Diagnosis of breast cancer using flexible pinball loss support vector machine

Abstract

Breast cancer is a common disease that affects feminine health, making it an active area of research. Also, support vector machine with pinball loss (pin-SVM) is an efficient classification algorithm to address noise sensitivity and re-sampling instability. The pinball loss function uses a loss parameter τ∈[0,1] which corresponds to the quantile level. However, the non-negativity condition on τ is not necessary, and it can be extended to the negative values for an improvement in classification accuracy. Also, instead of a positive loss parameter τ, two positive parameters, τ1 and τ2 are used in literature, which improve the generalization performance of the pin-SVM. Taking motivation from the aforementioned observations, in this paper, we propose an innovative loss function, termed the flexible pinball loss, which extends the parameters τ1 and τ2 to encompass negative values. This extension enables the function to take τ1 and τ2 values from −1 to 1 while preserving convexity. Subsequently, we integrate the proposed flexible pinball loss function into the support vector machine framework and propose a novel model named flexible pinball loss support vector machine (FP-SVM) for the prediction of breast cancer. FP-SVM provides loss to both incorrectly and correctly classified samples, leveraging the parameters τ1 and τ2, respectively. Importantly, FP-SVM strategically traverses the maximum solution path, ensuring the preservation of convexity within the optimization problem. The proposed FP-SVM outperforms the baseline models in terms of accuracy, which is empirically supported by numerical experiments on 30 UCI and KEEL benchmark datasets. Furthermore, to show the efficacy of the proposed FP-SVM in real-world application, we performed experiments on publicly available breast cancer dataset (BreakHis), and the results demonstrate that the proposed FP-SVM outperforms the baseline models. © 2024 Elsevier B.V.