i). pi:%0.2f"%(k, float(model_theta[0][0,k]))])
elif(distribution_name == "Watson"):
#### Plot the pdf of the distributino !
## Distribution parameters for Watson
kappa = float(theta[k][1])
mu = theta[k][0]
Nsa = 1000
# Draw 2D samples as transformation of the angle
Xalpha = np.linspace(0, 2*np.pi, Nsa)
Xgrid= np.array([np.cos(Xalpha), np.sin(Xalpha)])
probs = [] # Vector with probabilities
for i in range(Nsa):
probs.append(np.exp(Wad.Watson_pdf_log(Xgrid[:,i],[mu,kappa]) ))
probs = np.array(probs)
# Plot it in polar coordinates
X1_w = (1 + probs) * np.cos(Xalpha)
X2_w = (1 + probs) * np.sin(Xalpha)
gl.plot(X1_w,X2_w,
alpha = 1, lw = 3, ls = "-.",legend = ["Kw(%i). pi:%0.2f"%(k, float(model_theta[0][0,k]))])
elif(distribution_name == "vonMisesFisher"):
#### Plot the pdf of the distributino !
## Distribution parameters for Watson
kappa = float(theta[k][1]);
mu = theta[k][0]
Nsa = 1000
# Draw 2D samples as transformation of the angle
Xalpha = np.linspace(0, 2*np.pi, Nsa)
Xgrid= np.array([np.cos(Xalpha), np.sin(Xalpha)])
probs = [] # Vector with probabilities
for i in range(Nsa):
probs.append(np.exp(vMFd.vonMisesFisher_pdf_log(Xgrid[:,i],[mu,kappa]) ))
probs = np.array(probs)
probs = probs.reshape((probs.size,1)).T
# Plot it in polar coordinates
X1_w = (1 + probs) * np.cos(Xalpha)
X2_w = (1 + probs) * np.sin(Xalpha)
gl.plot(X1_w,X2_w,
alpha = 1, lw = 3, ls = "-.", legend = ["Kvmf(%i). pi:%0.2f"%(k, float(model_theta[0][0,k]))])
def plot_final_distribution(Xs,mus,covs, Ks ,myDManager, logl,theta_list,model_theta_list, folder_images):
colors = ["r","b","g"]
K_G,K_W,K_vMF = Ks
################## Print the Watson and Gaussian Distribution parameters ###################
for k_c in myDManager.clusterk_to_Dname.keys():
k = myDManager.clusterk_to_thetak[k_c]
distribution_name = myDManager.clusterk_to_Dname[k_c] # G W
if (distribution_name == "Gaussian"):
print ("------------ Gaussian Cluster. K = %i--------------------"%k)
print ("mu")
print (theta_list[-1][k][0])
print ("Sigma")
print (theta_list[-1][k][1])
elif(distribution_name == "Watson"):
print ("------------ Watson Cluster. K = %i--------------------"%k)
print ("mu")
print (theta_list[-1][k][0])
print ("Kappa")
print (theta_list[-1][k][1])
elif(distribution_name == "vonMisesFisher"):
print ("------------ vonMisesFisher Cluster. K = %i--------------------"%k)
print ("mu")
print (theta_list[-1][k][0])
print ("Kappa")
print (theta_list[-1][k][1])
print ("pimix")
print (model_theta_list[-1])
mus_Watson_Gaussian = []
# k_c is the number of the cluster inside the Manager. k is the index in theta
for k_c in myDManager.clusterk_to_Dname.keys():
k = myDManager.clusterk_to_thetak[k_c]
distribution_name = myDManager.clusterk_to_Dname[k_c] # G W
mus_k = []
for iter_i in range(len(theta_list)): # For each iteration of the algorihtm
if (distribution_name == "Gaussian"):
theta_i = theta_list[iter_i][k]
mus_k.append(theta_i[0])
elif(distribution_name == "Watson"):
theta_i = theta_list[iter_i][k]
mus_k.append(theta_i[0])
elif(distribution_name == "vonMisesFisher"):
theta_i = theta_list[iter_i][k]
mus_k.append(theta_i[0])
mus_k = np.concatenate(mus_k, axis = 1).T
mus_Watson_Gaussian.append(mus_k)
######## Plot the original data #####
gl.init_figure();
## First cluster
for xi in range(len( Xs)):
## First cluster
ax1 = gl.scatter(Xs[xi][0,:],Xs[xi][1,:], labels = ['EM Evolution. Kg:'+str(K_G)+ ', Kw:' + str(K_W) + ', K_vMF:' + str(K_vMF), "X1","X2"],
color = colors[xi] ,alpha = 0.2, nf = 0)
mean,w,h,theta = bMA.get_gaussian_ellipse_params( mu = mus[xi], Sigma = covs[xi], Chi2val = 2.4477)
r_ellipse = bMA.get_ellipse_points(mean,w,h,theta)
gl.plot(r_ellipse[:,0], r_ellipse[:,1], ax = ax1, ls = "--", lw = 2
,AxesStyle = "Normal2", color = colors[xi], alpha = 0.7)
indx = -1
# Only doable if the clusters dont die
Nit,Ndim = mus_Watson_Gaussian[0].shape
for k_c in myDManager.clusterk_to_Dname.keys():
k = myDManager.clusterk_to_thetak[k_c]
distribution_name = myDManager.clusterk_to_Dname[k_c] # G W
if (distribution_name == "Gaussian"):
## Plot the ecolution of the mu
#### Plot the Covariance of the clusters !
mean,w,h,theta = bMA.get_gaussian_ellipse_params( mu = theta_list[indx][k][0], Sigma = theta_list[indx][k][1], Chi2val = 2.4477)
r_ellipse = bMA.get_ellipse_points(mean,w,h,theta)
gl.plot(r_ellipse[:,0], r_ellipse[:,1], ax = ax1, ls = "-.", lw = 3,
AxesStyle = "Normal2",
legend = ["Kg(%i). pi:%0.2f"%(k, float(model_theta_list[indx][0][0,k]))])
gl.scatter(mus_Watson_Gaussian[k][:,0], mus_Watson_Gaussian[k][:,1], nf = 0, na = 0, alpha = 0.3, lw = 1,
color = "y")
gl.plot(mus_Watson_Gaussian[k][:,0], mus_Watson_Gaussian[k][:,1], nf = 0, na = 0, alpha = 0.8, lw = 2,
color = "y")
elif(distribution_name == "Watson"):
#### Plot the pdf of the distributino !
## Distribution parameters for Watson
kappa = float(theta_list[indx][k][1])
mu = theta_list[indx][k][0]
Nsa = 1000
# Draw 2D samples as transformation of the angle
Xalpha = np.linspace(0, 2*np.pi, Nsa)
Xgrid= np.array([np.cos(Xalpha), np.sin(Xalpha)])
probs = [] # Vector with probabilities
for i in range(Nsa):
probs.append(np.exp(Wad.Watson_pdf_log(Xgrid[:,i],[mu,kappa]) ))
probs = np.array(probs)
# Plot it in polar coordinates
X1_w = (1 + probs) * np.cos(Xalpha)
X2_w = (1 + probs) * np.sin(Xalpha)
gl.plot(X1_w,X2_w, legend = ["Kw(%i). pi:%0.2f"%(k, float(model_theta_list[indx][0][0,k]))] ,
alpha = 1, lw = 3, ls = "-.")
