Stacked 2D plots with interconnections in Matplotlib

Question

I need to visualize some complex multivariate datasets and the preferrable choice is to use a modification of parallel axis visualization, using stacked 2D plots, where each plot maps a degree of freedom/model parameter and data points belonging to the same data sets should be interconnected across different plots. I am attaching a conceptual sketch. How could I implement it in matplotlib?

Answer 1

To have a rough idea, this could be a possible solution in matplotlib using Axes3D

from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle, PathPatch
import mpl_toolkits.mplot3d.art3d as art3d


x = np.array([1,2,3])
y = np.array([2,3,1])
z = np.array([1,1,1])


fig = plt.figure(figsize=(6,6))
ax = fig.add_axes([0,0,1,1], projection='3d')

#plot the points
ax.scatter(x,y,z*0.4, c="r", facecolor="r", s=60)
ax.scatter(y,x,z*0.9, c="b", facecolor="b", s=60)
ax.scatter(x,y,z*1.6, c="g", facecolor="g", s=60)
#plot connection lines
ax.plot([x[0],y[0],x[0]],[y[0],x[0],y[0]],[0.4,0.9,1.6], color="k")
ax.plot([x[2],y[2],x[2]],[y[2],x[2],y[2]],[0.4,0.9,1.6], color="k")
#plot planes
p = Rectangle((0,0), 4,4, color="r", alpha=0.2)
ax.add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=0.4, zdir="z")

p = Rectangle((0,0), 4,4, color="b", alpha=0.2)
ax.add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=0.9, zdir="z")

p = Rectangle((0,0), 4,4, color="g", alpha=0.2)
ax.add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=1.6, zdir="z")



ax.set_aspect('equal')
ax.view_init(13,-63)
ax.set_xlim3d([0,4])
ax.set_ylim3d([0,4])
ax.set_zlim3d([0,2])

plt.savefig(__file__+".png")
plt.show()

---

Update

Creating three different axes is possible. One has to add the axes and make the upper ones transparent (ax2.patch.set_alpha(0.)). Then the grid has to be turned off (ax.grid(False)) and the panes and lines that we don't need set invisible.
However, I have no clue how to draw a connection with between the axes. The 2D approach of matplotlib.patches.ConnectionPatch does not work for 3D axes.

from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle
import mpl_toolkits.mplot3d.art3d as art3d


x = np.array([1,2,3])
y = np.array([2,3,1])
z = np.array([0,0,0])


fig = plt.figure(figsize=(6,6))

ax = fig.add_axes([0,0,1,1], projection='3d')
ax2 = fig.add_axes([0.0,0.24,1,1], projection='3d')
ax2.patch.set_alpha(0.)
ax3 = fig.add_axes([0.0,0.48,1,1], projection='3d')
ax3.patch.set_alpha(0.)
#plot the points
ax.scatter(x,y,z, c="r", facecolor="r", s=60)
ax2.scatter(y*4,x*4,z, c="b", facecolor="b", s=60)
ax3.scatter(x*100,y*100,z, c="g", facecolor="g", s=60)
#plot connection lines
#ax.plot([x[0],y[0],x[0]],[y[0],x[0],y[0]],[0.4,0.9,1.6], color="k")
#ax.plot([x[2],y[2],x[2]],[y[2],x[2],y[2]],[0.4,0.9,1.6], color="k")

#plot planes
p = Rectangle((0,0), 4,4, color="r", alpha=0.2)
ax.add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=0, zdir="z")

p = Rectangle((0,0), 16,16, color="b", alpha=0.2)
ax2.add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=0, zdir="z")

p = Rectangle((0,0), 400,400, color="g", alpha=0.2)
ax3.add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=0, zdir="z")



ax.set_aspect('equal')
ax2.set_aspect('equal')
ax3.set_aspect('equal')
ax.view_init(13,-63)
ax2.view_init(10,-63)
ax3.view_init(8,-63)
ax.set_xlim3d([0,4])
ax.set_ylim3d([0,4])
ax.set_zlim3d([0,2])
ax2.set_xlim3d([0,16])
ax2.set_ylim3d([0,16])
ax2.set_zlim3d([0,2])
ax3.set_xlim3d([0,400])
ax3.set_ylim3d([0,400])
ax3.set_zlim3d([0,2])
ax.grid(False)
ax2.grid(False)
ax3.grid(False)

def axinvisible(ax):
    for zax in (ax.w_zaxis, ax.w_xaxis, ax.w_yaxis):
        zax.pane.set_visible(False)
        if zax == ax.w_zaxis:
            zax.line.set_visible(False)
            for ll in zax.get_ticklines()+zax.get_ticklabels():
                    ll.set_visible(False)


axinvisible(ax)
axinvisible(ax2)
axinvisible(ax3)

# setting a ConnectionPatch does NOT work
from matplotlib.patches import ConnectionPatch
con = ConnectionPatch(xyA=(2,2), xyB=(2,2), 
                      coordsA='data', coordsB='data', 
                      axesA=ax, axesB=ax2,
                      arrowstyle='->', clip_on=True)
ax2.add_artist(con) # artist is not shown :-(

plt.show()

Answer 2

A solution could be based on matplotlib's 3D capabilities. You can use Axes3D.plot_surface to plot the axes, and user scatter and line plots for the rest.