SVM Classification for Breast Cancer Diagnosis Based on Breast Tissue Electrical Impedance Properties

(1) Support Vector Machines (SVM) are specifically developed for small-sample problems, enabling optimal solution derivation under limited data availability through maximum margin classification principles. The core implementation utilizes kernel functions (linear, RBF, or polynomial) to map data to higher-dimensional spaces for linear separation. (2) The SVM algorithm formulation converts into a quadratic programming optimization problem, which guarantees global optimum solutions theoretically - addressing the local optima limitations common in traditional neural networks. This is computationally implemented through Lagrange multipliers and Karush-Kuhn-Tucker conditions. (3) SVM's topological structure is automatically determined by support vectors (critical training samples near decision boundaries), eliminating the iterative architecture-tuning required in traditional neural networks. The number of support vectors directly influences model complexity through the Representer Theorem.

SVM classifiers exhibit these distinctive characteristics: (1) Specifically engineered for small-sample scenarios, SVMs achieve optimal decision boundaries even with limited datasets using structural risk minimization. Code implementation typically involves sklearn.svm.SVC with careful parameter tuning for C (regularization) and gamma (kernel coefficient). (2) By formulating classification as a convex quadratic programming problem, SVMs guarantee global optimal solutions - resolving local optima pitfalls common in neural network backpropagation. Practical implementation uses sequential minimal optimization (SMO) algorithms for efficient computation. (3) The network architecture self-adapts through support vector selection, avoiding manual neural network topology experiments. The support vectors can be programmatically extracted post-training using model.support_vectors_ attribute for model interpretation.