My goal is to plot the probability distribution functions (pdfs) of two classes. Each class has Gaussian likelihood and equivalent covariance matrices, but different mean vectors. I want both pdfs on the same plane in the z-axis, with the x and y axes containing the projections of the pdfs. The following code (mostly borrowed from here) plots one of the pdfs:
# Our 2-dimensional distribution will be over variables X and Y
N = 100
X = np.linspace(-10, 15, N)
Y = np.linspace(-10, 15, N)
X, Y = np.meshgrid(X, Y)
# Mean vector and covariance matrix
mu1 = np.array([8, 2])
mu2 = np.array([2,8])
Sigma1 = Sigma2 = np.array([[4.1,0],[0,2.8]])
# Pack X and Y into a single 3-dimensional array
pos = np.empty(X.shape + (2,))
pos[:, :, 0] = X
pos[:, :, 1] = Y
F1 = multivariate_normal(mu1, Sigma1)
F2 = multivariate_normal(mu2, Sigma2)
Z1 = F1.pdf(pos)
Z2 = F2.pdf(pos)
# Create a surface plot and projected filled contour plot under it.
fig1 = plt.figure(figsize=[10,10])
ax1 = fig1.gca(projection='3d')
ax1.plot_surface(X, Y, Z1, rstride=3, cstride=3, linewidth=1,
antialiased=True,cmap=cm.inferno)
cset = ax1.contourf(X, Y, Z1, zdir='z', offset=-0.15, cmap=cm.inferno)
# Adjust the limits, ticks and view angle
ax1.set_zlim(-0.15,0.2)
ax1.set_zticks(np.linspace(0,0.2,5))
ax1.view_init(27, -21)
plt.show()
This is the plot that results from the above code: plot_surfaces for plotting bivariate pdf. However, I need to plot both Z1 and Z2 on the same plane. If I try creating two plots, they overlap and the Z2 pdf cannot be seen. Tweaking the code slightly, I get roughly what I want:
ax1 = fig1.gca(projection='3d')
ax2 = fig1.gca(projection='3d')
ax1.plot_wireframe(X, Y, Z1, rstride=3, cstride=3, linewidth=1,
antialiased=True,cmap=cm.inferno)
ax2.plot_wireframe(X,Y,Z2,rstride=3, cstride=3, linewidth=1,
antialiased=True,cmap=cm.inferno)
the resulting plot of which can be found here: wireframe method to plot 2 bivariate pdfs. But these plots are still overlapping. How can I get around this issue? I want the result to be styled as the first plot, with the surface_plot method and projections on the x-y plane.
You can play with alpha:
ax1.plot_surface(X, Y, Z1, rstride=3, cstride=3, linewidth=1,
antialiased=True,cmap=cm.inferno, alpha = 0.5)
ax1.plot_surface(X, Y, Z2, rstride=3, cstride=3, linewidth=1,
antialiased=True,cmap=cm.inferno, alpha = 1)
cset = ax1.contourf(X, Y, Z1, zdir='z', offset=-0.15, cmap=cm.inferno, alpha=1)
cset = ax1.contourf(X, Y, Z2, zdir='z', offset=-0.15, cmap=cm.inferno, alpha=0.5)
But in some cases you can get the same results by just summing your pdf's
ax1.plot_surface(X, Y, Z1 + Z2, rstride=3, cstride=3, linewidth=1, antialiased=True,cmap=cm.inferno)
cset = ax1.contourf(X, Y, Z1 + Z2, zdir='z', offset=-0.15, cmap=cm.inferno)