934 research outputs found
Fuzzy Least Squares Twin Support Vector Machines
Least Squares Twin Support Vector Machine (LST-SVM) has been shown to be an
efficient and fast algorithm for binary classification. It combines the
operating principles of Least Squares SVM (LS-SVM) and Twin SVM (T-SVM); it
constructs two non-parallel hyperplanes (as in T-SVM) by solving two systems of
linear equations (as in LS-SVM). Despite its efficiency, LST-SVM is still
unable to cope with two features of real-world problems. First, in many
real-world applications, labels of samples are not deterministic; they come
naturally with their associated membership degrees. Second, samples in
real-world applications may not be equally important and their importance
degrees affect the classification. In this paper, we propose Fuzzy LST-SVM
(FLST-SVM) to deal with these two characteristics of real-world data. Two
models are introduced for FLST-SVM: the first model builds up crisp hyperplanes
using training samples and their corresponding membership degrees. The second
model, on the other hand, constructs fuzzy hyperplanes using training samples
and their membership degrees. Numerical evaluation of the proposed method with
synthetic and real datasets demonstrate significant improvement in the
classification accuracy of FLST-SVM when compared to well-known existing
versions of SVM
Support matrix machine: A review
Support vector machine (SVM) is one of the most studied paradigms in the
realm of machine learning for classification and regression problems. It relies
on vectorized input data. However, a significant portion of the real-world data
exists in matrix format, which is given as input to SVM by reshaping the
matrices into vectors. The process of reshaping disrupts the spatial
correlations inherent in the matrix data. Also, converting matrices into
vectors results in input data with a high dimensionality, which introduces
significant computational complexity. To overcome these issues in classifying
matrix input data, support matrix machine (SMM) is proposed. It represents one
of the emerging methodologies tailored for handling matrix input data. The SMM
method preserves the structural information of the matrix data by using the
spectral elastic net property which is a combination of the nuclear norm and
Frobenius norm. This article provides the first in-depth analysis of the
development of the SMM model, which can be used as a thorough summary by both
novices and experts. We discuss numerous SMM variants, such as robust, sparse,
class imbalance, and multi-class classification models. We also analyze the
applications of the SMM model and conclude the article by outlining potential
future research avenues and possibilities that may motivate academics to
advance the SMM algorithm
A fuzzy based Lagrangian twin parametric-margin support vector machine (FLTPMSVM)
© 2017 IEEE. In the spirit of twin parametric-margin support vector machine (TPMSVM) and support vector machine based on fuzzy membership values (FSVM), a new method termed as fuzzy based Lagrangian twin parametric-margin support vector machine (FLTPMSVM) is proposed in this paper to reduce the effect of the outliers. In FLTPMSVM, we assign the weights to each data samples on the basis of fuzzy membership values to reduce the effect of outliers. Also, we consider the square of the 2-norm of slack variables to make the objective function strongly convex and find the solution of the proposed FLTPMSVM by solving simple linearly convergent iterative schemes instead of solving a pair of quadratic programming problems as in case of SVM, TWSVM, FTSVM and TPMSVM. No need of external toolbox is required for FLTPMSVM. The numerical experiments are performed on artificial as well as well known real-world datasets which show that our proposed FLTPMSVM is having better generalization performance and less training cost in comparison to support vector machine, twin support vector machine, fuzzy twin support vector machine and twin parametric-margin support vector machine
Three-way Imbalanced Learning based on Fuzzy Twin SVM
Three-way decision (3WD) is a powerful tool for granular computing to deal
with uncertain data, commonly used in information systems, decision-making, and
medical care. Three-way decision gets much research in traditional rough set
models. However, three-way decision is rarely combined with the currently
popular field of machine learning to expand its research. In this paper,
three-way decision is connected with SVM, a standard binary classification
model in machine learning, for solving imbalanced classification problems that
SVM needs to improve. A new three-way fuzzy membership function and a new fuzzy
twin support vector machine with three-way membership (TWFTSVM) are proposed.
The new three-way fuzzy membership function is defined to increase the
certainty of uncertain data in both input space and feature space, which
assigns higher fuzzy membership to minority samples compared with majority
samples. To evaluate the effectiveness of the proposed model, comparative
experiments are designed for forty-seven different datasets with varying
imbalance ratios. In addition, datasets with different imbalance ratios are
derived from the same dataset to further assess the proposed model's
performance. The results show that the proposed model significantly outperforms
other traditional SVM-based methods
Class-Imbalanced Complementary-Label Learning via Weighted Loss
Complementary-label learning (CLL) is widely used in weakly supervised
classification, but it faces a significant challenge in real-world datasets
when confronted with class-imbalanced training samples. In such scenarios, the
number of samples in one class is considerably lower than in other classes,
which consequently leads to a decline in the accuracy of predictions.
Unfortunately, existing CLL approaches have not investigate this problem. To
alleviate this challenge, we propose a novel problem setting that enables
learning from class-imbalanced complementary labels for multi-class
classification. To tackle this problem, we propose a novel CLL approach called
Weighted Complementary-Label Learning (WCLL). The proposed method models a
weighted empirical risk minimization loss by utilizing the class-imbalanced
complementary labels, which is also applicable to multi-class imbalanced
training samples. Furthermore, we derive an estimation error bound to provide
theoretical assurance. To evaluate our approach, we conduct extensive
experiments on several widely-used benchmark datasets and a real-world dataset,
and compare our method with existing state-of-the-art methods. The proposed
approach shows significant improvement in these datasets, even in the case of
multiple class-imbalanced scenarios. Notably, the proposed method not only
utilizes complementary labels to train a classifier but also solves the problem
of class imbalance.Comment: 9 pages, 9 figures, 3 table
Fuzzy Support Vector Machine Using Function Linear Membership and Exponential with Mahanalobis Distance
Support vector machine (SVM) is one of effective biner classification technic with structural risk minimization (SRM) principle. SVM method is known as one of successful method in classification technic. But the real-life data problem lies in the occurrence of noise and outlier. Noise will create confusion for the SVM when the data is being processed. On this research, SVM is being developed by adding its fuzzy membership function to lessen the noise and outlier effect in data when trying to figure out the hyperplane solution. Distance calculation is also being considered while determining fuzzy value because it is a basic thing in determining the proximity between data elements, which in general is built depending on the distance between the point into the real class mass center. Fuzzy support vector machine (FSVM) uses Mahalanobis distances with the goal of finding the best hyperplane by separating data between defined classes. The data used will be going over trial for several dividing partition percentage transforming into training set and testing set. Although theoretically FSVM is able to overcome noise and outliers, the results show that the accuracy of FSVM, namely 0.017170689 and 0.018668421, is lower than the accuracy of the classical SVM method, which is 0.018838348. The existence of fuzzy membership function is extremely influential in deciding the best hyperplane. Based on that, determining the correct fuzzy membership is critical in FSVM problem
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