An Interval Type-2 Neural Fuzzy Classifier Learned Through Soft Margin Minimization and its Human Posture Classification Application

Abstract

This paper proposes an interval type-2 neural fuzzy classifier learned through soft margin minimization (IT2NFC-SMM) and applies it to human body posture classification. The IT2NFC-SMM consists of interval type-2, zero-order Takagi–Sugeno (T–S) fuzzy rules established through online structure learning. The antecedent part of the IT2NFC-SMM uses interval type-2 fuzzy sets to decrease the number of rules and manage noisy data. For parameter learning, the consequent parameters are learned through a linear support vector machine (SVM) for soft margin minimization to improve the generalization ability. The proposed SVM-based learning addresses the problem that the orders of the fuzzy rules in computing the outputs of an interval type-2 fuzzy system depend on the consequent values that are unknown in advance. To address this problem, the IT2NFC-SMM uses weighted bound-set boundaries to simplify the type-reduction operation and a novel crisp-to-interval linear SVM learning algorithm. Based on the soft margin minimization, the antecedent parameters are tuned using the gradient descent algorithm. The IT2NFC-SMM is applied to a vision-based human body posture classification system. The system uses two cameras and novel classification features extracted from a silhouette of the human body to classify the four postures of standing, bending, sitting, and lying. The classification performance of the IT2NFC-SMM is verified through results in clean and noisy classification examples and through the posture classification problem, as well as through comparisons with various type-1 and type-2 fuzzy classifiers. The overall result shows that the IT2NFC-SMM achieves higher classification rates with a smaller or similar model size than the classifiers used for comparison, especially for noisy classification problems.