Stochastic nonparallel hyperplane support vector machine for binary classification problems and no-free-lunch theorems
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RESEARCH PAPER
Stochastic nonparallel hyperplane support vector machine for binary classification problems and no‑free‑lunch theorems Ashish Sharma1 Received: 27 August 2019 / Revised: 28 July 2020 / Accepted: 27 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, the binary classification problem is considered and its solution is proposed as the formulated classification model, based on genetic algorithm (GA) and nonparallel hyperplane support vector machine (NHSVM), termed as stochastic nonparallel hyperplane support vector machine (SNHSVM). As GA provably violates the non-revisiting condition of the no-free-lunch theorems for optimization (NFLO), then SNHSVM have the natural property that NFLO do not apply to it. All the experiments are performed in a scenario in which no-free-lunch theorems for machine learning (NFLM) do not apply on all the compared machines. The hypothesis is that in such a scenario some classifier can perform better than others. The experiments are performed on the real world UCI datasets and the SNHSVM is compared with the state of art support vector based classifiers with performance measure as accuracy. SNHSVM achieves the highest accuracy in 100% of the cases and the Friedman test confirms the better performance of SNHSVM on all of the datasets used. These results validate the hypothesis empirically while apart from SNHSVM the NFLM floats up for the other compared classifiers. Keywords Machine learning · Optimization · No-free-lunch theorems · Parallel and non-parallel hyperplane support vector machines · Genetic algorithm
1 Introduction Machine learning is the creation of programs that can act like humans, and one of the most important human (and therefore machine learning) task is classification. In classification one needs to predict the class of an unknown object from the knowledge of training over example objects usually called a training data (there can be many classes while two classes are often called binary and in this paper by class I always mean binary until otherwise stated). The most popular algorithms to perform the classification tasks are based on support vectors. In this line the idea of binary support vector machine (SVM) [1–4] is to find two supporting hyperplanes (one for each class) such that they are as close as possible to their own classes and as far away as possible to the other class while the decision hyperplane is at the center of the two supporting hyperplanes. This idea was a great success in a wide variety of areas [5–10]. In the quest * Ashish Sharma [email protected] 1
Institute of Engineering and Science, IPS Academy, Rajendra Nagar A.B. Road, Indore 452012, India
of increasing the generalization ability and performance of SVM the idea is modified to get the category of nonparallel machines with support vectors by relaxing the requirement of parallel hyperplanes for the supporting hyperplanes. In this regard, for e.g. Generalized Eigenvalue Proximal Support Vector Machine (GEPSVM) [11] and
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