Mathematical modeling of human emotions using sub-band coefficients of wavelet analysis

Human emotion reflects on human behavior which plays a vital role in physiological research and real-time application. Mathematical modeling of emotional states plays a significant role in this scope which can correlate between human cognition, emotion and mental behavior. In this paper, we propose a new approach to model the emotional states with mathematical expressions based on wavelet analysis and trust region algorithm. The brain signals are collected using BIOPAC automated MP36 system and transformed on time-frequency domain using Daubechies4 wavelet function on different emotional states such as relax, memory, pleasant, fear, motor action, and enjoying music to extract the wavelet coefficients of these different states. The emotional states are modeled with different mathematical expressions which can be verified with these wavelet coefficients from the adjusted R-square percentage and the sum of square errors. The adjusted R- square percentage of the mathematical modeled states with the actual emotional states are 78.4% for relax, 77.18% for motor action and for memory, pleasant, enjoying music and fear they are 93%, 95.6%, 97.7% and 91.5% respectively. The main focus of this paper is to propose the mathematical modeling of these states which can be further applied for practical hardware implementation of human emotion based systems.