Semi-supervised clustering of quaternion time series: Application to gait analysis in multiple sclerosis using motion sensor data.

Recent approaches in gait analysis involve the use of wearable motion sensors to extract spatio-temporal parameters that characterize multiple aspects of an individual's gait. In particular, the medical community could largely benefit from this type of devices as they could provide the clinicians with a valuable tool for assessing gait impairment. Motion sensor data are however complex and there is an urgent unmet need to develop sound statistical methods for analyzing such data and extracting clinically relevant information. In this article, we measure gait by following the hip rotation over time and the resulting statistical unit is a time series of unit quaternions. We explore the possibility to form groups of patients with similar walking impairment by taking into account their walking data and their global decease severity with semi-supervised clustering. We generalize a compromise-based method named hclustcompro to unit quaternion time series by combining it with the proper dissimilarity quaternion dynamic time warping. We apply this method on patients diagnosed with multiple sclerosis to form groups of patients with similar walking deficiencies while accounting for the clinical assessment of their overall disability. We also compare the compromise-based clustering approach with the method mergeTrees that falls into a sub-class of ensemble clustering named collaborative clustering. The results provide a first proof of both the interest of using wearable motion sensors for assessing gait impairment and the use of prior knowledge to guide the clustering process. It also demonstrates that compromise-based clustering is a more appropriate approach in this context.

A Novel Walking Activity Recognition Model for Rotation Time Series Collected by a Wearable Sensor in a Free-Living Environment.

Solutions to assess walking deficiencies are widespread and largely used in healthcare. Wearable sensors are particularly appealing, as they offer the possibility to monitor gait in everyday life, outside a facility in which the context of evaluation biases the measure. While some wearable sensors are powerful enough to integrate complex walking activity recognition models, non-invasive lightweight sensors do not always have the computing or memory capacity to run them. In this paper, we propose a walking activity recognition model that offers a viable solution to this problem for any wearable sensors that measure rotational motion of body parts. Specifically, the model was trained and tuned using data collected by a motion sensor in the form of a unit quaternion time series recording the hip rotation over time. This time series was then transformed into a real-valued time series of geodesic distances between consecutive quaternions. Moving average and moving standard deviation versions of this time series were fed to standard machine learning classification algorithms. To compare the different models, we used metrics to assess classification performance (precision and accuracy) while maintaining the detection prevalence at the level of the prevalence of walking activities in the data, as well as metrics to assess change point detection capability and computation time. Our results suggest that the walking activity recognition model with a decision tree classifier yields the best compromise in terms of precision and computation time. The sensor that was used had purposely low computing and memory capacity so that reported performances can be thought of as the lower bounds of what can be achieved. Walking activity recognition is performed online, i.e., on-the-fly, which further extends the range of applicability of our model to sensors with very low memory capacity.