# Fourier Transform Analysis of GPS-Derived Mobility Patterns for Diagnosis and Mood Monitoring of Bipolar and Major Depressive Disorders: Prospective Study

## TL;DR

This study shows that GPS mobility patterns, analyzed using Fourier transforms, can help diagnose and monitor bipolar and major depressive disorders by capturing differences in movement behaviors.

## Contribution

The study introduces Fourier transform analysis of GPS data as a novel method for distinguishing and monitoring mood disorders through mobility patterns.

## Key findings

- Fourier transform analysis of GPS data revealed distinct mobility patterns between bipolar and major depressive disorder patients.
- Location variance's power spectrum was a significant predictor of depressed mood after adjusting for demographic factors.
- Daily GPS data correlated more strongly with real-time mood assessments than weekly or monthly data.

## Abstract

Mood disorders, including bipolar disorder (BP) and major depressive disorder (MDD), are characterized by significant psychological and behavioral fluctuations, with mobility patterns serving as potential markers of emotional states.

This study explores the diagnostic and monitoring capabilities of Fourier transform, a frequency-domain analysis method, in mood disorders by leveraging GPS data as an objective measure.

A total of 62 participants (BP: n=20, MDD: n=27, and healthy controls: n=15) contributed 5177 person-days of data over observation periods ranging from 5 days to 6 months. Key GPS indicators—location variance (LV), transition time (TT), and entropy—were identified as reflective of mood fluctuations and diagnostic differences between BP and MDD.

Fourier transform analysis revealed that the maximum power spectra of LV and entropy differed significantly between BP and MDD groups, with patients with BP exhibiting greater periodicity and intensity in mobility patterns. Notably, participants with BP demonstrated consistent periodic waves (eg, 1-d, 4-d, and 9-d cycles), while such patterns were absent in those with MDD. In addition, after adjusting for age, gender, and employment status, only the power spectrum of LV remained a significant predictor of depressed mood (odds ratio [OR] 0.9976, 95% CI 0.9956‐0.9996; P=.02). Daily GPS data showed stronger correlations with ecological momentary assessment (EMA)–reported mood states compared to weekly or monthly aggregations, emphasizing the importance of day-to-day monitoring. Depressive states were associated with reduced LV (OR 0.975, 95% CI 0.957‐0.993; P=.008) and TT (OR 0.048, 95% CI 0.012‐0.200; P<.001) on weekdays, and lower entropy (OR 0.662, 95% CI 0.520‐0.842; P=.001) on weekends, indicating that mobility features vary with social and temporal contexts.

This study underscores the potential of GPS-derived mobility data, analyzed through Fourier transform, as a noninvasive and real-time diagnostic and monitoring tool for mood disorders. The findings suggest that the intensity of mobility patterns, rather than their frequency, may better differentiate BP from MDD. Integrating GPS data with EMAs could enhance the precision of clinical assessments, provide early warnings for mood episodes, and support personalized interventions, ultimately improving mental health outcomes. This approach represents a promising step toward digital phenotyping and advanced mental health monitoring strategies.