elif(distribution_name == "vonMisesFisher"):
#### Plot the pdf of the distributino !
## Distribution parameters for Watson
kappa = float(theta_list[indx][k][1])
mu = theta_list[indx][k][0]
Nsa = 1000
# Draw 2D samples as transformation of the angle
Xalpha = np.linspace(0, 2*np.pi, Nsa)
Xgrid= np.array([np.cos(Xalpha), np.sin(Xalpha)])
probs = [] # Vector with probabilities
for i in range(Nsa):
probs.append(np.exp(vMFd.vonMisesFisher_pdf_log(Xgrid[:,i],[mu,kappa]) ))
probs = np.array(probs)
probs = probs.reshape((probs.size,1)).T
# Plot it in polar coordinates
X1_w = (1 + probs) * np.cos(Xalpha)
X2_w = (1 + probs) * np.sin(Xalpha)
# print X1_w.shape, X2_w.shape
gl.plot(X1_w,X2_w,
alpha = 1, lw = 3, ls = "-.", legend = ["Kvmf(%i). pi:%0.2f"%(k, float(model_theta_list[indx][0][0,k]))])
ax1.axis('equal')
gl.savefig(folder_images +'Final_State. K_G:'+str(K_G)+ ', K_W:' + str(K_W) + ', K_vMF:' + str(K_vMF) + '.png',
dpi = 100, sizeInches = [12, 6])
def plot_multiple_iterations(Xs,mus,covs, Ks ,myDManager, logl,theta_list,model_theta_list, folder_images):
######## Plot the original data #####
gl.init_figure();
gl.set_subplots(2,3);
Ngraph = 6
colors = ["r","b","g"]
K_G,K_W,K_vMF = Ks
for i in range(Ngraph):
indx = int(i*((len(theta_list)-1)/float(Ngraph-1)))
nf = 1
for xi in range(len( Xs)):
## First cluster
labels = ['EM Evolution. Kg:'+str(K_G)+ ', Kw:' + str(K_W) + ', K_vMF:' + str(K_vMF), "X1","X2"]
ax1 = gl.scatter(Xs[xi][0,:],Xs[xi][1,:],labels = ["","",""] ,
color = colors[xi] ,alpha = 0.2, nf = nf)
nf =0
mean,w,h,theta = bMA.get_gaussian_ellipse_params( mu = mus[xi], Sigma = covs[xi], Chi2val = 2.4477)
r_ellipse = bMA.get_ellipse_points(mean,w,h,theta)
gl.plot(r_ellipse[:,0], r_ellipse[:,1], ax = ax1, ls = "--", lw = 2
,AxesStyle = "Normal2", color = colors[xi], alpha = 0.7)
# Only doable if the clusters dont die
for k_c in myDManager.clusterk_to_Dname.keys():
k = myDManager.clusterk_to_thetak[k_c]
distribution_name = myDManager.clusterk_to_Dname[k_c] # G W
if (distribution_name == "Gaussian"):
## Plot the ecolution of the mu
#### Plot the Covariance of the clusters !
mean,w,h,theta = bMA.get_gaussian_ellipse_params( mu = theta_list[indx][k][0], Sigma = theta_list[indx][k][1], Chi2val = 2.4477)
r_ellipse = bMA.get_ellipse_points(mean,w,h,theta)
gl.plot(r_ellipse[:,0], r_ellipse[:,1], ax = ax1, ls = "-.", lw = 3,
AxesStyle = "Normal2",
legend = ["Kg(%i). pi:%0.2f"%(k, float(model_theta_list[indx][0][0,k]))])
elif(distribution_name == "Watson"):
#### Plot the pdf of the distributino !
## Distribution parameters for Watson
kappa = float(theta_list[indx][k][1])
mu = theta_list[indx][k][0]
Nsa = 1000
# Draw 2D samples as transformation of the angle
Xalpha = np.linspace(0, 2*np.pi, Nsa)
Xgrid= np.array([np.cos(Xalpha), np.sin(Xalpha)])
probs = [] # Vector with probabilities
for i in range(Nsa):
probs.append(np.exp(Wad.Watson_pdf_log(Xgrid[:,i],[mu,kappa]) ))
probs = np.array(probs)
# Plot it in polar coordinates
X1_w = (1 + probs) * np.cos(Xalpha)
X2_w = (1 + probs) * np.sin(Xalpha)
gl.plot(X1_w,X2_w,
alpha = 1, lw = 3, ls = "-.",legend = ["Kw(%i). pi:%0.2f"%(k, float(model_theta_list[indx][0][0,k]))])
elif(distribution_name == "vonMisesFisher"):
