IEEE Computational Intelligence Magazine - November 2022 - 55

decomposition-based algorithms can be
found in [13], [14], [15].
Despite that the two decompositionbased
methods have shown their competitiveness
in achieving accurate multiclass
classifiers, most of them solve each
decomposed binary classification subproblem
independently. However, a fact
is that since these sub-problems are not in
isolation, solving one sub-problem may
yield useful information for solving other
related sub-problems. Recently, transfer
learning, particularly, multitasking learning,
has gained much attention whose
basic idea is to transfer the knowledge
from related/similar tasks to facilitating
learning in a new task, which may greatly
improve performance ofthe new task by
avoiding much expensive data [16], [17].
Inspired by the idea of transfer learning,
in this paper, an evolutionary multitasking
method for multiclass classification is
proposed, where the " well-solved " subproblems
(their classifiers have high accuracy)
assist the " ill-solved " sub-problems
(their classifiers have low accuracy) to
achieve the final multiclass classifier with
better quality. Specifically, the main contributions
ofthis paper are summarized as
follows:
1) An evolutionary multitasking
method is suggested for solving the problem
of decomposition-based multiclass
classification. In the suggested method,
each decomposed binary classification subproblemisregardedasataskthat
evolves
with a sub-population. During the evolution,
the " ill-solved " tasks are aided by the
well-selected " assisting " tasks, while useful
informationingood classifiers can be transferred
to help " ill-solved " classifiers.
2) Based on the suggested method,
an evolutionary multi-objective algorithm,
termed EMT-MC, is proposed
for multiclass classification problem. In
EMT-MC, the OVO strategy is firstly
adopted to decompose the original multiclass
problem into several binary subproblems.
Then, for each sub-problem
(task), true positive rate and false positive
rate are used as two objectives to evaluate
individuals in each sub-population.
Thirdly, during the evolution, the
method suggested in (1) is applied to all
of the tasks, with which the final multiclass
classifier with higher accuracy can
be obtained.
3) The effectiveness of the proposed
EMT-MC is verified on various multiclass
datasets with different characteristics.
The experimental results show that compared
with the state-of-the-art multiclass
classification algorithms, the proposed
algorithm exhibits better performance in
terms of accuracy, MAUC (Multiclass
Area Under Curve), and F1-scores.
The remainder of the paper is organized
as follows. In Section II, the preliminaries
and the related work are
presented. Section III gives the details
of the proposed algorithm. The empirical
results of comparing our algorithm
with several state-of-the-art alternatives
on the benchmark datasets are reported
in Section IV. Section V concludes the
paper and discusses the directions for
future work.
II. Related Work
Multiclass classification problem has
been paid much attention due to its
wide applications in areas such as computer
vision [18], bioinformatics [19]
and so on. A variety ofmulticlass classification
algorithms, either from the data
level [20] or from the algorithm level [5],
have been proposed. Among them, the
decomposition-based algorithms have
gained much attention since they can
obtain multiclass classifiers with competitive
performance [4]. Here in this section,
first of all, some preliminaries on
the decomposition strategies for multiclass
classification problem will be briefly
discussed. Then, the related work on
evolutionary multitasking learning will
be reviewed, which is the main motivation
ofthe proposed method. Finally, as
our method is a decomposition-based
algorithm, the recent work on the
decomposition-based multiclass classification
algorithms will be reviewed in
the last part ofSection II.
A. Preliminaries on Decomposition
Strategies for Multiclass Classification
Problem
In the literature of classification, multiclass
classification problem is more difficult
than binary classification problem,
since the decision boundary of a multiclass
classification problem tends to be
more complex than that of a binary
one [21]. To this end, an intuitive way
is to extend the existing binary classification
algorithms (such as Support Vector
Machine, K-Nearest Neighbor and
Artificial Neural Network) to multiclass
situation [22]. Although these extended
algorithms can solve the multiclass classification
problem, most of them need
to solve a more complex and larger
optimization problem. To tackle this
issue, researchers proposed to use the
decomposition strategy which can solve
the problem of multiclass classification
in a much easier way. The basic idea of
the decomposition-based methods is to
decompose the original multiclass classification
problem into several binary
classification sub-problems which can
be solved easily.
Two decomposition strategies are
commonly used in multiclass classification,
which are OVA and OVO. Specifically,
for a multiclass classification
problem MC with m classes fc1; ...; cmg,
the OVA strategy divides the original
problem into m binary classification subproblems
fBC1; ...; BCmg.For
each
sub-problem BCi (i 2f1; .. .; mg), it
considers the i-th class (ci) as the positive
class, and all the other classes are viewed
as the negative class. For the OVO strategy,
it divides the original problem
into mðm 1Þ=2binary classification
sub-problems fBC1; .. .; BCmðm1Þ=2g.
In each sub-problem, the p-th class (cp)is
viewed as the positive class, and the q-th
class (cq; q 6¼ p) is viewed as the negative
one. When all ofthe binary classification
sub-problems in OVA or OVO are
solved, the obtained binary classifiers are
aggregated together to achieve the final
multiclass classifier by using the combining
strategy such as voting [9].
B. Evolutionary Multitasking Learning
Multitasking learning, as a sub-field of
machine learning, particularly, transfer
learning [16], uses auxiliary data or
knowledge from related/similar tasks to
facilitate the learning in a new task [17].
A better learned model for the new task
can be built with much less task-specific
training data. In multitasking learning,
multiple related learning tasks are
performed simultaneously by using a
(partially) shared model representation.
As a result, the common information
contained in these related tasks can be
NOVEMBER 2022 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 55
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