Instrumentation & Measurement Magazine 24-6 - 8

Fig. 2. Typical Signatures for Falls and ADLs events [16] (©2015 IEEE).
discouraged. The main reasons are related to the strong sensitivity
of this approach to user-dependent characteristics
(weight, height, etc.) or exogenous factors (noise, dynamic
not correlated to the user posture), which may seriously compromise
the classification performances. The use of effective
scores, as the one illustrated above, improves the opportunity
to build robust classification strategies.
Concerning the kind of classification paradigms, two main
classes are worthy of consideration: threshold based [16],
which perform quite well and are suitable for implementation
in low cost/low power embedded solutions; and the very performing
machine learning approaches [8], [9], which are not
always compliant with low-power embedded systems and
will not be further discussed in this paper.
Threshold-based classification algorithms compare scores
that are generated by the above-mentioned strategies with
threshold values. An event is classified as belonging to a specific
class if the comparison process succeeds.
The definition of a reliable threshold is a mandatory step in
the classification procedure. An appropriate strategy to define
suitable thresholds exploits the Receiver Operating Characteristic
(ROC) theory [27]. It has been widely used in signal
detection theory, to depict the tradeoff between hit rates and
false alarm rates of classifiers, as a function of working parameters
(such as the threshold value). The same theory has
8
been also widely applied to analyze the behavior of diagnostic
systems.
The ROC theory allows thresholds to be identified by maximizing
a functional index, adopted to assess the performances
of the classification strategy. In order to define above indexes,
the following quantities must be defined. Given a classifier
and an instance, there are four possible outcomes. If the instance
is positive and it is classified as positive, it is counted as
a TP (True Positive); if it is classified as negative, it is counted as
a FN (False Negative). If the instance is negative and it is classified
as negative, it is counted as a TN (True Negative); and if
it is classified as positive, it is counted as a FP (False Positive).
These quantities allow to define the following indexes:
True Positive Rate TPR 
:
False Positive Rate FPR 
:
TP FN
TP

FP TN
FP

(1)
(2)
ROC curves are two-dimensional curves in which TPR
is plotted against FPR, to depict relative tradeoffs between
benefits (TPR) and cost (FPR). An example of ROC curve is presented
in Fig. 3.
ROC graphs can be successfully used for the identification
of threshold maximizing a given metric. For each threshold
IEEE Instrumentation & Measurement Magazine
September 2021

Instrumentation & Measurement Magazine 24-6

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