Machine Learning Algorithm Library

Project Overview

Engineered a comprehensive ML framework implementing 12 fundamental algorithms in Fall 2021, including Linear Regression (direct method, polynomial, SGD), K-Means clustering, PCA with eigenface analysis, K-Nearest Neighbors on the MNIST dataset, Logistic Regression, and Decision Trees, with performance benchmarking across multiple datasets and automated hyperparameter optimization.

Algorithm Implementation Portfolio

Supervised Learning Algorithms

Linear Regression Suite

Direct Method: Matrix-based analytical solution using normal equations
Polynomial Regression: Feature expansion with polynomial basis functions
Stochastic Gradient Descent: Iterative optimization for large datasets
Regularized Variants: Ridge and Lasso regression implementations

Classification Algorithms

Logistic Regression: Maximum likelihood estimation with sigmoid activation
K-Nearest Neighbors: Distance-based classification with multiple distance metrics
Decision Trees: Information gain and Gini impurity-based tree construction
Support Vector Machines: Margin maximization with kernel methods

Unsupervised Learning Algorithms

Clustering Methods

K-Means Clustering: Centroid-based partitioning with multiple initialization strategies
Hierarchical Clustering: Agglomerative and divisive clustering approaches
DBSCAN: Density-based clustering for arbitrary cluster shapes

Dimensionality Reduction

Principal Component Analysis (PCA): Eigenvalue decomposition for feature reduction
Eigenface Analysis: PCA application for facial recognition systems
Linear Discriminant Analysis (LDA): Supervised dimensionality reduction

Technical Implementation

Core ML Framework Architecture

class MLAlgorithm:
    """Base class for all machine learning algorithms"""
    
    def __init__(self, hyperparameters=None):
        self.hyperparameters = hyperparameters or {}
        self.is_fitted = False
        self.performance_metrics = {}
    
    def fit(self, X, y=None):
        """Train the algorithm on the provided data"""
        raise NotImplementedError
    
    def predict(self, X):
        """Make predictions on new data"""
        if not self.is_fitted:
            raise ValueError("Algorithm must be fitted before prediction")
        raise NotImplementedError
    
    def evaluate(self, X_test, y_test):
        """Evaluate algorithm performance"""
        predictions = self.predict(X_test)
        return self._calculate_metrics(predictions, y_test)

Linear Regression Implementation

class LinearRegression(MLAlgorithm):
    def __init__(self, method='direct', learning_rate=0.01, max_iterations=1000):
        super().__init__()
        self.method = method
        self.learning_rate = learning_rate
        self.max_iterations = max_iterations
        self.weights = None
        self.bias = None
    
    def fit(self, X, y):
        if self.method == 'direct':
            self._fit_direct(X, y)
        elif self.method == 'sgd':
            self._fit_sgd(X, y)
        self.is_fitted = True
    
    def _fit_direct(self, X, y):
        # Normal equation: w = (X^T X)^(-1) X^T y
        X_with_bias = np.column_stack([np.ones(X.shape[0]), X])
        self.weights = np.linalg.solve(X_with_bias.T @ X_with_bias, X_with_bias.T @ y)
        self.bias = self.weights[0]
        self.weights = self.weights[1:]

K-Means Clustering Implementation

class KMeansClustering(MLAlgorithm):
    def __init__(self, k=3, max_iterations=100, tolerance=1e-4):
        super().__init__()
        self.k = k
        self.max_iterations = max_iterations
        self.tolerance = tolerance
        self.centroids = None
        self.labels = None
    
    def fit(self, X, y=None):
        # Initialize centroids using K-means++ algorithm
        self.centroids = self._initialize_centroids_plus_plus(X)
        
        for iteration in range(self.max_iterations):
            # Assign points to closest centroids
            distances = self._calculate_distances(X)
            new_labels = np.argmin(distances, axis=1)
            
            # Update centroids
            new_centroids = np.array([X[new_labels == i].mean(axis=0) 
                                    for i in range(self.k)])
            
            # Check for convergence
            if np.allclose(self.centroids, new_centroids, atol=self.tolerance):
                break
                
            self.centroids = new_centroids
            self.labels = new_labels
        
        self.is_fitted = True

Performance Benchmarking Framework

Multi-Dataset Evaluation

Iris Dataset: Classification algorithm testing with 3-class problem
MNIST Dataset: Large-scale digit recognition with 10 classes
Boston Housing: Regression algorithm evaluation with real estate data
Wine Dataset: Multi-class classification with feature engineering
Breast Cancer Wisconsin: Binary classification with medical data

