Linear SVM Models for Online Activity Recognition - Smartphone-Based Human Activity Recognition - page 100

of features. This means that the discarded features do not need to be estimated
in our HAR system, speeding up the recognition process from feature extraction.
The average dimensionality reduction

is also showing that each binary classifier
needs less than 20% of the total number of available features for classification. This
indicates that some features help to classify better certain activities from others.
Moreover, the execution time of the FFP of each L1-SVM can be up to 5 times faster
than L2-SVM, assuming a single process implementation. Overall, we can argue that
the use of the L1 models is a suitable option for our HAR system because it brings
the advantages of a linear classifier that performs dimensionality reduction while
maintaining the system performance.
Figure 6.1 depicts the results of the hyperparameter optimization process for the
MC-L1-SVM and MC-L2-SVM where the C m values for each activity classifier are
selected using a KCV with k

ˁ

= 10 on the training set. All the values are contained

within the [1 100] interval. It is also visible that initial values of C present low

accuracy, specially in the L1-SVM classifiers which display a sharp reduction in this
area. Greater values display a nearly constant accuracywithin the explored range. The
selection process consist of a sequential evaluation of the accuracy with different C
values. Only if a new value delivers greater accuracy than a previous recorded one,
it is replaced and selected as optimal C . This procedure prevents the model from
overfitting by taking very large values of C .
As a final remark, the results obtained with the MC-L1-SVM algorithm are analo-
gous to the ones obtained at the ESANN 2013 HAR competition (Refer to Sect. 4.4.2 )
in which contestants were challenged to propose novel approaches for the recogni-
tion of activities using the same HAR dataset. The work of (Romera-Paredes et al.
2013 ) achieved a maximum classification accuracy of 96.4%, where an OVO SVM
classification approach (Rifkin and Klautau 2004 ) was employed for the recognition
task instead of our OVA MC-L1-SVM approach.

,

6.4.4 L1-L2 SVM with HAR Data

In order to derive the experimental results with the MC-L1-L2-SVM algorithm, we
replicated the model selection methodology adopted in Sect. 6.4.1 with the difference
that we have an additional hyperparameter to tune: ʻ ∈ ( 0 , 1]. In order to compare

L1, L2 and L1-L2 SVM solutions, we set .

After an inspection of the results obtained in the previous two sections with
the different combinations of features, we decided to work only with time features
because the improvement granted with frequency domain features is minimal and it
also increases the system's computational load in the feature extraction and prediction
stages. Therefore, we work with

ʻ = { 0 . 001 , 0 . 005 , 0 . 01 , 0 . 05 , 0 . 1 , 0 . 5 , 1 }

D 2 T in this experiment. Table 6.5 compares the
training times for the EX-SMO training approach described in Algorithm 2 against
commonly used solvers for L1 (the SimplexMethod for Linear Programming (SMLP)