  Identification of falls while performing normal activities of daily living
(ADL) is important to ensure personal safety and well-being. However, falling
is a short term activity that occurs infrequently. This poses a challenge to
traditional classification algorithms, because there may be very little
training data for falls (or none at all). This paper proposes an approach for
the identification of falls using a wearable device in the absence of training
data for falls but with plentiful data for normal ADL. We propose three
`X-Factor' Hidden Markov Model (XHMMs) approaches. The XHMMs model unseen falls
using "inflated" output covariances (observation models). To estimate the
inflated covariances, we propose a novel cross validation method to remove
"outliers" from the normal ADL that serve as proxies for the unseen falls and
allow learning the XHMMs using only normal activities. We tested the proposed
XHMM approaches on two activity recognition datasets and show high detection
rates for falls in the absence of fall-specific training data. We show that the
traditional method of choosing a threshold based on maximum of negative of
log-likelihood to identify unseen falls is ill-posed for this problem. We also
show that supervised classification methods perform poorly when very limited
fall data are available during the training phase.
