Automated legend creation for 3D plot

In the function to visualize the clusters, you need ax.legend instead of plt.legend

from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d.axes3d import Axes3D
import numpy as np
import pandas as pd

color_names = ["red", "blue", "yellow", "black", "pink", "purple", "orange"]

def plot_3d_transformed_data(df, title, colors="red"):
 
  ax = plt.figure(figsize=(12,10)).gca(projection='3d')
  #fig = plt.figure(figsize=(8, 8))
  #ax = fig.add_subplot(111, projection='3d')
  

  if type(colors) is np.ndarray:
    for cname, class_label in zip(color_names, np.unique(colors)):
      X_color = df[colors == class_label]
      ax.scatter(X_color[:, 0], X_color[:, 1], X_color[:, 2], marker="x", c=cname, label=f"Cluster {class_label}" if type(colors) is np.ndarray else None)
  else:
      ax.scatter(df.Type, df.Length, df.Freq, alpha=0.6, c=colors, marker="x", label=str(clusterSizes)  )

  ax.set_xlabel("PC1: Type")
  ax.set_ylabel("PC2: Length")
  ax.set_zlabel("PC3: Frequency")
  ax.set_title(title)
  
  if type(colors) is np.ndarray:
    #ax.legend()
    plt.gca().legend()
    
  
  ax.legend(bbox_to_anchor=(.9,1), loc="upper left")
  plt.show()

clusterSizes = 10

test_df = pd.DataFrame({'Type':np.random.randint(0,5,10),
                        'Length':np.random.randint(0,20,10),
                        'Freq':np.random.randint(0,10,10),
                        'Colors':np.random.choice(color_names,10)})

plot_3d_transformed_data(test_df,
                         'Clustering rare URL parameters for data of date:haha\nMethod: KMeans over PCA \nn_clusters={n_clusters} , Distance_Measure={DistanceMeasure}',
                         colors=test_df.Colors)

Running this example code, you will have legend handle as expected

You need to save the reference to the first legend and add it to your ax as a separate artist before creating the second legend. That way, the second call to ax.legend(...) does not erase the first legend.

For the second legend, I simply created a circle for each unique color and added it in. I forgot how to draw real circles, so instead I use a Line2D with lw=0, marker="o" which results in a circle.

Play around with the legend's bbox_to_anchor and loc keywords to get a result that satisfies you.

I got rid of everything relying on plt.<something> because it's the best way to forget which method is attached to which object. Now everything is in ax.<something> or fig.<something>. It's also the right approach for when you have several axes, or when you want to embed your canvas in a PyQt app. plt will not do what you expect there.

The initial code is the one provided by @r-beginners and I simply built upon it.

# Imports.
import matplotlib as mpl
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import pandas as pd
import numpy as np

# Figure.
figure = plt.figure(figsize=(12, 10))
ax = figure.add_subplot(projection="3d")
ax.set_xlabel("PC1: Type")
ax.set_ylabel("PC2: Length")
ax.set_zlabel("PC3: Frequency")
ax.set_title("scatter 3D legend") 

# Data and 3D scatter.
colors = ["red", "blue", "yellow", "black", "pink", "purple", "orange", "black", "red" ,"blue"]

df = pd.DataFrame({"type": np.random.randint(0, 5, 10),
                   "length": np.random.randint(0, 20, 10),
                   "freq": np.random.randint(0, 10, 10),
                   "size": np.random.randint(20, 200, 10),
                   "colors": np.random.choice(colors, 10)})

sc = ax.scatter(df.type, df.length, df.freq, alpha=0.6, c=colors, s=df["size"], marker="o")

# Legend 1.
handles, labels = sc.legend_elements(prop="sizes", alpha=0.6)
legend1 = ax.legend(handles, labels, bbox_to_anchor=(1, 1), loc="upper right", title="Sizes")
ax.add_artist(legend1) # <- this is important.

# Legend 2.
unique_colors = set(colors)
handles = []
labels = []
for n, color in enumerate(unique_colors, start=1):
    artist = mpl.lines.Line2D([], [], color=color, lw=0, marker="o")
    handles.append(artist)
    labels.append(str(n))
legend2 = ax.legend(handles, labels, bbox_to_anchor=(0.05, 0.05), loc="lower left", title="Classes")

figure.show()

Not related to the question: because of how markersize works for circles, one could use s = df["size"]**2 instead of s = df["size"].