title: Mathematical Modeling and Evaluation of Human Motions in Physical Therapy Using Mixture Density Neural Networks.
abstract: OBJECTIVE
  The objective of the proposed research is to develop a methodology for modeling and evaluation of human motions, which will potentially benefit patients undertaking a physical rehabilitation therapy (e.g., following a stroke or due to other medical conditions). The ultimate aim is to allow patients to perform home-based rehabilitation exercises using a sensory system for capturing the motions, where an algorithm will retrieve the trajectories of a patient's exercises, will perform data analysis by comparing the performed motions to a reference model of prescribed motions, and will send the analysis results to the patient's physician with recommendations for improvement.
  
  
  METHODS
  The modeling approach employs an artificial neural network, consisting of layers of recurrent neuron units and layers of neuron units for estimating a mixture density function over the spatio-temporal dependencies within the human motion sequences. Input data are sequences of motions related to a prescribed exercise by a physiotherapist to a patient, and recorded with a motion capture system. An autoencoder subnet is employed for reducing the dimensionality of captured sequences of human motions, complemented with a mixture density subnet for probabilistic modeling of the motion data using a mixture of Gaussian distributions.
  
  
  RESULTS
  The proposed neural network architecture produced a model for sets of human motions represented with a mixture of Gaussian density functions. The mean log-likelihood of observed sequences was employed as a performance metric in evaluating the consistency of a subject's performance relative to the reference dataset of motions. A publically available dataset of human motions captured with Microsoft Kinect was used for validation of the proposed method.
  
  
  CONCLUSIONS
  The article presents a novel approach for modeling and evaluation of human motions with a potential application in home-based physical therapy and rehabilitation. The described approach employs the recent progress in the field of machine learning and neural networks in developing a parametric model of human motions, by exploiting the representational power of these algorithms to encode nonlinear input-output dependencies over long temporal horizons.
authors.affiliation: Industrial Technology, University of Idaho, Idaho Falls, United States.
authors.forename: A
authors.initials: A
authors.lastname: Vakanski
authors.affiliation: Center for Modeling Complex Interactions, University of Idaho, Moscow, United States.
authors.forename: J M
authors.initials: JM
authors.lastname: Ferguson
authors.affiliation: Department of Statistical Science, University of Idaho, Moscow, United States.
authors.forename: S
authors.initials: S
authors.lastname: Lee
keywords: Auto-encoder; Mathematical model; Mixture density network; Neural networks; Performance metric; Physical rehabilitation; Recurrent neural networks; Time series