#### Plot the pdf of the distributino !
## Distribution parameters for Watson
kappa = float(theta_list[indx][k][1]); mu = theta_list[indx][k][0]
Nsa = 1000
# Draw 2D samples as transformation of the angle
Xalpha = np.linspace(0, 2*np.pi, Nsa)
Xgrid= np.array([np.cos(Xalpha), np.sin(Xalpha)])
probs = [] # Vector with probabilities
for i in range(Nsa):
probs.append(np.exp(vMFd.vonMisesFisher_pdf_log(Xgrid[:,i],[mu,kappa]) ))
probs = np.array(probs)
probs = probs.reshape((probs.size,1)).T
# Plot it in polar coordinates
X1_w = (1 + probs) * np.cos(Xalpha)
X2_w = (1 + probs) * np.sin(Xalpha)
# print X1_w.shape, X2_w.shape
gl.plot(X1_w,X2_w,
alpha = 1, lw = 3, ls = "-.", legend = ["Kvmf(%i). pi:%0.2f"%(k, float(model_theta_list[indx][0][0,k]))])
ax1.axis('equal')
gl.subplots_adjust(left=.09, bottom=.10, right=.90, top=.95, wspace=.2, hspace=0.01)
gl.savefig(folder_images +'Final_State2. K_G:'+str(K_G)+ ', K_W:' + str(K_W) + '.png',
dpi = 100, sizeInches = [18, 8])
gl.init_figure()
ax1 = gl.scatter(
ret1,
ret2,
alpha=0.2,
color="k",
legend=["Data points %i" % (ret1.size)],
labels=["EM algorithm %i Gaussian fits" % (K), symbol_ID1, symbol_ID2])
for k in range(K):
mu_k = theta_list[-1][k][0]
std_k = theta_list[-1][k][1]
model_theta_last = model_theta_list[-1]
mean, w, h, theta = bMA.get_gaussian_ellipse_params(mu=mu_k,
Sigma=std_k,
Chi2val=2.4477)
r_ellipse = bMA.get_ellipse_points(mean, w, h, theta)
if (len(model_theta_last) == 1):
pi = model_theta_last[0]
gl.plot(r_ellipse[:, 0],
r_ellipse[:, 1],
ax=ax1,
ls="-.",
lw=3,
AxesStyle="Normal2",
legend=["Kg(%i), pi:%.2f" % (k + 1, pi[0, k])])
else:
pi = model_theta_last[0]
A = model_theta_last[1]
def generate_gaussian_data(folder_images, plot_original_data, N1 = 200, N2 = 300, N3 = 50):
mu1 = np.array([[0],[0]])
cov1 = np.array([[0.8,-1.1],
[-1.1,1.6]])
mu2 = np.array([[0],[0]])
cov2 = np.array([[0.3,0.45],
[0.45,0.8]])
mu3 = np.array([[0],[0]])
cov3 = np.array([[0.1,0.0],
[0.0,0.1]])
X1 = np.random.multivariate_normal(mu1.flatten(), cov1, N1).T
X2 = np.random.multivariate_normal(mu2.flatten(), cov2, N2).T
X3 = np.random.multivariate_normal(mu3.flatten(), cov3, N3).T
# samples_X1 = np.array(range(X1.shape[1]))[np.where([X1[0,:] > 0])[0]]
# samples_X1 = np.where(X1[0,:] > 0)[0] # np.array(range(X1.shape[1]))
# print samples_X1
# X1 = X1[:,samples_X1]
# X2 = np.concatenate((X2,X3),axis = 1)
######## Plotting #####
if (plot_original_data):
gl.init_figure();
## First cluster
ax1 = gl.scatter(X1[0,:],X1[1,:], labels = ["Gaussian Generated Data", "x1","x2"],
legend = ["K = 1"], color = "r",alpha = 0.5)
mean,w,h,theta = bMA.get_gaussian_ellipse_params( mu = mu1, Sigma = cov1, Chi2val = 2.4477)
r_ellipse = bMA.get_ellipse_points(mean,w,h,theta)
gl.plot(r_ellipse[:,0], r_ellipse[:,1], ax = ax1, ls = "--", lw = 2
,AxesStyle = "Normal2", color = "r")
## Second cluster
ax1 = gl.scatter(X2[0,:],X2[1,:], legend = ["K = 2"], color = "b", alpha = 0.5)
mean,w,h,theta = bMA.get_gaussian_ellipse_params( mu = mu2, Sigma = cov2, Chi2val = 2.4477)
r_ellipse = bMA.get_ellipse_points(mean,w,h,theta)
gl.plot(r_ellipse[:,0], r_ellipse[:,1], ax = ax1, ls = "--", lw = 2,AxesStyle = "Normal2", color = "b")
## Third cluster
ax1 = gl.scatter(X3[0,:],X3[1,:], legend = ["K = 3"], color = "g", alpha = 0.5)
mean,w,h,theta = bMA.get_gaussian_ellipse_params( mu = mu3, Sigma = cov3, Chi2val = 2.4477)
r_ellipse = bMA.get_ellipse_points(mean,w,h,theta)
gl.plot(r_ellipse[:,0], r_ellipse[:,1], ax = ax1, ls = "--", lw = 2,AxesStyle = "Normal2", color = "g")
ax1.axis('equal')
gl.savefig(folder_images +'Original data.png',
dpi = 100, sizeInches = [12, 6])
############ ESTIMATE THEM ################
theta1 = Gae.get_Gaussian_muSigma_ML(X1.T, parameters = dict([["Sigma","full"]]))
print ("mu1:")
print (theta1[0])
print ("Sigma1")
print(theta1[1])
############## Estimate Likelihood ###################
ll = Gad.Gaussian_pdf_log (X1, [mu1,cov1])
ll2 = []
for i in range (ll.size):
ll2.append( multivariate_normal.logpdf(X1[:,i], mean=mu1.flatten(), cov=cov1))
ll2 = np.array(ll2).reshape(ll.shape)
print ("ll ours")
print (ll.T)
print ("ll scipy")
print (ll2.T)
print ("Difference in ll")
print ((ll - ll2).T)
###### Multiple clusters case
ll_K = Gad.Gaussian_K_pdf_log(X1, [[mu1,cov1],[mu2,cov2]])
if(0):
X1 = gf.remove_module(X1.T).T
X2 = gf.remove_module(X2.T).T
X3 = gf.remove_module(X3.T).T
Xdata = np.concatenate((X1,X2,X3), axis =1).T
return X1,X2,X3,Xdata, mu1,mu2,mu3, cov1,cov2, cov3
# Y distribution
ax3 = gl.subplot2grid((4,4), (1,3), rowspan=3, colspan=1,sharey = ax1,)
gl.histogram(X = ret2, ax = ax3, orientation = "horizontal",
AxesStyle = "Normal - No yaxis",
color = "k", alpha = 0.5)
x_grid, y_val = bMA.gaussian1D_points(X = ret2, std_K = 3)
gl.plot(y_val, x_grid, color = "k",
labels = ["","",""], legend = ["M: %.2e, std: %.2e"%(mean[0], cov[1,1])])