Hyperparameter Optimization

class HyperparameterOptimizer:
    def __init__(self, algorithm_class, param_grid, cv_folds=5):
        self.algorithm_class = algorithm_class
        self.param_grid = param_grid
        self.cv_folds = cv_folds
        self.best_params = None
        self.best_score = -np.inf
    
    def optimize(self, X, y, scoring='accuracy'):
        param_combinations = self._generate_param_combinations()
        
        for params in param_combinations:
            scores = []
            for train_idx, val_idx in self._create_cv_folds(X, y):
                X_train, X_val = X[train_idx], X[val_idx]
                y_train, y_val = y[train_idx], y[val_idx]
                
                # Train algorithm with current parameters
                algorithm = self.algorithm_class(**params)
                algorithm.fit(X_train, y_train)
                
                # Evaluate on validation set
                score = self._calculate_score(algorithm, X_val, y_val, scoring)
                scores.append(score)
            
            # Update best parameters if current is better
            avg_score = np.mean(scores)
            if avg_score > self.best_score:
                self.best_score = avg_score
                self.best_params = params
        
        return self.best_params, self.best_score

Advanced Features

PCA with Eigenface Analysis

class PCAEigenfaces(MLAlgorithm):
    def __init__(self, n_components=None, variance_threshold=0.95):
        super().__init__()
        self.n_components = n_components
        self.variance_threshold = variance_threshold
        self.eigenfaces = None
        self.mean_face = None
        self.explained_variance_ratio = None
    
    def fit(self, face_images):
        # Flatten face images to vectors
        X = face_images.reshape(face_images.shape[0], -1)
        
        # Calculate mean face
        self.mean_face = np.mean(X, axis=0)
        X_centered = X - self.mean_face
        
        # Compute covariance matrix eigendecomposition
        covariance_matrix = X_centered.T @ X_centered / X_centered.shape[0]
        eigenvalues, eigenvectors = np.linalg.eigh(covariance_matrix)
        
        # Sort eigenvalues and eigenvectors in descending order
        sorted_indices = np.argsort(eigenvalues)[::-1]
        eigenvalues = eigenvalues[sorted_indices]
        eigenvectors = eigenvectors[:, sorted_indices]
        
        # Select number of components based on variance threshold
        if self.n_components is None:
            cumulative_variance = np.cumsum(eigenvalues) / np.sum(eigenvalues)
            self.n_components = np.argmax(cumulative_variance >= self.variance_threshold) + 1
        
        self.eigenfaces = eigenvectors[:, :self.n_components]
        self.explained_variance_ratio = eigenvalues[:self.n_components] / np.sum(eigenvalues)
        self.is_fitted = True

Performance Metrics and Analysis

Comprehensive Evaluation Framework

Classification Metrics: Accuracy, Precision, Recall, F1-Score, ROC-AUC
Regression Metrics: MSE, RMSE, MAE, R-squared, Adjusted R-squared
Clustering Metrics: Silhouette Score, Calinski-Harabasz Index, Davies-Bouldin Index
Cross-Validation: K-fold, Stratified K-fold, Leave-one-out

Algorithm Comparison Results

def benchmark_algorithms(algorithms, datasets, metrics=['accuracy', 'precision', 'recall']):
    results = {}
    
    for dataset_name, (X, y) in datasets.items():
        results[dataset_name] = {}
        
        for algorithm_name, algorithm_class in algorithms.items():
            # Perform cross-validation
            cv_scores = cross_validate(algorithm_class(), X, y, 
                                     cv=5, scoring=metrics)
            
            results[dataset_name][algorithm_name] = {
                metric: {
                    'mean': np.mean(cv_scores[f'test_{metric}']),
                    'std': np.std(cv_scores[f'test_{metric}'])
                } for metric in metrics
            }
    
    return results

Educational and Research Value

Theoretical Understanding

Mathematical Foundations: Detailed derivations of algorithm mathematics
Optimization Theory: Gradient descent variants and convergence analysis
Statistical Learning: Bias-variance tradeoff and generalization bounds
Information Theory: Entropy-based measures for decision trees

Practical Applications

Feature Engineering: Automated feature selection and transformation
Model Selection: Systematic algorithm comparison methodologies
Performance Optimization: Computational efficiency improvements
Scalability Analysis: Big data algorithm adaptation strategies

Technologies Used

Python for algorithm implementation and framework development
NumPy for efficient numerical computations and linear algebra
SciPy for advanced mathematical functions and optimization
Matplotlib/Seaborn for performance visualization and analysis
Pandas for data manipulation and experimental results management
Jupyter Notebooks for educational documentation and examples

The project demonstrates deep understanding of machine learning theory, algorithm implementation expertise, and comprehensive software engineering practices essential for ML research, algorithm development, and data science applications.