A fuzzy universum least squares twin support vector machine (FULSTSVM)

Abstract

Universum based twin support vector machines give prior information about the distribution of data to the classifier. This leads to better generalization performance of the model, due to the universum. However, in many applications the data points are not equally useful for the classification task. This leads to the use of fuzzy membership functions for the datasets. Similarly, in universum based algorithms, all the universum data points are not equally important for the classifier. To solve these problems, a novel fuzzy universum least squares twin support vector machine (FULSTSVM) is proposed in this work. In FULSTSVM, the membership values are used to provide weights for the data samples of the classes, as well as to the universum data. Further, the optimization problem of proposed FULSTSVM is obtained by solving a system of linear equations. This leads to an efficient fuzzy based algorithm. Numerical experiments are performed on various benchmark datasets, with discussions on generalization performance, and computational cost of the algorithms. The proposed FULSTSVM outperformed the existing algorithms on most datasets. A comparison is presented for the performance of the proposed and other baseline algorithms using statistical significance tests. To show the applicability of FULSTSVM, applications are also presented, such as detection of Alzheimer’s disease, and breast cancer.

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Acknowledgements

The funding for this work is obtained from Science and Engineering Research Board (SERB), INDIA under Ramanujan fellowship grant no. SB/S2/RJN-001/2016, and also under Early Career Research Award grant no. ECR/2017/000053. We also acknowledge Council of Scientific & Industrial Research (CSIR), New Delhi, INDIA for funding under Extra Mural Research (EMR) Scheme grant no. 22(0751)/17/EMR-II. We want to acknowledge our institute, the Indian Institute of Technology Indore for providing various facilities and resources for this work. We also thank the Indian Institute of Technology Indore for providing Institute fellowship to Mr. Bharat Richhariya. The collection of data and sharing of this project was funded by the Alzheimer’s Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904), and DOD ADNI (Department of Defense award number W81XWH-12-2-0012). The funding for ADNI is provided by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: AbbVie, Alzheimer’s Association; Alzheimer’s Drug Discovery Foundation; Araclon Biotech; BioClinica, Inc.; Biogen; Bristol-Myers Squibb Company; CereSpir, Inc.; Cogstate; Eisai Inc.; Elan Pharmaceuticals, Inc.; Eli Lilly and Company; EuroImmun; F. Hoffmann-La Roche Ltd and its affiliated company Genentech, Inc.; Fujirebio; GE Healthcare; IXICO Ltd.; Janssen Alzheimer Immunotherapy Research & Development, LLC.; Johnson & Johnson Pharmaceutical Research & Development LLC.; Lumosity; Lundbeck; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.; NeuroRx Research; Neurotrack Technologies; Novartis Pharmaceuticals Corporation; Pfizer Inc.; Piramal Imaging; Servier; Takeda Pharmaceutical Company; and Transition Therapeutics. The Canadian Institutes of Health Research is providing funds to support ADNI clinical sites in Canada. Private sector contributions are facilitated by the Foundation for the National Institutes of Health (www.fnih.org). The grantee organization is the Northern California Institute for Research and Education, and the study is coordinated by the Alzheimer’s Therapeutic Research Institute at the University of Southern California. The dissemination of ADNI data is carried out by the Laboratory for Neuro Imaging at the University of Southern California.

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Correspondence to M. Tanveer.

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Data used in preparation of this article were obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at: http://adni.loni.usc.edu/wp-content/uploads/how_to _apply/ADNI_Acknowledgement_List.pdf

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Richhariya, B., Tanveer, M. & for the Alzheimer’s Disease Neuroimaging Initiative. A fuzzy universum least squares twin support vector machine (FULSTSVM). Neural Comput & Applic (2021). https://doi.org/10.1007/s00521-021-05721-4

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Keywords

  • Universum
  • Fuzzy membership
  • Least squares twin support vector machine
  • Outliers
  • Alzheimer’s disease