gl.subplots_adjust(left=.09, bottom=.10, right=.90, top=.95, wspace=.01, hspace=0.01)
if(ellipse_graph):
################# Draw the error ellipse #################
mean,w,h,theta = bMA.get_gaussian_ellipse_params(data, Chi2val = 2.4477)
vecs,vals = bMA.get_eigenVectorsAndValues(data)
r_ellipse = bMA.get_ellipse_points(mean,w,h,theta)
gl.plot(r_ellipse[:,0], r_ellipse[:,1], ax = ax1, ls = "--",color = "k", lw = 2,
legend = ["Corr: %.2f"%(corr[0,1])])
gl.plot([mean[0], mean[0] + vecs[0,0]*w],
[mean[1], mean[1] + vecs[0,1]*w], ax = ax1, ls = "--",color = "k")
gl.plot([mean[0], mean[0] + vecs[1,0]*h],
[mean[1], mean[1] + vecs[1,1]*h], ax = ax1, ls = "--",color = "k")
gl.plot([mean[0], mean[0] - vecs[0,0]*w],
[mean[1], mean[1] - vecs[0,1]*w], ax = ax1, ls = "--",color = "k")
gl.plot([mean[0], mean[0] - vecs[1,0]*h],
[mean[1], mean[1] - vecs[1,1]*h], ax = ax1, ls = "--",color = "k")
def plot_final_distribution(Xs, mus, covs, Ks, myDManager, logl, theta_list,
model_theta_list, folder_images):
colors = ["r", "b", "g"]
K_G, K_W, K_vMF = Ks
################## Print the Watson and Gaussian Distribution parameters ###################
for k_c in myDManager.clusterk_to_Dname.keys():
k = myDManager.clusterk_to_thetak[k_c]
distribution_name = myDManager.clusterk_to_Dname[k_c] # G W
if (distribution_name == "Gaussian"):
print("------------ Gaussian Cluster. K = %i--------------------" %
k)
print("mu")
print(theta_list[-1][k][0])
print("Sigma")
print(theta_list[-1][k][1])
elif (distribution_name == "Watson"):
print("------------ Watson Cluster. K = %i--------------------" %
k)
print("mu")
print(theta_list[-1][k][0])
print("Kappa")
print(theta_list[-1][k][1])
elif (distribution_name == "vonMisesFisher"):
print(
"------------ vonMisesFisher Cluster. K = %i--------------------"
% k)
print("mu")
print(theta_list[-1][k][0])
print("Kappa")
print(theta_list[-1][k][1])
print("pimix")
print(model_theta_list[-1])
mus_Watson_Gaussian = []
# k_c is the number of the cluster inside the Manager. k is the index in theta
for k_c in myDManager.clusterk_to_Dname.keys():
k = myDManager.clusterk_to_thetak[k_c]
distribution_name = myDManager.clusterk_to_Dname[k_c] # G W
mus_k = []
for iter_i in range(
len(theta_list)): # For each iteration of the algorihtm
if (distribution_name == "Gaussian"):
theta_i = theta_list[iter_i][k]
mus_k.append(theta_i[0])
elif (distribution_name == "Watson"):
theta_i = theta_list[iter_i][k]
mus_k.append(theta_i[0])
elif (distribution_name == "vonMisesFisher"):
theta_i = theta_list[iter_i][k]
mus_k.append(theta_i[0])
mus_k = np.concatenate(mus_k, axis=1).T
mus_Watson_Gaussian.append(mus_k)
######## Plot the original data #####
gl.init_figure()
## First cluster
for xi in range(len(Xs)):
## First cluster
ax1 = gl.scatter(Xs[xi][0, :],
Xs[xi][1, :],
labels=[
'EM Evolution. Kg:' + str(K_G) + ', Kw:' +
str(K_W) + ', K_vMF:' + str(K_vMF), "X1", "X2"
],
color=colors[xi],
alpha=0.2,
nf=0)
mean, w, h, theta = bMA.get_gaussian_ellipse_params(mu=mus[xi],
Sigma=covs[xi],
Chi2val=2.4477)
r_ellipse = bMA.get_ellipse_points(mean, w, h, theta)
gl.plot(r_ellipse[:, 0],
r_ellipse[:, 1],
ax=ax1,
ls="--",
lw=2,
AxesStyle="Normal2",
color=colors[xi],
alpha=0.7)
indx = -1
# Only doable if the clusters dont die
Nit, Ndim = mus_Watson_Gaussian[0].shape
for k_c in myDManager.clusterk_to_Dname.keys():
k = myDManager.clusterk_to_thetak[k_c]
distribution_name = myDManager.clusterk_to_Dname[k_c] # G W
if (distribution_name == "Gaussian"):
## Plot the ecolution of the mu
#### Plot the Covariance of the clusters !
mean, w, h, theta = bMA.get_gaussian_ellipse_params(
mu=theta_list[indx][k][0],
Sigma=theta_list[indx][k][1],
Chi2val=2.4477)
r_ellipse = bMA.get_ellipse_points(mean, w, h, theta)
gl.plot(r_ellipse[:, 0],
r_ellipse[:, 1],
ax=ax1,
ls="-.",
lw=3,
AxesStyle="Normal2",
legend=[
"Kg(%i). pi:%0.2f" %
(k, float(model_theta_list[indx][0][0, k]))
])
gl.scatter(mus_Watson_Gaussian[k][:, 0],
mus_Watson_Gaussian[k][:, 1],
nf=0,
na=0,
alpha=0.3,
lw=1,
color="y")
gl.plot(mus_Watson_Gaussian[k][:, 0],
mus_Watson_Gaussian[k][:, 1],
nf=0,
na=0,
alpha=0.8,
lw=2,
color="y")
elif (distribution_name == "Watson"):
#### Plot the pdf of the distributino !
## Distribution parameters for Watson
kappa = float(theta_list[indx][k][1])
mu = theta_list[indx][k][0]
Nsa = 1000
# Draw 2D samples as transformation of the angle
Xalpha = np.linspace(0, 2 * np.pi, Nsa)
Xgrid = np.array([np.cos(Xalpha), np.sin(Xalpha)])
probs = [] # Vector with probabilities
for i in range(Nsa):
probs.append(
np.exp(Wad.Watson_pdf_log(Xgrid[:, i], [mu, kappa])))
probs = np.array(probs)
# Plot it in polar coordinates
X1_w = (1 + probs) * np.cos(Xalpha)
X2_w = (1 + probs) * np.sin(Xalpha)
gl.plot(X1_w,
X2_w,
legend=[
"Kw(%i). pi:%0.2f" %
(k, float(model_theta_list[indx][0][0, k]))
],
alpha=1,
lw=3,
ls="-.")
elif (distribution_name == "vonMisesFisher"):
