Online Recognition with Postural Transition Awareness - Smartphone-Based Human Activity Recognition - page 117

Table 7.1 Classification error assessment conditions for BAs and PTs
Ground-truth

Prediction Error evaluation

Basic activities
A1 - A1 - A1 A1 - A1 - A1 Correct

A1 - A1 - A1 A1 - A2 - A1 Incorrect

A1 - A1 - A1 A1-UA-A1 Incorrect

Incorrect a A1 - A1 - A1 A1 - PT - A1

Postural transitions
A1 - PT - A2 A1 - A1 ∨ A2 - A2 Correct

A1 - PT - A2 A1 - A3 - A2 Incorrect

A1 - PT - A2 A1-UA-A2 Correct

Correct a A1 - PT - A2 A1 - PT - A2

A Activity, U Unknown a Only applicable to the PTA-7A method

7.4.2 Online System Error Estimation and Performance
Evaluation

The method for the evaluation of the online system error requires some modifications
given that PTs are now taken into account. Table 7.1 explains our error assessment
method during the occurrence of PTs and BAs. It defines the conditions when a
prediction is considered correct or not. It also takes into account the detection of the
unknown-activity.
From these conditions we have developed an error metric to evaluate the system
performance as a function of the predicted activity c t and the ground truth targets of

the labeled data in the vicinity of time t : y t − 1 , y t , and y t + 1 .ItisvalidforPTA-6A
and PTA-7A methods, and it has the following formulation:

ˆ

⊧
⊨
⊩

⊧
⊨
⊩

y t =ˆ c t ∨

y t ˆ

y t + 1 ∨

ˆ y t + 1

0f = PT ∧ y t − 1 = y t + 1 ∧ c t = y t − 1 ∨ˆ c t =

c t , y t − 1 , y , y t

UA = PT ∧ˆ c t =

1 otherwise ,

(7.3)

Notice that the error function penalizes the detection of either unknown-activity
or PT during the occurrence of BAs as on this dataset we expect them to occur only
during transitions. Consequently, any aim to reduce the error in PTs can reduce the
overall performance as it can have unfavorable effects in the predictions of BAs.
Moreover, we make use of the confusion matrix for evaluating the system classi-
fication performance. As we presented in Sect. 2.5.4.1 , in a typical confusion matrix
C ∈ R

m , the number of actual classes matches the number of predicted classes.
For the evaluation of our methods, however, we slightly modify this idea because
the number of classes of our ground truth (7 classes: 6 BAs plus the PT class) is

m ×