Dimension reduction for objects composed of vector sets

Marton Szemenyei ; Ferenc Vajda

International Journal of Applied Mathematics and Computer Science, Tome 27 (2017), p. 169-180 / Harvested from The Polish Digital Mathematics Library

Résumé

Dimension reduction and feature selection are fundamental tools for machine learning and data mining. Most existing methods, however, assume that objects are represented by a single vectorial descriptor. In reality, some description methods assign unordered sets or graphs of vectors to a single object, where each vector is assumed to have the same number of dimensions, but is drawn from a different probability distribution. Moreover, some applications (such as pose estimation) may require the recognition of individual vectors (nodes) of an object. In such cases it is essential that the nodes within a single object remain distinguishable after dimension reduction. In this paper we propose new discriminant analysis methods that are able to satisfy two criteria at the same time: separating between classes and between the nodes of an object instance. We analyze and evaluate our methods on several different synthetic and real-world datasets.

Détail

Publié le : 2017-01-01
EUDML-ID : urn:eudml:doc:288092

Bibliographie

[000] Agarwal, S., Awan, A. and Roth, D. (2004). Learning to detect objects in images via a sparse, part-based representation, IEEE Transactions on Pattern Analysis and Machine Intelligence 26(11): 1475-1490.

[001] Bååth, R. (2014). Bayesian first aid: A package that implements Bayesian alternatives to the classical *.test functions in R, International R User Conference UseR! 2014, Los Angeles, CA, USA, pp. 86.

[002] Baudat, G. and Anouar, F. (2000). Generalized discriminant analysis, Neural Computation 12(1): 2385-2404.

[003] Boutsidis, C., Zouzias, A., Mahoney, M.W. and Drineas, P. (2011). Stochastic dimensionality reduction for k-means clustering, CoRR abs/1110.2897, http://arxiv.org/abs/1110.2897. | Zbl 1359.62232

[004] Bronstein, A.M., Bronstein, M.M. and Ovsjanikov, M. (2010). Feature-based methods in 3D shape analysis, in N. Pears et al. (Eds.), 3D Imaging Analysis and Applications, Springer-Verlag, London, pp. 185-216.

[005] Chai, D., He, X., Zhou, K., Han, J. and Bao, H. (2007). Locality sensitive discriminant analysis, International Joint Conference on Artificial Intelligence, Hyderabad, India, pp. 708-713.

[006] Cunningham, J.P. and Ghahramani, Z. (2015). Linear dimensionality reduction: Survey, insights, and generalizations, Journal of Machine Learning Research 16(1): 2859-2900. | Zbl 1351.62123

[007] Demirci, M.F., Osmanlioglu, Y., Shokoufandeh, A. and Dickinson, S. (2011). Efficient many-to-many feature matching under the l1 norm, Computer Vision and Image Understanding 115(7): 967-983.

[008] Dempster, A.P., Laird, N.M. and Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society 39(1): 1-38. | Zbl 0364.62022

[009] Fei-Fei, L., Fergus, R. and Perona, P. (2007). Learning generative visual models from few training examples: An incremental Bayesian approach tested on 101 object categories, Journal Computer Vision and Image Understanding 106(1): 59-70.

[010] Fei-Fei, L. and Perona, P. (2005). A Bayesian hierarchical model for learning natural scene categories, IEEE Conference on Computer Vision and Pattern Recognition, San Diego, CA, USA, pp. 524-531.

[011] Felzenszwalb, P.F., Girshick, R.B., McAllester, D. and Ramanan, D. (2010). Object detection with discriminatively trained part-based models, IEEE Transactions on Pattern Analysis and Machine Intelligence 32(9): 1627-1645.

[012] Fukunaga, K. (1990). Introduction to Statistical Pattern Recognition, Academic Press, San Diego, CA. | Zbl 0711.62052

[013] Gkalelis, N., Mezaris, V. and Kompatsiaris, I. (2011). Mixture subclass discriminant analysis, IEEE Signal Processing Letters 18(5): 319-322.