#### Plot the pdf of the distributino !
## Distribution parameters for Watson
kappa = float(theta_list[indx][k][1])
mu = theta_list[indx][k][0]
Nsa = 1000
# Draw 2D samples as transformation of the angle
Xalpha = np.linspace(0, 2 * np.pi, Nsa)
Xgrid = np.array([np.cos(Xalpha), np.sin(Xalpha)])
probs = [] # Vector with probabilities
for i in range(Nsa):
probs.append(
np.exp(
vMFd.vonMisesFisher_pdf_log(Xgrid[:, i], [mu, kappa])))
probs = np.array(probs)
probs = probs.reshape((probs.size, 1)).T
# Plot it in polar coordinates
X1_w = (1 + probs) * np.cos(Xalpha)
X2_w = (1 + probs) * np.sin(Xalpha)
# print X1_w.shape, X2_w.shape
gl.plot(X1_w,
X2_w,
alpha=1,
lw=3,
ls="-.",
legend=[
"Kvmf(%i). pi:%0.2f" %
(k, float(model_theta_list[indx][0][0, k]))
])
ax1.axis('equal')
gl.savefig(folder_images + 'Final_State. K_G:' + str(K_G) + ', K_W:' +
str(K_W) + ', K_vMF:' + str(K_vMF) + '.png',
dpi=100,
sizeInches=[12, 6])
if(final_clusters_graph):
K = len(theta_list[-1])
gl.init_figure()
ax1 = gl.scatter(ret1, ret2, alpha = 0.2, color = "k",
legend = ["Data points %i"%(ret1.size)], labels = ["EM algorithm %i Gaussian fits"%(K),symbol_ID1,symbol_ID2])
for k in range(K):
mu_k = theta_list[-1][k][0]
std_k = theta_list[-1][k][1]
model_theta_last = model_theta_list[-1]
mean,w,h,theta = bMA.get_gaussian_ellipse_params( mu = mu_k, Sigma = std_k, Chi2val = 2.4477)
r_ellipse = bMA.get_ellipse_points(mean,w,h,theta)
if (len(model_theta_last) == 1):
pi = model_theta_last[0]
gl.plot(r_ellipse[:,0], r_ellipse[:,1], ax = ax1, ls = "-.", lw = 3,
AxesStyle = "Normal2",
legend = ["Kg(%i), pi:%.2f"%(k+1,pi[0,k])])
else:
pi = model_theta_last[0]
A = model_theta_last[1]
gl.plot(r_ellipse[:,0], r_ellipse[:,1], ax = ax1, ls = "-.", lw = 3,
AxesStyle = "Normal2",
legend = ["Kg(%i), pi:%.2f, A: %s"%(k+1,pi[0,k], str(A[k,:]))])
gl.init_figure()
X_1,X_2 = X2D[:,[0]], X2D[:,[1]]
mu_1, mu_2 = np.mean(Xproj, axis =0)
std_1,std_2 = np.std(Xproj,axis =0)
cov = np.cov(np.concatenate((X_1,X_2),axis = 1).T).T
std_K = 3
## Do stuff now
ax0 = gl.subplot2grid((1,2), (0,0), rowspan=1, colspan=1)
gl.scatter(X_1,X_2, alpha = 0.5, ax = ax0, lw = 4, AxesStyle = "Normal",
labels = ["Original 2D data","X1: %s" %(symbolIDs[AAPL_id]), "X2: %s" %(symbolIDs[GOOGL_id])])
ax0.axis('equal')
################# Draw the error ellipse #################
mean,w,h,theta = bMA.get_gaussian_ellipse_params(X2D, Chi2val = 2.4477)
corr = bMA.get_corrMatrix(X2D)
cov = bMA.get_covMatrix(X2D)
vecs,vals = bMA.get_eigenVectorsAndValues(X2D)
r_ellipse = bMA.get_ellipse_points(mean,w,h,theta)
gl.plot(r_ellipse[:,0], r_ellipse[:,1], ax = ax0, ls = "--",color = "k", lw = 2,
legend = ["Corr: %.2f"%(corr[0,1])])
gl.plot([mean[0], mean[0] + vecs[0,0]*w],
[mean[1], mean[1] + vecs[0,1]*w], ax = ax0, ls = "--",color = "k")
gl.plot([mean[0], mean[0] + vecs[1,0]*h],
[mean[1], mean[1] + vecs[1,1]*h], ax = ax0, ls = "--",color = "k")
gl.plot([mean[0], mean[0] - vecs[0,0]*w],
[mean[1], mean[1] - vecs[0,1]*w], ax = ax0, ls = "--",color = "k")
gl.plot([mean[0], mean[0] - vecs[1,0]*h],
def plot_2D_clusters(myDManager, clusters_relation, theta, model_theta, ax):
"""
This function plots the 2D clusters in the axes provided
"""
if (clusters_relation == "MarkovChain1"):
model_theta[0] = HMMlf.get_stationary_pi(model_theta[0],
model_theta[1])
# Only doable if the clusters dont die
for k_c in myDManager.clusterk_to_Dname.keys():
k = myDManager.clusterk_to_thetak[k_c]
distribution_name = myDManager.clusterk_to_Dname[k_c] # G W
if (distribution_name == "Gaussian"):
## Plot the ecolution of the mu
#### Plot the Covariance of the clusters !
mean, w, h, angle_theta = bMA.get_gaussian_ellipse_params(
mu=theta[k][0], Sigma=theta[k][1], Chi2val=2.4477)
r_ellipse = bMA.get_ellipse_points(mean, w, h, angle_theta)
gl.plot(
r_ellipse[:, 0],
r_ellipse[:, 1],
ax=ax,
ls="-.",
lw=3,
AxesStyle="Normal2",
legend=["Kg(%i). pi:%0.2f" % (k, float(model_theta[0][0, k]))])
if (distribution_name == "Gaussian2"):
## Plot the ecolution of the mu
#### Plot the Covariance of the clusters !
mean, w, h, angle_theta = bMA.get_gaussian_ellipse_params(
mu=theta[k][0], Sigma=theta[k][1], Chi2val=2.4477)
r_ellipse = bMA.get_ellipse_points(mean, w, h, angle_theta)
gl.plot(r_ellipse[:, 0],
r_ellipse[:, 1],
ax=ax,
ls="-.",
lw=3,
AxesStyle="Normal2",
legend=[
"Kgd(%i). pi:%0.2f" % (k, float(model_theta[0][0, k]))
])
elif (distribution_name == "Watson"):
#### Plot the pdf of the distributino !
## Distribution parameters for Watson
kappa = float(theta[k][1])
mu = theta[k][0]
Nsa = 1000
# Draw 2D samples as transformation of the angle
Xalpha = np.linspace(0, 2 * np.pi, Nsa)
Xgrid = np.array([np.cos(Xalpha), np.sin(Xalpha)])
probs = [] # Vector with probabilities
for i in range(Nsa):
probs.append(
np.exp(Wad.Watson_pdf_log(Xgrid[:, i], [mu, kappa])))
probs = np.array(probs)
# Plot it in polar coordinates
X1_w = (1 + probs) * np.cos(Xalpha)
X2_w = (1 + probs) * np.sin(Xalpha)
gl.plot(
X1_w,
X2_w,
alpha=1,
lw=3,
ls="-.",
legend=["Kw(%i). pi:%0.2f" % (k, float(model_theta[0][0, k]))])
elif (distribution_name == "vonMisesFisher"):
