A Novel Fuzzy Large Margin Distribution Machine With Unified Pinball Loss

Based on the support vector machine (SVM), the 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 handling noise, such as: i) LDMs fail to effectively discern the noise samples and consequently fall short in robust defenses. ii) The hinge loss of LDMs is predicated upon the minimal inter-category separation, rendering the classifier highly susceptible to perturbations. 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 membership degree indicates the likelihood of a sample being classified as noise. As a result, the model gains the remarkable ability to accurately identify and distinguish noise. ii) A unified pinball (UP) loss is utilized to replace the hinge loss. The UP function is based on interquartile distance, which is less affected by noise and helps improve the noise immunity. 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 that demonstrate the effectiveness and superiority of FUPLDM.