Suárez Carlos Aníbal, Castro Mauricio, Leon Mariuxi, Martin-Barreiro Carlos, Liut Michael
Faculty of Natural Sciences and Mathematics, Escuela Superior Politécnica del Litoral (ESPOL), Campus Gustavo Galindo, Km. 30.5 Vía Perimetral, 090902 Guayaquil, Guayas Ecuador.
Department of Mathematical and Computational Sciences, University of Toronto, Mississauga, Canada.
Complex Intell Systems. 2025;11(8):356. doi: 10.1007/s40747-025-01989-4. Epub 2025 Jun 21.
In the dual optimization problem behind Support Vector Machine (SVM), each data point corresponds to a decision variable. Therefore, removing data points is equivalent to reducing the dimensionality of the dual problem, leading to a more efficient optimization process. We introduce linear programming models to determine whether two sets of points are linearly separable efficiently, compute the misclassification rate, and reduce the dimension of the optimization problems behind the SVM procedure. Data reduction can be conducted using a simple convexity property for the linearly separable case. The misclassification rate is a key indicator of the complexity of separating the two sets, providing valuable insights into the classification performance. Our approach combines SVM optimization with linear programming techniques to offer a comprehensive classification and complexity analysis framework.
在支持向量机（SVM）背后的对偶优化问题中，每个数据点都对应一个决策变量。因此，去除数据点等同于降低对偶问题的维度，从而带来更高效的优化过程。我们引入线性规划模型来有效确定两组点是否线性可分，计算误分类率，并降低SVM过程背后优化问题的维度。对于线性可分的情况，可以利用简单的凸性属性进行数据约简。误分类率是分离两组数据复杂性的关键指标，能为分类性能提供有价值的见解。我们的方法将SVM优化与线性规划技术相结合，提供了一个全面的分类和复杂性分析框架。