#### Plot the pdf of the distributino !
## Distribution parameters for Watson
kappa = float(theta[k][1])
mu = theta[k][0]
Nsa = 1000
# Draw 2D samples as transformation of the angle
Xalpha = np.linspace(0, 2 * np.pi, Nsa)
Xgrid = np.array([np.cos(Xalpha), np.sin(Xalpha)])
probs = [] # Vector with probabilities
for i in range(Nsa):
probs.append(
np.exp(
vMFd.vonMisesFisher_pdf_log(Xgrid[:, i], [mu, kappa])))
probs = np.array(probs)
probs = probs.reshape((probs.size, 1)).T
# Plot it in polar coordinates
X1_w = (1 + probs) * np.cos(Xalpha)
X2_w = (1 + probs) * np.sin(Xalpha)
gl.plot(X1_w,
X2_w,
alpha=1,
lw=3,
ls="-.",
legend=[
"Kvmf(%i). pi:%0.2f" % (k, float(model_theta[0][0, k]))
])
def generate_images_iterations_ll(Xs, mus, covs, Ks, myDManager, logl,
theta_list, model_theta_list,
folder_images_gif):
# os.remove(folder_images_gif) # Remove previous images if existing
"""
WARNING: MEANT FOR ONLY 3 Distributions due to the color RGB
"""
import shutil
ul.create_folder_if_needed(folder_images_gif)
shutil.rmtree(folder_images_gif)
ul.create_folder_if_needed(folder_images_gif)
######## Plot the original data #####
Xdata = np.concatenate(Xs, axis=1).T
colors = ["r", "b", "g"]
K_G, K_W, K_vMF = Ks
### FOR EACH ITERATION
for i in range(len(theta_list)): # theta_list
indx = i
gl.init_figure()
ax1 = gl.subplot2grid((1, 2), (0, 0), rowspan=1, colspan=1)
## Get the relative ll of the Gaussian denoising cluster.
ll = myDManager.pdf_log_K(Xdata, theta_list[indx])
N, K = ll.shape
# print ll.shape
for j in range(N): # For every sample
#TODO: Can this not be done without a for ?
# Normalize the probability of the sample being generated by the clusters
Marginal_xi_probability = gf.sum_logs(ll[j, :])
ll[j, :] = ll[j, :] - Marginal_xi_probability
ax1 = gl.scatter(
Xdata[j, 0],
Xdata[j, 1],
labels=[
'EM Evolution. Kg:' + str(K_G) + ', Kw:' + str(K_W) +
', K_vMF:' + str(K_vMF), "X1", "X2"
],
color=(np.exp(ll[j, 1]), np.exp(ll[j, 0]),
np.exp(ll[j, 2])), ### np.exp(ll[j,2])
alpha=1,
nf=0)
# Only doable if the clusters dont die
for k_c in myDManager.clusterk_to_Dname.keys():
k = myDManager.clusterk_to_thetak[k_c]
distribution_name = myDManager.clusterk_to_Dname[k_c] # G W
if (distribution_name == "Gaussian"):
## Plot the ecolution of the mu
#### Plot the Covariance of the clusters !
mean, w, h, theta = bMA.get_gaussian_ellipse_params(
mu=theta_list[indx][k][0],
Sigma=theta_list[indx][k][1],
Chi2val=2.4477)
r_ellipse = bMA.get_ellipse_points(mean, w, h, theta)
gl.plot(r_ellipse[:, 0],
r_ellipse[:, 1],
ax=ax1,
ls="-.",
lw=3,
AxesStyle="Normal2",
legend=[
"Kg(%i). pi:%0.2f" %
(k, float(model_theta_list[indx][0][0, k]))
])
elif (distribution_name == "Watson"):
#### Plot the pdf of the distributino !
## Distribution parameters for Watson
kappa = float(theta_list[indx][k][1])
mu = theta_list[-1][k][0]
Nsa = 1000
# Draw 2D samples as transformation of the angle
Xalpha = np.linspace(0, 2 * np.pi, Nsa)
Xgrid = np.array([np.cos(Xalpha), np.sin(Xalpha)])
probs = [] # Vector with probabilities
for i in range(Nsa):
probs.append(
np.exp(Wad.Watson_pdf_log(Xgrid[:, i], [mu, kappa])))
probs = np.array(probs)
# Plot it in polar coordinates
X1_w = (1 + probs) * np.cos(Xalpha)
X2_w = (1 + probs) * np.sin(Xalpha)
gl.plot(X1_w,
X2_w,
alpha=1,
lw=3,
ls="-.",
legend=[
"Kw(%i). pi:%0.2f" %
(k, float(model_theta_list[indx][0][0, k]))
])
elif (distribution_name == "vonMisesFisher"):
#### Plot the pdf of the distributino !
## Distribution parameters for Watson
kappa = float(theta_list[indx][k][1])
mu = theta_list[indx][k][0]
Nsa = 1000
# Draw 2D samples as transformation of the angle
Xalpha = np.linspace(0, 2 * np.pi, Nsa)
Xgrid = np.array([np.cos(Xalpha), np.sin(Xalpha)])
probs = [] # Vector with probabilities
for i in range(Nsa):
probs.append(
np.exp(
vMFd.vonMisesFisher_pdf_log(
Xgrid[:, i], [mu, kappa])))
probs = np.array(probs)
probs = probs.reshape((probs.size, 1)).T
# Plot it in polar coordinates
X1_w = (1 + probs) * np.cos(Xalpha)
X2_w = (1 + probs) * np.sin(Xalpha)
# print X1_w.shape, X2_w.shape
gl.plot(X1_w,
X2_w,
alpha=1,
lw=3,
ls="-.",
legend=[
"Kvmf(%i). pi:%0.2f" %
(k, float(model_theta_list[indx][0][0, k]))
])
gl.set_zoom(xlim=[-6, 6], ylim=[-6, 6], ax=ax1)
ax2 = gl.subplot2grid((1, 2), (0, 1), rowspan=1, colspan=1)
if (indx == 0):
gl.add_text(positionXY=[0.1, .5],
text=r' Initilization Incomplete LogLike: %.2f' %
(logl[0]),
fontsize=15)
pass
elif (indx >= 1):
gl.plot(
range(1,
np.array(logl).flatten()[1:].size + 1),
np.array(logl).flatten()[1:(indx + 1)],
ax=ax2,
legend=["Iteration %i, Incom LL: %.2f" % (indx, logl[indx])],
labels=[
"Convergence of LL with generated data", "Iterations", "LL"
],
lw=2)
gl.scatter(1, logl[1], lw=2)
pt = 0.05
gl.set_zoom(xlim=[0, len(logl)],
ylim=[
logl[1] - (logl[-1] - logl[1]) * pt,
logl[-1] + (logl[-1] - logl[1]) * pt
],
ax=ax2)
gl.subplots_adjust(left=.09,
bottom=.10,
right=.90,
top=.95,
wspace=.2,
hspace=0.01)
gl.savefig(folder_images_gif + 'gif_' + str(indx) + '.png',
dpi=100,
sizeInches=[16, 8],
close="yes",
bbox_inches=None)
gl.close("all")
def plot_multiple_iterations(Xs, mus, covs, Ks, myDManager, logl, theta_list,
model_theta_list, folder_images):
######## Plot the original data #####
gl.init_figure()
gl.set_subplots(2, 3)
Ngraph = 6
colors = ["r", "b", "g"]
K_G, K_W, K_vMF = Ks
for i in range(Ngraph):
indx = int(i * ((len(theta_list) - 1) / float(Ngraph - 1)))
nf = 1
for xi in range(len(Xs)):
## First cluster
labels = [
'EM Evolution. Kg:' + str(K_G) + ', Kw:' + str(K_W) +
', K_vMF:' + str(K_vMF), "X1", "X2"
]
ax1 = gl.scatter(Xs[xi][0, :],
Xs[xi][1, :],
labels=["", "", ""],
color=colors[xi],
alpha=0.2,
nf=nf)
nf = 0
mean, w, h, theta = bMA.get_gaussian_ellipse_params(mu=mus[xi],
Sigma=covs[xi],
Chi2val=2.4477)
r_ellipse = bMA.get_ellipse_points(mean, w, h, theta)
gl.plot(r_ellipse[:, 0],
r_ellipse[:, 1],
ax=ax1,
ls="--",
lw=2,
AxesStyle="Normal2",
color=colors[xi],
alpha=0.7)
# Only doable if the clusters dont die
for k_c in myDManager.clusterk_to_Dname.keys():
k = myDManager.clusterk_to_thetak[k_c]
distribution_name = myDManager.clusterk_to_Dname[k_c] # G W
if (distribution_name == "Gaussian"):
