KNN k-Nearest Neighbors Algorithm with Distance Metric Options

In machine learning, the KNN (k-Nearest Neighbors) algorithm is a fundamental supervised learning method. The core principle involves classifying or predicting values for test instances by identifying the k closest neighbors from the training dataset. The k-value serves as a critical hyperparameter that requires careful tuning based on specific dataset characteristics and problem requirements. The algorithm's implementation requires selecting an appropriate distance metric function. Commonly used metrics include Euclidean distance (calculated as the square root of the sum of squared differences between coordinates) and Manhattan distance (computed as the sum of absolute differences between coordinates). These metrics have distinct applications - Euclidean distance works well with continuous, correlated features, while Manhattan distance often performs better with high-dimensional or sparse data. When implementing KNN in code, developers typically create a distance calculation function that can switch between metrics using conditional logic or strategy pattern. The algorithm workflow involves: 1) Computing distances between the test instance and all training samples, 2) Sorting distances to find k-nearest neighbors, 3) Aggregating neighbor labels (for classification) or values (for regression). Key implementation considerations include handling data normalization, optimizing distance computations for large datasets using vectorization, and selecting k through cross-validation techniques. Distance metric selection should account for data distribution patterns, feature scales, presence of outliers, and computational efficiency requirements. Proper metric choice significantly impacts model performance, particularly when dealing with noisy data or features with varying importance.