Online Recognition with Postural Transition Awareness - Smartphone-Based Human Activity Recognition - page 112

and 50% overlap between them. Features are extracted from these window samples
through measures in the time domain (Sect. 4.3.3 ) , that we represent with the

ˆ ()

function, in order to match a reduced set of features from dataset D 3 T according

to the MC-L1-SVM learning intrinsic feature selection (Sect. 6.2 ) . In Chap. 6 we
opted to work with this set of features in order to reduce computational costs without
noticeably affecting classification accuracy.

7.3.2 Implementation of the SVM Feed Forward Phase

The ML algorithm chosen to be implemented for the PTA-HAR system was the
MC-L1-SVM. This linear algorithm provides a fast approach for performing activity
recognition with a reduced set of features without affecting the prediction accuracy
as presented in the results of Sect. 6.4.3 . Model training is performed offline and the
SVM FFP is performed online. The FFP formulation for each class c , as depicted
in Eq. ( 6.4 ) , avoids the non-zero weights ( 0) making the computation faster.

The outputs of the classifiers are compared after a normalization procedure. For this,
we use probability estimates as we have previously described in Sect. 5.2.2 in order
to obtain the probability output vector p

w i =

which represents, for a given window
sample x , the collection of probabilities of being classified as a certain class c :

( x )

1

p c ( x ) =

e ( c f c ( x ) + c ) ,

(7.1)

+

1

where the c parameters can be learned for each class by solving the mini-

mization problem in Eq. ( 5.8 ) . At this point, it is possible to determine which of the
classes (activity c ∗ ) is the one that best represents an input sample x :

c and

c ∗ = arg max

c

p c ( x ) . (7.2)

This classification approach is applicable to the PTA-6A and PTA-7A methods.

7.3.3 Temporal Activity Filtering

The classification approach presented above (Eq. ( 7.2 )) produces only a discrete
output that indicates the class that best represents a test input (window sample).
Moreover, it is known that the SVM is itself a static method which only depends
on its input x and it is not affected, for instance, by other factors such as previously
predicted samples or how probable the other activities are during the FFP.
Considering the fact that, in real world situations, activities can be described as
a sequence of correlated events, we take advantage of the SVM with probability
estimates in a more extensive way rather than utilizing just one discrete prediction.