The growth and acceptance of wearable devices (e.g., accelerometers) and personal technologies (e.g.,
smartphones), coupled with larger storage capacities, waterproofing, and more unobtrusive wear locations, has
made long-term monitoring of behaviors throughout the 24-hour spectrum more feasible. Wearable devices
relevant for human activity (e.g., GENEActiv accelerometer) contain several complementary sensors
(accelerometers, gyro, heart- rate monitor etc.) and sample at high rates (e.g., 100Hz for accelerometer). These
high-sampling rates and the long duration of capture result in life-log data that truly qualifies as multimodal and
big time-series data. The challenges and opportunities involved in fully harvesting these types of data, for widely
applicable interventions, suggest that an interdisciplinary approach spanning mathematical sciences, signal
processing, and health is needed. Our innovation includes the use of functional-data analysis tools to represent
and process the dense time-series data. Functional data analysis is then integrated into machine learning and
pattern discovery algorithms for activity classification, prediction of attributes, and discovery of new activity
classes. We anticipate that the proposed framework will lead to new insights about human activity and its impact
on health outcomes. This interdisciplinary project builds on several research activities of the team. Our past work
includes: a) new mathematical developments for computing statistics on time-series data viewed as elements of
a function-spaces, b) algorithms for activity recognition that integrate the function-space techniques, and c) data
from long-term observational studies of human activity from multimodal sensors. The new work we propose
addresses the unique mathematical and computational challenges posed by densely multimodal, long-term,
densely-sampled Iifelog big-data in a comprehensive framework. The fusion of ideas from human activity
modeling, functional-analysis, geometric metrics, and algorithmic machine learning, present unique opportunities
for fundamental advancement of the state-of-the-art in objective measurement and quantification of behavioral
markers from wearable devices. The proposed approach also brings to fore: a) new mathematical developments
of elastic metrics over multi-modal time-series data, b) comparing sequences evolving on different feature
manifolds, c) estimation of quasi- periodicities, d) and a new generation of machine-learning and pattern
discovery algorithms. The mathematical and algorithmic tools proposed have the potential to significantly
advance how wearable data from contemporary devices with high-sampling rates and large storage capabilities
are represented, processed, and transformed into accurate inferences about human activity. Wearable devices
are becoming more widely adopted in recent years for general health and recreational uses by the broad
populace. This research will result in improved algorithms to process the data available from such wearable
devices. The long-term goal of the research is to enable personalized home-based physical activity regimens for
conditions such as stroke and diabetes.