15
$\begingroup$

I'd like to recreate this visualization (from python) in Mathematica:

enter image description here

I'm not sure how to extract the decision boundaries from a classifier with "Method" set to "RandomForest".

Here's the code:

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs
from sklearn.ensemble import RandomForestClassifier

X, y = make_blobs(centers=[[0, 0], [1, 1]], random_state=61526, n_samples=50)

def plot_forest(max_depth=1):
    plt.figure()
    ax = plt.gca()
    h = 0.02

    x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
    y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))

    if max_depth != 0:
        forest = RandomForestClassifier(n_estimators=20, max_depth=max_depth,
                                        random_state=1).fit(X, y)
        Z = forest.predict_proba(np.c_[xx.ravel(), yy.ravel()])[:, 1]
        Z = Z.reshape(xx.shape)
        ax.contourf(xx, yy, Z, alpha=.4)
        ax.set_title("max_depth = %d" % max_depth)
    else:
        ax.set_title("data set")
    ax.scatter(X[:, 0], X[:, 1], c=np.array(['b', 'r'])[y], s=60)
    ax.set_xlim(x_min, x_max)
    ax.set_ylim(y_min, y_max)
    ax.set_xticks(())
    ax.set_yticks(())


def plot_forest_interactive():
    from IPython.html.widgets import interactive, IntSlider
    slider = IntSlider(min=0, max=8, step=1, value=0)
    return interactive(plot_forest, max_depth=slider)
$\endgroup$
  • 1
    $\begingroup$ Would you be able to provide some more detail for your question? How do you generate the data? Can you provide a sample data set / a generator function? etc. $\endgroup$ – MarcoB Nov 6 '15 at 17:18
  • $\begingroup$ Sure, I added the code used to make the manipulate in ipython. The data can be random/anything this demo is just for explanation/fun purposes. $\endgroup$ – M.R. Nov 6 '15 at 17:23
11
$\begingroup$

Firstly I'm not sure if Mathematica's Random Tree method has an equivalent max_depth option (I don't know too much about random tree). The options available to the Random Tree method are: "TreeNumber", "LeafSize", and "VariableSampleSize".

Now as for plotting the classifier boundaries, one can simply pass the ClassifierFunction for ContourPlot (or similar).

My mock data:

    n = 50;
    blobs = RandomReal[{0, 1}, {n, 2}];

    blobsRed = RandomSample[(Norm /@ blobs)^4 -> blobs, Round[n/2]];
    blobsBlue = Complement[blobs, blobsRed];

    training = Join[Thread[blobsRed -> Red], Thread[blobsBlue -> Blue]];

Create the ClassifierFunction:

    c = Classify[training, Method -> {"RandomForest", "LeafSize" -> 5}];

And plot:

    ContourPlot[c[{x, y}, {"Probability", Red}], {x, 0, 1}, {y, 0, 1},
     ColorFunction -> Function[z, Directive[Opacity[0.6], ColorData["Rainbow"][z]]],
     Contours -> 7,
     FrameTicks -> None,
     Method -> {"TransparentPolygonMesh" -> True},
     PlotRangePadding -> None,
     Epilog -> {
       PointSize[0.02],
       {Red, Point[blobsRed]},
       {Blue, Point[blobsBlue]}
       }
     ]

enter image description here

You could also classify a grid of points and then use ListContourPlot, which will be much faster, to get an image more like:

enter image description here

I trust you can then use ListAnimate or Manipulate to recreate the animated aspect if that's what you wanted, if not I can expand my reply to cover that.

Hope this helps!

$\endgroup$
  • $\begingroup$ That is awesome! $\endgroup$ – garej Nov 8 '15 at 8:19
  • 2
    $\begingroup$ @Quantum_Oli thanks for the great answer +1, the Countour plot is really slow! $\endgroup$ – M.R. Nov 10 '15 at 2:21

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.