Machine Learning - Capitalmind

Explore Machine Learning Fundamentals

Master the core concepts that power modern AI and machine learning systems. Each topic provides comprehensive coverage from mathematical foundations to practical implementations, designed for both beginners and experienced practitioners.

Click on any topic below to dive deep into detailed explanations, working code examples, and interactive visualizations. Each dedicated page combines decades of hands-on experience with clear, accessible teaching.

Available

Graph Theory Fundamentals

12 min deep dive Intermediate Python + SVG

Understand the mathematical foundation behind neural networks, social network analysis, and pathfinding algorithms. Graph theory provides the structural framework for representing relationships and dependencies in complex data systems.

Why This Matters:

Neural networks are graphs. Social networks are graphs. Knowledge bases are graphs. Master graph theory and you understand the backbone of modern AI architecture and data relationships.

class Graph: def __init__(self, directed=False): self.directed = directed self.adjacency_list = {} def add_edge(self, vertex1, vertex2, weight=1): # Core graph operations for ML applications self.adjacency_list[vertex1].append((vertex2, weight))

Data Structures Neural Networks Pathfinding Network Analysis Algorithms

Click to explore interactive graph visualizations and complete implementations

Available

Linear Algebra for Machine Learning

15 min deep dive Intermediate NumPy + Math

The mathematical language of machine learning. Every ML algorithm operates on vectors and matrices. Understanding linear algebra means understanding how data flows through neural networks, how PCA reduces dimensions, and how optimization works.

Why This Matters:

ML is linear algebra at scale. Images are matrices, text is vectors, neural networks are matrix multiplications. This isn't just math theory—it's the operational foundation of every AI system you'll build.

# Neural network forward pass is just matrix multiplication def forward_pass(X, W, b): return np.dot(X, W) + b # PCA dimensionality reduction using eigendecomposition eigenvals, eigenvecs = np.linalg.eig(covariance_matrix)

Vectors Matrices PCA Eigenvalues SVD Optimization

Click to master vectors, matrices, and the math that powers modern AI

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Gradient Descent Optimization

10 min deep dive Intermediate Python + Visualization

The heart of machine learning—how algorithms actually learn from data. Gradient descent is the optimization engine that powers neural networks, linear regression, and most ML training processes.

Why This Matters:

This is how AI learns. Every time a neural network improves its predictions, gradient descent is working behind the scenes, finding optimal parameters through iterative optimization.

# Core gradient descent algorithm def gradient_descent(X, y, learning_rate=0.01, iterations=1000): for i in range(iterations): gradient = compute_gradient(X, y, weights) weights = weights - learning_rate * gradient

Optimization Learning Algorithms Neural Networks Calculus Convergence

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Decision Trees & Random Forests

12 min deep dive Beginner to Intermediate Scikit-learn + Custom

Interpretable machine learning algorithms that make decisions through a series of questions. From simple classification trees to powerful ensemble methods like Random Forests, these algorithms balance performance with explainability.

Why This Matters:

When you need to explain your model's decisions, decision trees excel. They're interpretable, handle mixed data types naturally, and Random Forests often outperform complex deep learning on tabular data.

# Information gain calculation for tree splitting def information_gain(parent, left_child, right_child): return entropy(parent) - weighted_entropy(left_child, right_child) # Random Forest ensemble forest = [build_tree(bootstrap_sample(data)) for _ in range(n_trees)]

Classification Ensemble Methods Interpretability Information Theory Feature Selection

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Support Vector Machines

14 min deep dive Advanced Mathematical + Practical

Sophisticated classification algorithm that finds optimal decision boundaries by maximizing margins between classes. SVMs use the kernel trick to handle non-linear data and provide robust classification with mathematical rigor.

Why This Matters:

SVMs demonstrate advanced ML concepts: optimization theory, kernel methods, and the mathematical elegance of maximum margin classification. Understanding SVMs bridges traditional ML and modern deep learning concepts.

# SVM optimization objective def svm_objective(w, b, X, y, C): margin_loss = np.sum(np.maximum(0, 1 - y * (X @ w + b))) regularization = 0.5 * np.sum(w**2) return regularization + C * margin_loss

Classification Kernel Methods Optimization Margin Maximization Non-linear

Building Comprehensive ML Education

These foundational topics form the core of modern machine learning understanding. Each deep-dive combines mathematical rigor with practical implementations, interactive visualizations, and real-world applications.

More advanced topics coming soon: Neural Networks, Probability Theory, Information Theory, and specialized algorithms for time series, NLP, and computer vision.