A Novel Fuzzy Large Margin Distribution Machine with Unified Pinball Loss

On the basis of the support vector machine (SVM), Large Margin Distribution Machine (LDM) improves the generalization performance by incorporating the marginal distribution theory. Nevertheless, the current LDM models (LDMs) still exhibit limitations when it comes to handling noisy data, such as: i) LDMs fails to effectively discern the samples being noise and consequently falls short in robust defenses. ii) The hinge loss of LDMs is predicated upon the minimal inter-category separation, rendering the corresponding classifier highly susceptible to perturbations induced by noise. To address these limitations, we leverage the fuzzy set theory and pinball loss function, and propose a novel Fuzzy Large Margin Distribution Machine with Unified Pinball Loss (FUPLDM), which is performed as: i) An innovative fuzzy membership function is developed, utilizing two distinct types of feature centers and their associations with the samples. The function assigns a probability to each sample, indicating the likelihood of it being classified as noise. As a result, the model gains the remarkable ability to accurately identify and distinguish noise from other data. ii) Replace the hinge loss function with the unified pinball loss. The pinball loss function is based on interquartile distance, which is less affected by noise and can well improve the noise immunity of the classifier at the boundary. Therefore, FUPLDM has superior noise recognition capabilities and substantial noise resistance against its detrimental effects. Furthermore, We also analyzed the properties of FUPLDM, including noise insensitivity, intra-class distance, inter-class scatter, and misclassification error. At last, we conduct a series of comparative experiments on artificial synthetic datasets, UCI benchmark datasets, and noise-added UCI datasets, which demonstrate the effectiveness and superiority of FUPLDM.