3D plotting in Python - Adding a Legend to Scatterplot

Question

from mpl_toolkits.mplot3d import Axes3D

ax.scatter(X_lda[:,0], X_lda[:,1], X_lda[:,2], alpha=0.4, c=y_train, cmap='rainbow', s=20)

plt.legend()
plt.show()

Essentially I'd like to add a legend for the scatterplot that shows the unique values in y_train and what color point it corresponds to on the plot.

The output plot:

Answer 1

Producing either a legend or a colorbar for a scatter is usually quite simple:

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

x,y,z = (np.random.normal(size=(300,4))+np.array([0,2,4,6])).reshape(3,400)
c = np.tile([1,2,3,4], 100)

fig, ax = plt.subplots(subplot_kw=dict(projection="3d"))
sc = ax.scatter(x,y,z, alpha=0.4, c=c, cmap='rainbow', s=20)

plt.legend(*sc.legend_elements())
plt.colorbar(sc)
plt.show()

Answer 2

Edit: After seeing @bigreddot's solution, I agree that this approach is somewhat more complicated than strictly necessary. I leave it here in case somebody needs more fine-tuning for their colorbar or legend.

Here is a way to create both a custom legend and a custom colorbar for the 3D graph. So you can chose one or the other, depending on specific needs. I'm not sure how the y_train is distributed; in the code some float values of a limited set are simulated. Also, it is not clear what the labels should mention, so now they just put the value of y_train.

from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib as mpl

N = 1000
X_lda = np.random.gamma(9.0, 0.5, (N,3))
y_train = np.random.randint(0, 6, N)
X0 = np.random.gamma(5.0, 1.5, (N,3))
X1 = np.random.gamma(1.0, 1.5, (N,3))
for i in range(3):
    X_lda[:,i] = np.where (y_train == 0, X0[:,i], X_lda[:,i])
    X_lda[:,i] = np.where (y_train == 1, X1[:,i], X_lda[:,i])
y_train = np.sin(y_train*.2 + 10) * 10.0 + 20.0

fig = plt.figure(figsize = (15,15))
ax = fig.add_subplot(111, projection = '3d')
ax.scatter(X_lda[:,0], X_lda[:,1], X_lda[:,2], alpha=0.4, c=y_train, cmap='rainbow', s=20)

norm = mpl.colors.Normalize(np.min(y_train), np.max(y_train))
cmap = plt.get_cmap('rainbow')

y_unique = np.unique(y_train)
legend_lines = [mpl.lines.Line2D([0],[0], linestyle="none", marker='o', c=cmap(norm(y))) for y in y_unique]
legend_labels = [f'{y:.2f}' for y in y_unique]
ax.legend(legend_lines, legend_labels, numpoints = 1, title='Y-train')

sm = plt.cm.ScalarMappable(cmap=cmap, norm=norm)
sm.set_array([])
plt.colorbar(sm, ticks=y_unique, label='Y-train')
plt.show()