Yıl: 2021 Cilt: 29 Sayı: 2 Sayfa Aralığı: 913 - 928 Metin Dili: İngilizce DOI: 10.3906/elk-2005-142 İndeks Tarihi: 07-06-2022

The nearest polyhedral convex conic regions for high-dimensional classification

Öz:
In the nearest-convex-model type classifiers, each class in the training set is approximated with a convex class model, and a test sample is assigned to a class based on the shortest distance from the test sample to these class models. In this paper, we propose new methods for approximating the distances from test samples to the convex regions spanned by training samples of classes. To this end, we approximate each class region with a polyhedral convex conic region by utilizing polyhedral conic functions (PCFs) and its extension, extended PCFs. Then, we derive the necessary formulations for computing the distances from test samples to these new models. We tested the proposed methods on different high-dimensional classification tasks including face, digit, and generic object classification as well as on some lower-dimensional classification problems. The experimental results on different datasets show that the proposed classifiers achieve either the best or comparable results on high-dimensional classification problems compared to other nearest-convex-model classifiers, which shows the superiority of the proposed methods
Anahtar Kelime:

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  • [1] Watanabe S, Pakvasa N. Subspace method in pattern recognition. In: International Conference on Pattern Recognition; Washington DC, USA; 1973. pp. 25-32.
  • [2] Liu Y, Ge SS, Li C, You Z. k-ns: A classifier by the distance to the nearest subspace. IEEE Transactions on Neural Networks 2011; 22: 1256-1268.
  • [3] Cevikalp H, Larlus D, Neamtu M, Triggs B, Jurie F. Manifold based local classifiers: Linear and nonlinear approaches. Journal of Signal Processing Systems 2010; 61: 61-73.
  • [4] Cevikalp H, Triggs B, Polikar R. Nearest hyperdisk methods for high-dimensional classification. In: The 25th International Conference on Machine Learning; Helsinki, Finland; 2008. pp. 120 - 127.
  • [5] Nalbantov GI, Groenen PJF, Bioch JC. Nearest convex hull classification. Technical report, Econometric Institute and Erasmus Research Institute of Management, 2007.
  • [6] Kobayashi T, Otsu N. Cone-restricted subspace methods. In: 19th International Conference on Pattern Recognition; Tampa, FL, USA; 2008.pp.1-25.
  • [7] Tax DMJ, Duin RPW. Support vector data description. Machine Learning 2004; 54: 45-66.
  • [8] Vincent P, Bengio Y. K-local hyperplane and convex distance nearest neighbor algorithms. In: Advances in Neural Information Processing Systems; Vancouver, Canada; 2001. pp. 1-20
  • 9] Oja E. Subspace Methods of Pattern Recognition. New York, NY, USA: Research Studies Press, 1983.
  • [10] Laaksonen J. Subspace classifiers in recognition of handwritten digits. Ph.D. thesis, Helsinki University of Technology, 1997.
  • [11] Ho J, Yang M, Lim J, Lee K, Kriegman D. Clustering appearances of objects under varying illumination conditions. In: 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR); Madison, WI, USA; 2003.pp.1-20.
  • [12] Costeira J, Kanade T. A multibody factorization method for independently moving objects. International Journal of Computer Vision 1998; 29: 159-179.
  • [13] Cheema MS, Eweiwi A, Bauckhage C. High dimensional low samples size activity recognition using geometric classifiers. Digital Signal Processing 2015; 42: 61-69.
  • [14] Gulmezoglu M, Dzhafarov V, Keskin M, Barkana A. A novel approach to isolated word recognition. IEEE Transactions on Speech and Audio Processing 1999; 7(6):620-628.
  • [15] Suykens JAK, Vandewalle J. Least squares support vector machine classifiers. Neural Processing Letters 1999; 9: 293-300.
  • [16] Cevikalp H, Triggs B. Face recognition based on image sets. In: 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR); San Francisco, CA, USA; 2010. pp. 2567-2573.
  • [17] Wright J, Yang A, Ganes A, Sastry S, Ma Y. Robust face recognition via sparse representation. IEEE Transactions on Pattern Analysis and Machine Intelligence 2009; 31: 210-227.
  • [18] Hu Y, Mian AS, Owens R. Face recognition using sparse approximated nearest points between image sets. IEEE Transactions on Pattern Analysis and Machine Intelligence 2012; 34(3): 1992-2004.
  • [19] Bourreau Y, Bach F, LeCun Y, Ponce J. Learning mid-level features for recognition. In: 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR); San Francisco, CA, USA; 2010. pp. 2559-2566.
  • [20] Yang J, Yu K, Gong Y, Huang TS. Linear spatial pyramid matching using sparse coding for image classification. In: 2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR); Miami, FL, USA; 2009. pp. 1794-1801.
  • [21] Yang M, Zhu P, Gool LV, Zhang L. Face recognition based on regularized nearest points between image sets. In: 10th IEEE International Conference on Automatic Face and Gesture Recognition; Shanghai, China; 2013. pp. 1-20.
  • [22] Nemirko AP. Lightweight nearest convex hull classifier. Pattern Recognition and Image Analysis 2019; 3: 360-365.
  • [23] Zhou X, Shi Y. Nearest neighbor convex hull classification method for face recognition. In: The International Conference on Computational Science; Louisiana, USA; 2009. pp. 570-577.
