Abstract
The prior knowledge plays an important role in increasing the performance of the support vector machines (SVMs). Traditional SVMs do not consider any prior knowledge of the training set. In this paper, the neighbors’ distribution knowledge is incorporated into SVMs. The neighbors’ distribution can be measured by the sum of the cosine value of the angle, which is between the difference between the sample and its corresponding neighbor, and the difference between the sample and the mean of corresponding neighbors. The neighbors’ distribution knowledge reflects the sample’s importance in the training processing. It can be explained as the relative margin or instance weight. In this paper, the neighbors’ distribution knowledge is regarded as the relative margin and incorporated into the framework of density-induced margin support vector machines whose relative margin is measured by relative density degree. The results of the experiments, performed on both artificial synthetic datasets and real-world benchmark datasets, demonstrate that SVMs performs better after incorporating neighbors’ distribution. Furthermore, experimental results also show that neighbors’ distribution are more suitable than relative density degree to represent the relative margin.
Similar content being viewed by others
References
Alcala-Fdez J, Sanchez L, Garcia S, del Jesus MJ, Ventura S, Garrell JM, Otero CR, Bacardit J, Rivas VM, Fernández JC, Herrera F (2009) KEEL: a software tool to assess evolutionary algorithms for data mining problems. Soft Comput 13(3):307–318
Alcalá J, Fernández A, Luengo J, Derrac J, García S, Sánchez L, Herrera F (2010) Keel data-mining software tool: Data set repository, integration of algorithms and experimental analysis framework. J Multiple-Valued Logic Soft Comput 17(2–3):255–287
Bertelli L, Yu T, Vu D, Gokturk, B (2011) Kernelized structural SVMlearning for supervised object segmentation. In: 2011 IEEE conference on computer vision and pattern recognition (CVPR). IEEE, Milpitas, pp 2153–2160
Bottou L (2010) Large-scale machine learning with stochastic gradient descent. In: Proceedings of COMPSTAT’2010. Physica-Verlag HD, pp 177–186
Chang CC, Lin CJ (2011) LIBSVM: A library for support vector machines. ACM Trans Intell Syst Technol 2(3):27
Chapelle O, Schölkopf B (2001) Incorporating invariances in non-linear support vector machines. In: Advances in neural information processing systems. MIT Press, Vancouver, pp 609–616
Cristianini N, Shawe-Taylor J (2000) An introduction to support vector machines and other kernel-based learning methods. Cambridge University Press, Cambridge
Friedman JH, Bentley JL, Finkel RA (1977) An algorithm for finding best matches in logarithmic expected time. ACM Trans Math Softw 3(3):209–226
García S, Fernández A, Luengo J, Herrera F (2010) Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: experimental analysis of power. Inf Sci 180(10):2044–2064
Gumus E, Kilic N, Sertbas A, Ucan ON (2010) Evaluation of face recognition techniques using PCA, wavelets and SVM. Expert Syst Appl 37(9):6404–6408
Hsieh CJ, Chang KW, Lin CJ, Keerthi SS, Sundararajan S (2008) A dual coordinate descent method for large-scale linear SVM. In: Proceedings of the 25th international conference on machine learning. ACM, Helsinki, pp 408–415
Hua X, Ding S (2015) Weighted least squares projection twin support vector machines with local information. Neurocomputing 160:228–237
Hwang JP, Park S, Kim E (2011) A new weighted approach to imbalanced data classification problem via support vector machine with quadratic cost function. Expert Syst Appl 38(7):8580–8585
Karasuyama M, Harada N, Sugiyama M, Takeuchi I (2012) Multi-parametric solution-path algorithm for instance-weighted support vector machines. Mach Learn 88(3):297–330
Khemchandani R, Chandra S (2007) Twin support vector machines for pattern classification. IEEE Trans Pattern Anal Mach Intell 29(5):905–910
Kruskal WH, Wallis WA (1952) Use of ranks in one-criterion variance analysis. J Am Stat Assoc 47(260):583–621
Lauer F, Bloch G (2008) Incorporating prior knowledge in support vector machines for classification: a review. Neurocomputing 71(7):1578–1594
Lee K, Kim DW, Lee D, Lee KH (2005) Improving support vector data description using local density degree. Pattern Recogn 38(10):1768–1771
