Sequential Minimal Optimization (SMO) Algorithm for Support Vector Machines

For image classification tasks, the Sequential Minimal Optimization (SMO) algorithm serves as an efficient approach for Support Vector Machine training. This algorithm effectively categorizes images into distinct classes by optimizing the separation boundaries between different categories. In implementation, the process requires extracting meaningful features from images using descriptors such as HOG (Histogram of Oriented Gradients) or SURF (Speeded-Up Robust Features). The SMO algorithm then optimizes the Lagrange multipliers of the SVM dual problem by iteratively solving the smallest possible quadratic programming subproblems—typically involving only two multipliers at a time—using analytical methods rather than numerical optimization. Key functions include kernel computation (e.g., linear or RBF kernels), error calculation, and multiplier update rules with bias adjustment. Through SMO, we achieve higher classification accuracy and algorithm reliability by ensuring efficient convergence and handling large-scale datasets with optimized memory usage. The implementation typically involves steps like data normalization, kernel matrix caching, and convergence checks using KKT (Karush-Kuhn-Tucker) conditions.