2 research outputs found
A general model for plane-based clustering with loss function
In this paper, we propose a general model for plane-based clustering. The
general model contains many existing plane-based clustering methods, e.g.,
k-plane clustering (kPC), proximal plane clustering (PPC), twin support vector
clustering (TWSVC) and its extensions. Under this general model, one may obtain
an appropriate clustering method for specific purpose. The general model is a
procedure corresponding to an optimization problem, where the optimization
problem minimizes the total loss of the samples. Thereinto, the loss of a
sample derives from both within-cluster and between-cluster. In theory, the
termination conditions are discussed, and we prove that the general model
terminates in a finite number of steps at a local or weak local optimal point.
Furthermore, based on this general model, we propose a plane-based clustering
method by introducing a new loss function to capture the data distribution
precisely. Experimental results on artificial and public available datasets
verify the effectiveness of the proposed method.Comment: 13 pages, 43 figure
Single Versus Union: Non-parallel Support Vector Machine Frameworks
Considering the classification problem, we summarize the nonparallel support
vector machines with the nonparallel hyperplanes to two types of frameworks.
The first type constructs the hyperplanes separately. It solves a series of
small optimization problems to obtain a series of hyperplanes, but is hard to
measure the loss of each sample. The other type constructs all the hyperplanes
simultaneously, and it solves one big optimization problem with the ascertained
loss of each sample. We give the characteristics of each framework and compare
them carefully. In addition, based on the second framework, we construct a
max-min distance-based nonparallel support vector machine for multiclass
classification problem, called NSVM. It constructs hyperplanes with large
distance margin by solving an optimization problem. Experimental results on
benchmark data sets and human face databases show the advantages of our NSVM