Lichman M (2013) UCI machine learning repository. http://archive.ics.uci.edu/ml. University of California, School of Information and Computer Science, Irvine, CA
Mangasarian OL, Wild EW (2001) Proximal support vector machine classifiers. In: Proceedings KDD-2001: knowledge discovery and data mining. ACM, San Francisco
Mangasarian OL, Wild EW (2006) Multisurface proximal support vector machine classification via generalized eigenvalues. IEEE Trans Pattern Anal Mach Intell 28(1):69–74
Niu XX, Suen CY (2012) A novel hybrid CNN-SVM classifier for recognizing handwritten digits. Pattern Recogn 45(4):1318–1325
Palmieri F, Fiore U, Castiglione A, De Santis A (2013) On the detection of card-sharing traffic through wavelet analysis and support vector machines. Appl Soft Comput 13(1):615–627
Palmieri F, Fiore U, Castiglione A (2014) A distributed approach to network anomaly detection based on independent component analysis. Concurr Comput Pract Exp 26(5):1113–1129
Shao YH, Chen WJ, Zhang JJ, Wang Z, Deng NY (2014) An efficient weighted Lagrangian twin support vector machine for imbalanced data classification. Pattern Recogn 47(9):3158–3167
Tian J, Gu H, Liu W, Gao C (2011) Robust prediction of protein subcellular localization combining PCA and WSVMs. Comput Biol Med 41(8):648–652
Vapnik V (2013) The nature of statistical learning theory. Springer, Berlin
Vapnik V, Vashist A (2009) A new learning paradigm: learning using privileged information. Neural Netw 22(5):544–557
Wang F, Zhang D (2013) A new locality-preserving canonical correlation analysis algorithm for multi-view dimensionality reduction. Neural Process Lett 37(2):135–146
Wang J, Shen HT, Song J, Ji J (2014) Hashing for similarity search: a survey. arXiv preprint arXiv:1408.2927
Wu X, Srihari R (2004) Incorporating prior knowledge with weighted margIn support vector machines. In: Proceedings of the tenth ACM SIGKDD international conference on knowledge discovery and data mining. ACM, Seattle, pp 326–333
Wu Y, Wei B, Liu H, Li T, Rayner S (2011) MiRPara: a SVM-based software tool for prediction of most probable microRNA coding regions in genome scale sequences. BMC Bioinform 12(1):107
Xiong T, Cherkassky V (2005) A combined SVM and LDA approach for classification. In: 2005 IEEE international joint conference on neural networks, 2005. IJCNN’05. Proceedings, vol 3. IEEE, Montreal, pp 1455–1459
Yang X, Song Q, Wang Y (2007) A weighted support vector machine for data classification. Int J Pattern Recogn Artif Intell 21(05):961–976
Yang X, Chen S, Chen B, Pan Z (2009) Proximal support vector machine using local information. Neurocomputing 73(1):357–365
Zafeiriou S, Tefas A, Pitas I (2007) Minimum class variance support vector machines. IEEE Trans Image Process 16(10):2551–2564
Zhang L, Zhou WD (2011) Density-induced margin support vector machines. Pattern Recogn 44(7):1448–1460
Zhang H, Cao L, Gao S (2014) A locality correlation preserving support vector machine. Pattern Recogn 47(9):3168–3178
Zhu F, Ye N, Yu W, Xu S, Li G (2014a) Boundary detection and sample reduction for one-class support vector machines. Neurocomputing 123:166–173
Zhu F, Yang J, Ye N, Gao C, Li G, Yin T (2014b) Neighbors’ distribution property and sample reduction for support vector machines. Appl Soft Comput 16:201–209
Acknowledgments
The authors would like to thank the editor and the anonymous reviewers for their critical and constructive comments and suggestions. This work was partially supported by the National Science Fund for Distinguished Young Scholars under Grant Nos. 61125305, 61472187, 61233011 and 61373063, the Key Project of Chinese Ministry of Education under Grant No. 313030, the 973 Program (No. 2014CB349303), Fundamental Research Funds for the Central Universities (No. 30920140121005), Program for Changjiang Scholars and Innovative Research Team in University No. IRT13072, National Basic Research Program of China (973 Program) (2012CB114505), China National Funds for Distinguished Young Scientists (31125008).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest to this work.
Additional information
Communicated by V. Loia.
Rights and permissions
About this article
Cite this article
Zhu, F., Yang, J., Xu, S. et al. Incorporating neighbors’ distribution knowledge into support vector machines. Soft Comput 21, 6407–6420 (2017). https://doi.org/10.1007/s00500-016-2199-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-016-2199-6