A MATLAB Program for K-Nearest Neighbors Classification

The K-Nearest Neighbors (KNN) algorithm is a simple yet effective classification method widely used in pattern recognition and machine learning domains. Implementing a KNN classifier in MATLAB primarily involves three core steps: data preparation, distance computation, and voting decision.

First, the KNN algorithm operates on instance-based learning principles. Given a training dataset where each sample has known labels, when classifying new unknown samples, the algorithm calculates distances between the target sample and all training samples. Common distance metrics include Euclidean distance (calculated using norm or vector operations) and Manhattan distance (implemented with sum of absolute differences). In MATLAB, distance computation can be efficiently vectorized using matrix operations like pdist2 or custom distance functions.

Second, K-value selection is critical for performance. K represents the number of nearest neighbors considered during classification decisions. Smaller K values may make the model sensitive to noise, while larger K values might oversmooth decision boundaries. MATLAB provides cross-validation techniques through functions like crossval to optimize K-value selection programmatically, typically by evaluating classification accuracy across different K values.

Finally, KNN classification determines new sample categories through majority voting. Among the K nearest neighbors, the most frequently occurring class label is assigned to the new sample. MATLAB's Statistics and Machine Learning Toolbox offers built-in functions such as fitcknn for model training (which handles distance metric selection, K-value specification, and weight adjustments) and predict for classification inference, significantly simplifying KNN implementation. The fitcknn function supports various parameters including Distance (metric selection), NumNeighbors (K-value setting), and Standardize (data normalization options).

KNN's advantages include intuitive implementation and no explicit training phase, but computational complexity increases with dataset size. Practical applications often employ data normalization (using zscore or normalize functions) and dimensionality reduction techniques (like PCA through pca function) to enhance KNN performance and efficiency. MATLAB's vectorization capabilities allow optimized computation of nearest neighbors through efficient sorting algorithms and distance matrix operations.