  • [24] Takahashi T, Kudo M, Nakamura A. Construction of convex hull classifiers in high dimensions. Pattern Recognition Letters 2011; 32(16): 2224-2230.
  • [25] Cheng Z, Wang R. Nearest neighbor convex hull tensor classification for gear intelligent fault diagnosis based on multi-sensor signals. IEEE Access 2019; 7: 140781-140793.
  • [26] Cevikalp H, Triggs B. Hyperdisk based large margin classifier. Pattern Recognition 2013; 46: 1523-1531.
  • [27] Sogi N, Nakayama T, Fukui K. A method based on convex cone model for image-set classification with cnn features. In: International Joint Conference on Neural Networks (IJCNN); Rio de Janeiro, Brazil; 2018. pp. 1-25.
  • [28] Zhao K, Wiliem A, Chen S, Lovell BC. Convex class model on symmetric positive definite manifolds. Image and Vision Computing 2019; 87: 57-67.
  • [29] Cevikalp H. High-dimensional data clustering by using local affine/convex hulls. Pattern Recognition Letters 2019; 128: 427-432.
  • [30] Bennett KP, Bredensteiner EJ. Duality and geometry in svm classifiers. In: 17th International Conference on Machine Learning (ICML); Stanford, CA, USA; 2000.pp.1-20.
  • 31] Cevikalp H, Triggs B. Large margin classifiers based on convex class models. In: International Conference on Computer Vision Workshops (ICCVW); Kyoto, Japan; 2009. pp. 101-108.
  • [32] Zhu R, Wang Z, Sogi N, Fukui K, Xue JH. A novel separating hyperplane classification framework to unify nearest- class-model methods for high-dmensional data. IEEE Transactions on Neural Networks and Learning Systems 2020; 1: 1-11.
  • [33] Gasimov RN, Ozturk G. Separation via polyhedral conic functions. Optimization Methods and Software 2006; 21: 527-540.
  • [34] Cevikalp H, Triggs B. Polyhedral conic classifiers for visual object detection and classification. In: 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR); Honolulu, HI, USA; 2017. pp. 4114-4122.
  • [35] Cevikalp H, Saglamlar H. Polyhedral conic classifiers for computer vision applications and open set recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence 2019; 1-15.
  • [36] Ozturk G, Cimen E. Polyhedral conic kernel-like functions for SVMs. Turkish Journal of Electrical Engineering and Computer Sciences 2019; 27: 1172-1180.
  • [37] Cimen E, Ozturk G, Gerek ON. Incremental conic functions algorithm for large scale classification problems. Digital Signal Processing 2018; 77: 187-194.
  • [38] Krizhevsky A, Sutskever I, Hinton GE. Imagenet classification with deep convolutional neural networks. In: The 26th Annual Conference on Neural Information Processing Systems (NIPS); Harrahs and Harveys, USA; 2012.pp.1- 20
APA Cevikalp H, Cimen E, Ozturk G (2021). The nearest polyhedral convex conic regions for high-dimensional classification. , 913 - 928. 10.3906/elk-2005-142
Chicago Cevikalp Hakan,Cimen Emre,Ozturk Gurkan The nearest polyhedral convex conic regions for high-dimensional classification. (2021): 913 - 928. 10.3906/elk-2005-142
MLA Cevikalp Hakan,Cimen Emre,Ozturk Gurkan The nearest polyhedral convex conic regions for high-dimensional classification. , 2021, ss.913 - 928. 10.3906/elk-2005-142
AMA Cevikalp H,Cimen E,Ozturk G The nearest polyhedral convex conic regions for high-dimensional classification. . 2021; 913 - 928. 10.3906/elk-2005-142
Vancouver Cevikalp H,Cimen E,Ozturk G The nearest polyhedral convex conic regions for high-dimensional classification. . 2021; 913 - 928. 10.3906/elk-2005-142
IEEE Cevikalp H,Cimen E,Ozturk G "The nearest polyhedral convex conic regions for high-dimensional classification." , ss.913 - 928, 2021. 10.3906/elk-2005-142
ISNAD Cevikalp, Hakan vd. "The nearest polyhedral convex conic regions for high-dimensional classification". (2021), 913-928. https://doi.org/10.3906/elk-2005-142
APA Cevikalp H, Cimen E, Ozturk G (2021). The nearest polyhedral convex conic regions for high-dimensional classification. Turkish Journal of Electrical Engineering and Computer Sciences, 29(2), 913 - 928. 10.3906/elk-2005-142
Chicago Cevikalp Hakan,Cimen Emre,Ozturk Gurkan The nearest polyhedral convex conic regions for high-dimensional classification. Turkish Journal of Electrical Engineering and Computer Sciences 29, no.2 (2021): 913 - 928. 10.3906/elk-2005-142
MLA Cevikalp Hakan,Cimen Emre,Ozturk Gurkan The nearest polyhedral convex conic regions for high-dimensional classification. Turkish Journal of Electrical Engineering and Computer Sciences, vol.29, no.2, 2021, ss.913 - 928. 10.3906/elk-2005-142
AMA Cevikalp H,Cimen E,Ozturk G The nearest polyhedral convex conic regions for high-dimensional classification. Turkish Journal of Electrical Engineering and Computer Sciences. 2021; 29(2): 913 - 928. 10.3906/elk-2005-142
Vancouver Cevikalp H,Cimen E,Ozturk G The nearest polyhedral convex conic regions for high-dimensional classification. Turkish Journal of Electrical Engineering and Computer Sciences. 2021; 29(2): 913 - 928. 10.3906/elk-2005-142
IEEE Cevikalp H,Cimen E,Ozturk G "The nearest polyhedral convex conic regions for high-dimensional classification." Turkish Journal of Electrical Engineering and Computer Sciences, 29, ss.913 - 928, 2021. 10.3906/elk-2005-142
ISNAD Cevikalp, Hakan vd. "The nearest polyhedral convex conic regions for high-dimensional classification". Turkish Journal of Electrical Engineering and Computer Sciences 29/2 (2021), 913-928. https://doi.org/10.3906/elk-2005-142