Multidimensional Data Visualization Based on the Minimum Distance Between Convex Hulls of Classes
- 1 Downloads
The problem of data visualization in the analysis of two classes in a multidimensional feature space is considered. The two orthogonal axes by which the classes are maximally separated from each other are found in the mapping of classes as a result of linear transformation of coordinates. The proximity of the classes is estimated based on the minimum-distance criterion between their convex hulls. This criterion makes it possible to show cases of full class separability and random outliers. A support vector machine is used to obtain orthogonal vectors of the reduced space. This method ensures the obtaining of the weight vector that determines the minimum distance between the convex hulls of classes for linearly separable classes. Algorithms with reduction, contraction, and offset of convex hulls are used for intersecting classes. Experimental studies are devoted to the application of the considered visualization methods to biomedical data analysis.
Keywordsmultidimensional data visualization machine learning support vector machine biomedical data analysis
Unable to display preview. Download preview PDF.
- 4.T. Maszczyk and W. Duch, “Support vector machines for visualization and dimensionality reduction,” in Artificial Neural Networks — ICANN 2008, Ed. by V. Kůrková, R. Neruda, and J. Koutník, Lecture Notes in Computer Science (Springer, Berlin, Heidelberg, 2008), Vol. 5163, pp. 346–356.CrossRefGoogle Scholar
- 8.K. P. Bennett and E. J. Bredensteiner, “Duality and geometry in SVM classifiers,” in Proc. 17th Int. Conf. on Machine Learning (ICML'00) (Morgan Kaufmann, San Francisco, 2000), pp. 57–64.Google Scholar
- 12.M. C. Lin, D. Manocha, and Y. J. Kim, “Collision and proximity queries”, in Handbook of Discrete and Computational Geometry, Ed. by J. E. Goodman, J. O’Rourke, and C. D. Tóth, 3rd ed. (CRC Press, Boca Raton, FL, 2018), pp. 1029–1056.Google Scholar
- 14.Z. Liu, J. G. Liu, C. Pan, and G. Wang. “A novel geometric approach to binary classification based on scaled convex hulls,” IEEE Trans. Neural Netw. 20 (7) 1215–1220 (2009).Google Scholar
- 15.D. J. Crisp and C. J. C. Burges, “A geometric interpretation of ν–SVM classifiers,” in Advances in Neural Information Processing Systems 12 (NIPS 1999) (MIT Press, Cambridge, MA, 1999), pp. 244–250.Google Scholar
- 17.Iris Data Set. UCI Machine Learning Repository. Available at: https://archive.ics.uci.edu/ml/datasets/iris (accessed April 2018).Google Scholar
- 19.S. S. Keerthi, S. K. Shevade, C. Bhattacharyya, and K. R. K. Murthy, Improvements to Platt’s SMO Algorithm for SVM Classifier Design, Technical Report CD–99–14, Control Division, Dept. of Mechanical and Production Engineering, National University of Singapore, 1999. Available at: http://citeseerx. ist.psu.edu/viewdoc/summary?doi=10.1.1.46.8538 (accessed May 2018).zbMATHGoogle Scholar
- 21.Breast Tissue Data Set. UCI Machine Learning Repository. Available at: http://archive.ics.uci.edu/ml/datasets/breast+tissue (accessed April 2018).Google Scholar
- 22.Breast Cancer Wisconsin (Original) Data Set. UCI Machine Learning Repository. Available at: https://archive.ics.uci.edu/ml/datasets/breast+cancer+ wisconsin+(original) (accessed May 2018).Google Scholar