Dementia is a progressive condition that significantly impairs quality of life, with limited effective treatments available for managing its late stages. Music therapy has emerged as a promising intervention, potentially improving well-being in dementia patients through physiological and emotional engagement. This study explores the physiological responses of late-stage dementia patients undergoing a music therapy intervention, utilizing manifold learning to analyze data recorded over three sessions: a control session, after 1 week of intervention, and after 6 weeks. We focus on characterizing changes in heart rate (HR), electrodermal activity (EDA), movement (ACC), and skin temperature (ST) to identify patterns associated with potential improvements in well-being. Manifold learning was applied to these physiological metrics to discern nonlinear relationships that may highlight the intervention's effects. Statistical analyses further examine these differences, providing quantitative support for improvements in physiological responses, indicating enhanced well-being in response to prolonged music therapy interventions.