Background - Smartphone-Based Human Activity Recognition - page 27

2.5.3.2 Extension to the Multiclass SVM

It is possible to generalize binary ML models to solve problems with more than two
classes. This process is known as multiclass or multinomial classification. Figure 2.4
shows a simple example of a set of elements from 3 different classes in a space of two
dimensions, each one represented with a different shape ( black circles , white circles
and crosses ). Also, separating hyperplanes are chosen as a possible linear solution
to this problem.
There are several methods that have been previously proposed for solving multi-
class problems from binary formulations (Hsu and Lin 2002 ), but generally the two
most commonly used are: one-vs-all (OVA) and one-vs-one (OVO). Their difference
relies in the way they compare each class of interest against the remaining ones:
either all together for the first case and one by one for the latter. In this work we use
OVA (Rifkin and Klautau 2004 ) and take advantage of it because its output directly
represents how likely is each class to match a new test sample against the rest.
The OVA approach consists on constructing a set of m binary SVMs, each one
associated to each existing class c . They are built from positive training samples
coming from the class of interest (labeled as + 1) and negative samples which contain

the remaining samples (labeled as 1). Once the SVMs are learned, its is possible to

compare them to determine which class is the most likely to represent a test sample.
The output of the FFP for every class ( f c (

−

) is either positive or negative and its
sign represents if the new sample is either classified as a given class or not. Ideally,
for a given sample in a multiclass problem, only one of the binary classifiers should
be positive. Therefore the classification of a new sample can be then formulated as
a winner-take-all arbiter which selects the label c ∗ corresponding to the class with
the maximum value of the SVM:

x )

c ∗ = arg max

c

f c ( x ) (2.19)

In the following chapters, we will deal with better approaches to compare the
output of the SVMs from multiple classes such as the use of probability estimates
(refer to Sect. 5.2.2 ) .

2.5.4 Performance Evaluation

The evaluation ofML algorithms is predominantlymade through the statistical analy-
sis of the models using the available experimental data. The most common method is
the confusion matrix which allows representing the algorithmperformance by clearly
identifying the types of errors (false positives and negatives) and correctly predicted
samples over the test data. From it, various metrics can also be extracted such as
model accuracy, sensitivity, specificity, precision and F1-Score (Bulling et al. 2014 ;
Lara and Labrador 2012 ). In addition, other comparative qualitative indicators, such