  The study of ground reaction forces (GRF) is used to characterize the
mechanical loading experienced by individuals in movements such as running,
which is clinically applicable to identify athletes at risk for stress-related
injuries. Our aim in this paper is to determine if data collected with inertial
measurement units (IMUs), that can be worn by athletes during outdoor runs, can
be used to predict GRF with sufficient accuracy to allow the analysis of its
derived biomechanical variables (e.g., contact time and loading rate).
  In this paper, we consider lightweight approaches in contrast to
state-of-the-art prediction using LSTM neural networks. Specifically, we
compare use of LSTMs to k-Nearest Neighbors (KNN) regression as well as propose
a novel solution, SVD Embedding Regression (SER), using linear regression
between singular value decomposition embeddings of IMUs data (input) and GRF
data (output). We evaluate the accuracy of these techniques when using training
data collected from different athletes, from the same athlete, or both, and we
explore the use of acceleration and angular velocity data from sensors at
different locations (sacrum and shanks). Our results illustrate that simple
machine learning methods such as SER and KNN can be similarly accurate or more
accurate than LSTM neural networks, with much faster training times and
hyperparameter optimization; in particular, SER and KNN are more accurate when
personal training data are available, and KNN comes with benefit of providing
provenance of prediction. Notably, the use of personal data reduces prediction
errors of all methods for most biomechanical variables.
