The Geometry of Feelings: Mathematical Modeling of Affective States

Researchers have struggled for a long time to measure human emotion because it sits at the crossroads of psychology, physiology, and computer science. Recent research show that emotional states are better understood as complicated geometric forms inside high-dimensional spaces, whereas conventional models usually define them as simple coordinates on a valence-arousal plane. The study looks at how to mathematically model emotional states and suggests a system that combines multimodal signal variance, text-based sentiment analysis, and behavioral indicators into one geometric depiction. Using ideas from signal processing and category theory, we hope to create a map of how psychological outcomes change in response to changes in physiological inputs. We consider the restrictions of present linear methods and contend that a topological viewpoint—treating emotions as objects with morphisms—provides a more reliable route for predictive accuracy in human-computer interaction.