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📊 Classic Machine Learning Visualizations

Learning Path Stage 2 of 4  •  Previous: Stage 1: Math Foundations  •  Next: Stage 3: Deep Learning

Animora provides one-call visualizers for foundational machine learning algorithms. Every algorithm runs on pure NumPy data structures, traces exact mathematical steps, and renders without manual Manim choreography.

1. Linear Regression

Animora calculates the exact analytical least-squares fit $(X^T X)^{-1} X^T y$ and animates the regression line converging to the optimal fit:

Linear Regression Fitting 

from animora.core import Scene
from animora.ml.classic import linear_regression
from animora.theme import ModernDark, use_theme


class LinearRegressionDemo(Scene):
    def construct(self) -> None:
        with use_theme(ModernDark):
            x = [1.0, 2.0, 3.0, 4.0, 5.0]
            y = [2.2, 3.8, 6.1, 7.9, 10.2]

            # 1-Line: Animates axes, scatter points, and fitting line
            self.play(*linear_regression(x, y, steps=10))

2. Logistic Regression

Visualizes binary classification with sigmoid probability and cross-entropy gradient descent, showing the linear decision boundary $w^T x + b = 0$ settling between classes:

Logistic Regression Decision Boundary 

from animora.core import Scene
from animora.ml.classic import logistic_regression
from animora.theme import ModernDark, use_theme


class LogisticRegressionDemo(Scene):
    def construct(self) -> None:
        with use_theme(ModernDark):
            X = [[-2.0, -1.5], [-1.0, -2.0], [1.5, 1.0], [2.0, 2.2]]
            y = [0, 0, 1, 1]

            self.play(*logistic_regression(X, y, steps=12))

3. K-Means Clustering

Visualizes Lloyd's algorithm: centroid initialization, nearest-cluster sample recoloring, and centroid translation:

K-Means Clustering Iteration 

from animora.core import Scene
from animora.ml.classic import kmeans
from animora.theme import ModernDark, use_theme


class KMeansDemo(Scene):
    def construct(self) -> None:
        with use_theme(ModernDark):
            data = [[-3, -3], [-2.8, -3.2], [3, 3], [3.2, 2.8], [0, 3], [-0.5, 3.2]]

            self.play(*kmeans(data, k=3, max_iters=5))

4. Decision Tree Classifier

Constructs a binary classification tree using exact Gini impurity or Shannon entropy, rendered automatically via TreeLayout and styled Panel cards:

Decision Tree Graph Layout 

from animora.core import Scene
from animora.ml.classic import decision_tree
from animora.theme import ModernDark, use_theme


class DecisionTreeDemo(Scene):
    def construct(self) -> None:
        with use_theme(ModernDark):
            X = [[1.2, 0.5], [1.8, 0.7], [4.5, 3.2], [5.0, 3.8]]
            y = [0, 0, 1, 1]

            self.play(*decision_tree(X, y, max_depth=2, criterion="gini"))

5. Support Vector Machine (SVM)

Visualizes the maximum-margin hyperplane $w \cdot x + b = 0$, dashed margin boundaries $w \cdot x + b = \pm 1$, and highlights the exact support vectors:

SVM Maximum Margin Hyperplane 

from animora.core import Scene
from animora.ml.classic import svm
from animora.theme import ModernDark, use_theme


class SVMDemo(Scene):
    def construct(self) -> None:
        with use_theme(ModernDark):
            X = [[-2.0, 0.0], [-1.0, 1.0], [1.0, -1.0], [2.0, 0.0]]
            y = [-1, -1, 1, 1]

            self.play(*svm(X, y))

6. Principal Component Analysis (PCA)

Computes covariance eigendecomposition via numpy.linalg.eigh, draws principal component eigenvectors from the data centroid, and animates orthogonal projections onto the primary axis:

PCA Principal Eigenvectors and Projection 

from animora.core import Scene
from animora.ml.classic import pca
from animora.theme import ModernDark, use_theme


class PCADemo(Scene):
    def construct(self) -> None:
        with use_theme(ModernDark):
            X = [[1.0, 1.2], [2.0, 1.9], [3.0, 3.1], [4.0, 3.8]]

            self.play(*pca(X, n_components=1))

⚠️ Common Pitfalls

  1. Non-Separable SVM Data: The canonical svm() visualizer implements a hard-margin SVM. Providing heavily overlapping, non-linearly separable classes will prevent the margin from fully opening. For overlapping datasets, logistic regression is recommended.
  2. K-Means Degenerate Clusters: Ensure the sample size $N$ is at least as large as the requested cluster count $k$.