## Plot the ecolution of the mu
#### Plot the Covariance of the clusters !
mean, w, h, theta = bMA.get_gaussian_ellipse_params(
mu=theta_list[indx][k][0],
Sigma=theta_list[indx][k][1],
Chi2val=2.4477)
r_ellipse = bMA.get_ellipse_points(mean, w, h, theta)
gl.plot(r_ellipse[:, 0],
r_ellipse[:, 1],
ax=ax1,
ls="-.",
lw=3,
AxesStyle="Normal2",
legend=[
"Kg(%i). pi:%0.2f" %
(k, float(model_theta_list[indx][0][0, k]))
])
elif (distribution_name == "Watson"):
#### Plot the pdf of the distributino !
## Distribution parameters for Watson
kappa = float(theta_list[indx][k][1])
mu = theta_list[indx][k][0]
Nsa = 1000
# Draw 2D samples as transformation of the angle
Xalpha = np.linspace(0, 2 * np.pi, Nsa)
Xgrid = np.array([np.cos(Xalpha), np.sin(Xalpha)])
probs = [] # Vector with probabilities
for i in range(Nsa):
probs.append(
np.exp(Wad.Watson_pdf_log(Xgrid[:, i], [mu, kappa])))
probs = np.array(probs)
# Plot it in polar coordinates
X1_w = (1 + probs) * np.cos(Xalpha)
X2_w = (1 + probs) * np.sin(Xalpha)
gl.plot(X1_w,
X2_w,
alpha=1,
lw=3,
ls="-.",
legend=[
"Kw(%i). pi:%0.2f" %
(k, float(model_theta_list[indx][0][0, k]))
])
elif (distribution_name == "vonMisesFisher"):
#### Plot the pdf of the distributino !
## Distribution parameters for Watson
kappa = float(theta_list[indx][k][1])
mu = theta_list[indx][k][0]
Nsa = 1000
# Draw 2D samples as transformation of the angle
Xalpha = np.linspace(0, 2 * np.pi, Nsa)
Xgrid = np.array([np.cos(Xalpha), np.sin(Xalpha)])
probs = [] # Vector with probabilities
for i in range(Nsa):
probs.append(
np.exp(
vMFd.vonMisesFisher_pdf_log(
Xgrid[:, i], [mu, kappa])))
probs = np.array(probs)
probs = probs.reshape((probs.size, 1)).T
# Plot it in polar coordinates
X1_w = (1 + probs) * np.cos(Xalpha)
X2_w = (1 + probs) * np.sin(Xalpha)
# print X1_w.shape, X2_w.shape
gl.plot(X1_w,
X2_w,
alpha=1,
lw=3,
ls="-.",
legend=[
"Kvmf(%i). pi:%0.2f" %
(k, float(model_theta_list[indx][0][0, k]))
])
ax1.axis('equal')
gl.subplots_adjust(left=.09,
bottom=.10,
right=.90,
top=.95,
wspace=.2,
hspace=0.01)
gl.savefig(folder_images + 'Final_State2. K_G:' + str(K_G) + ', K_W:' +
str(K_W) + '.png',
dpi=100,
sizeInches=[18, 8])
labels = ["","",""], legend = ["M: %.2e, std: %.2e"%(mu_Z[0], SigmaZ[0,0])])
# Y distribution
ax3 = gl.subplot2grid((4,4), (1,3), rowspan=3, colspan=1,sharey = ax1,)
x_grid, y_val = bMA.gaussian1D_points(mean = mu_Y[1], std = SigmaY[1,1], std_K = 3)
gl.plot(y_val, x_grid, color = "k",
labels = ["","",""], legend = ["M: %.2e, std: %.2e"%(mu_Y[1], SigmaY[1,1])])
x_grid, y_val = bMA.gaussian1D_points(mean = mu_Z[1], std = SigmaZ[1,1], std_K = 3)
gl.plot( y_val,x_grid , color = "g",
labels = ["","",""], legend = ["M: %.2e, std: %.2e"%(mu_Z[1], SigmaZ[1,1])])
ax1.axis('equal')
gl.subplots_adjust(left=.09, bottom=.10, right=.90, top=.95, wspace=.01, hspace=0.01)
if(ellipse_graph):
################# Draw the error ellipse #################
mean,w,h,theta = bMA.get_gaussian_ellipse_params( mu = mu_Y, Sigma = SigmaY, Chi2val = 2.4477)
# mean,vecs = bMA.get_gaussian_mean_and_vects(Y.T)
vecs,vals = bMA.get_eigenVectorsAndValues(Sigma = SigmaY)
r_ellipse = bMA.get_ellipse_points(mean,w,h,theta)
gl.plot(r_ellipse[:,0], r_ellipse[:,1], ax = ax1, ls = "--",color = "k", lw = 2,
legend = ["Corr: .2f"],AxesStyle = "Normal2")
gl.plot([mean[0] - vecs[0,0]*w, mean[0] + vecs[0,0]*w],
[mean[1] - vecs[0,1]*w, mean[1] + vecs[0,1]*w], ax = ax1, ls = "--",color = "k")
gl.plot([mean[0] - vecs[1,0]*h, mean[0] + vecs[1,0]*h],
[mean[1] - vecs[1,1]*h, mean[1] + vecs[1,1]*h], ax = ax1, ls = "--",color = "k")
ax1.axis('equal')
gl.set_zoom(ax = ax1, X =r_ellipse[:,0], Y = r_ellipse[:,1],
ylimPad = [0.2,0.2],xlimPad = [0.2,0.2])
gl.plot(y_val,
x_grid,
color="k",
labels=["", "", ""],
legend=["M: %.2e, std: %.2e" % (mean[0], cov[1, 1])])
gl.subplots_adjust(left=.09,
bottom=.10,
right=.90,
top=.95,
wspace=.01,
hspace=0.01)
if (ellipse_graph):
