Complex and Hypercomplex-Valued Support Vector Machines: A Survey

Abstract

In recent years, the field of complex, hypercomplex-valued and geometric Support Vector Machines (SVM) has undergone immense progress due to the compatibility of complex and hypercomplex number representations with analytic signals, as well as the power of description that geometric entities provide to object descriptors. Thus, several interesting applications can be developed using these types of data and algorithms, such as signal processing, pattern recognition, classification of electromagnetic signals, light, sonic/ultrasonic and quantum waves, chaos in the complex domain, phase and phase-sensitive signal processing and nonlinear filtering, frequency, time-frequency and spatiotemporal domain processing, quantum computation, robotics, control, time series prediction, and visual servoing, among others. This paper presents and discusses the importance, recent progress, prospective applications, and future directions of complex, hypercomplex-valued and geometric Support Vector Machines.

Remote Monitoring and Fault Diagnosis of Ocean Current Energy Hydraulic Transmission and Control Power Generation System

“…In the case of multiple concurrent faults in hydraulic transmission and control power generation systems, the main diagnostic methods are extreme learning machines and support vector machines (SVMs). Arana-Daniel reviewed proposals to extend the SVM algorithm to deal with complex and hypercomplex-valued inputs, outputs, and kernels [21]. As we know, support vector machine (SVM) and k-Nearest Neighbor (kNN) algorithms can manage the nonlinearity issues.…”