Abstract:

Classification problem is the central problem in machine learning.
Support vector machines (SVMs) are supervised learning models with associated
learning algorithms and are used for classification in machine learning. In this paper,
we establish two consensus proximal support vector machines (PSVMs) models,
based on methods for binary classification. The first one is to separate the objective
functions into individual convex functions by using the number of the sample points
of the training set. The constraints contain two types of the equations with global
variables and local variables corresponding to the consensus points and sample
points, respectively. To get more sparse solutions, the second one is l1–l2 consensus
PSVMs in which the objective function contains an ‘1-norm term and an ‘2-norm
term which is responsible for the good classification performance while ‘1-norm
term plays an important role in finding the sparse solutions. Two consensus PSVMs
are solved by the alternating direction method of multipliers. Furthermore, they are
implemented by the real-world data taken from the University of California, Irvine
Machine Learning Repository (UCI Repository) and are compared with the existed
models such as ‘1-PSVM, ‘p-PSVM, GEPSVM, PSVM, and SVM-light. Numerical
results show that our models outperform others with the classification accuracy and
the sparse solutions.

Key words: Classification problems  , Support vector machine ,  Proximal
support vector machine ,   Consensus , Alternating direction method
of multipliers