################# Draw the error ellipse #################
mean, w, h, theta = bMA.get_gaussian_ellipse_params(data,
Chi2val=2.4477)
vecs, vals = bMA.get_eigenVectorsAndValues(data)
r_ellipse = bMA.get_ellipse_points(mean, w, h, theta)
gl.plot(r_ellipse[:, 0],
r_ellipse[:, 1],
ax=ax1,
ls="--",
color="k",
lw=2,
legend=["Corr: %.2f" % (corr[0, 1])])
gl.plot([mean[0], mean[0] + vecs[0, 0] * w],
[mean[1], mean[1] + vecs[0, 1] * w],
ax=ax1,
ls="--",
color="k")
X1 = np.random.multivariate_normal(mu1.flatten(), cov1, N1).T
X2 = np.random.multivariate_normal(mu2.flatten(), cov2, N2).T
X3 = np.random.multivariate_normal(mu3.flatten(), cov3, N3).T
######## Plotting #####
gl.init_figure()
## First cluster
ax1 = gl.scatter(X1[0, :],
X1[1, :],
labels=["Gaussian Generated Data", "x1", "x2"],
legend=["K = 1"],
color="r",
alpha=0.5)
mean, w, h, theta = bMA.get_gaussian_ellipse_params(mu=mu1,
Sigma=cov1,
Chi2val=2.4477)
r_ellipse = bMA.get_ellipse_points(mean, w, h, theta)
gl.plot(r_ellipse[:, 0],
r_ellipse[:, 1],
ax=ax1,
ls="--",
lw=2,
AxesStyle="Normal2",
color="r")
## Second cluster
ax1 = gl.scatter(X2[0, :],
X2[1, :],
legend=["K = 2"],
color="b",
def generate_gaussian_data(folder_images,
plot_original_data,
N1=200,
N2=300,
N3=50):
mu1 = np.array([[0], [0]])
cov1 = np.array([[0.8, -1.1], [-1.1, 1.6]])
mu2 = np.array([[0], [0]])
cov2 = np.array([[0.3, 0.45], [0.45, 0.8]])
mu3 = np.array([[0], [0]])
cov3 = np.array([[0.1, 0.0], [0.0, 0.1]])
X1 = np.random.multivariate_normal(mu1.flatten(), cov1, N1).T
X2 = np.random.multivariate_normal(mu2.flatten(), cov2, N2).T
X3 = np.random.multivariate_normal(mu3.flatten(), cov3, N3).T
# samples_X1 = np.array(range(X1.shape[1]))[np.where([X1[0,:] > 0])[0]]
# samples_X1 = np.where(X1[0,:] > 0)[0] # np.array(range(X1.shape[1]))
# print samples_X1
# X1 = X1[:,samples_X1]
# X2 = np.concatenate((X2,X3),axis = 1)
######## Plotting #####
if (plot_original_data):
gl.init_figure()
## First cluster
ax1 = gl.scatter(X1[0, :],
X1[1, :],
labels=["Gaussian Generated Data", "x1", "x2"],
legend=["K = 1"],
color="r",
alpha=0.5)
mean, w, h, theta = bMA.get_gaussian_ellipse_params(mu=mu1,
Sigma=cov1,
Chi2val=2.4477)
r_ellipse = bMA.get_ellipse_points(mean, w, h, theta)
gl.plot(r_ellipse[:, 0],
r_ellipse[:, 1],
ax=ax1,
ls="--",
lw=2,
AxesStyle="Normal2",
color="r")
## Second cluster
ax1 = gl.scatter(X2[0, :],
X2[1, :],
legend=["K = 2"],
color="b",
alpha=0.5)
mean, w, h, theta = bMA.get_gaussian_ellipse_params(mu=mu2,
Sigma=cov2,
Chi2val=2.4477)
r_ellipse = bMA.get_ellipse_points(mean, w, h, theta)
gl.plot(r_ellipse[:, 0],
r_ellipse[:, 1],
ax=ax1,
ls="--",
lw=2,
AxesStyle="Normal2",
color="b")
## Third cluster
ax1 = gl.scatter(X3[0, :],
X3[1, :],
legend=["K = 3"],
color="g",
alpha=0.5)
mean, w, h, theta = bMA.get_gaussian_ellipse_params(mu=mu3,
Sigma=cov3,
Chi2val=2.4477)
r_ellipse = bMA.get_ellipse_points(mean, w, h, theta)
gl.plot(r_ellipse[:, 0],
r_ellipse[:, 1],
ax=ax1,
ls="--",
lw=2,
AxesStyle="Normal2",
color="g")
ax1.axis('equal')
gl.savefig(folder_images + 'Original data.png',
dpi=100,
sizeInches=[12, 6])
############ ESTIMATE THEM ################
theta1 = Gae.get_Gaussian_muSigma_ML(X1.T,
parameters=dict([["Sigma", "full"]]))
print("mu1:")
print(theta1[0])
print("Sigma1")
print(theta1[1])
############## Estimate Likelihood ###################
ll = Gad.Gaussian_pdf_log(X1, [mu1, cov1])
ll2 = []
for i in range(ll.size):
ll2.append(
multivariate_normal.logpdf(X1[:, i], mean=mu1.flatten(), cov=cov1))
ll2 = np.array(ll2).reshape(ll.shape)
print("ll ours")
print(ll.T)
print("ll scipy")
print(ll2.T)
print("Difference in ll")
print((ll - ll2).T)
###### Multiple clusters case
ll_K = Gad.Gaussian_K_pdf_log(X1, [[mu1, cov1], [mu2, cov2]])
if (0):
X1 = gf.remove_module(X1.T).T
X2 = gf.remove_module(X2.T).T
X3 = gf.remove_module(X3.T).T
Xdata = np.concatenate((X1, X2, X3), axis=1).T
return X1, X2, X3, Xdata, mu1, mu2, mu3, cov1, cov2, cov3