[014] Górecki, T. and Łuczak, M. (2013). Linear discriminant analysis with a generalization of the Moore-Penrose pseudoinverse, International Journal of Applied Mathematics and Computer Science 23(2): 463-471, DOI: 10.2478/amcs-2013-0035.

[015] Harandi, M.T., Sanderson, C., Shirazi, S. and Lovell, B.C. (2011). Graph embedding discriminant analysis on Grassmannian manifolds for improved image set matching, IEEE Conference on Computer Vision and Pattern Recognition, Colorado Springs, CO, USA, pp. 2705-2712.

[016] Hastie, T., Buja, A. and Tibshirani, R. (1995). Penalized discriminant analysis, Annals of Statistics 23(1): 73-102. | Zbl 0821.62031

[017] Hastie, T. and Tibshirani, R. (1996). Discriminant analysis by Gaussian mixtures, Journal of the Royal Statistical Society 58(1): 155-176. | Zbl 0850.62476

[018] Hyvärinen, A., Karhunen, J. and Oja, E. (2001). Independent Component Analysis, John Wiley and Sons, New York, NY.

[019] Jolliffe, I.-T. (2002). Principal Component Analysis, Springer-Verlag, New York, NY. | Zbl 1011.62064

[020] Kruschke, J.K. (2013). Bayesian estimation supersedes the t-test, Journal of Experimental Psychology: General 142(2): 573-603.

[021] Kulczycki, P. and Łukasik, S. (2014). An algorithm for reducing the dimension and size of a sample for data exploration procedures, International Journal of Applied Mathematics and Computer Science 24(1): 133-149, DOI: 10.2478/amcs-2014-0011. | Zbl 1292.93044

[022] Kumar, C.A. (2009). Analysis of unsupervised dimensionality reduction techniques, Computer Science and Information Systems 6(2): 217-227.

[023] Lazebnik, S., Schmid, C. and Ponce, J. (2005). A maximum entropy framework for part-based texture and object recognition, IEEE International Conference on Computer Vision, Beijing, China, pp. 832-838.

[024] Lin, T.-S. (1992). Statistical feature extraction and selection for IC test pattern analysis, IEEE International Symposium on Circuits and Systems, San Diego, CA, USA, pp. 391-394.

[025] Liu, X., Wang, Z., Liu, J. and Feng, Z. (2008). Face recognition with locality sensitive discriminant analysis based on matrix representation, IEEE International Joint Conference on Neural Networks, Montreal, Canada, pp. 4052-4058.

[026] Lowe, D.G. (2004). Distinctive image features from scale-invariant keypoints, International Journal of Computer Vision 60(2): 91-110.

[027] Marszałek, M. and Schmid, C. (2007). Accurate object localization with shape masks, IEEE Conference on Computer Vision and Pattern Recognition, Minneapolis, MN, USA, pp. 1-8.

[028] McLachlan, G.-J. (2004). Discriminant Analysis and Statistical Pattern Recognition, John Wiley and Sons, New York, NY. | Zbl 1108.62317

[029] Nilsback, M.-E. and Zisserman, A. (2008). Automated flower classification over a large number of classes, Indian Conference on Computer Vision, Graphics and Image Processing, Bhubaneswar, India, pp. 722-729.

[030] Schnabel, R., Wahl, R. and Klein, R. (2007). Efficient RANSAC for point-cloud shape detection, Computer Graphics Forum 26(2): 214-226.

[031] Schnabel, R., Wessel, R., Wahl, R. and Klein, R. (2008). Shape recognition in 3D point-clouds, 16th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, Pilzen, Czech Republic, pp. 65-72.

[032] Song, F., Z.Guo and Mei, D. (2010). Feature selection using principal component analysis, International Conference on System Science, Engineering Design and Manufacturing Informatization, Guiyang, China, pp. 27-30.

[033] Surendiran, B. and Vadivel, A. (2011). Feature selection using stepwise ANOVA discriminant analysis for mammogram mass classification, ACEEE International Journal on Signal and Image Processing 2(1): 17-19.

[034] Szemenyei, M. and Vajda, F. (2015). Learning 3D object recognition using graphs based on primitive shapes, Workshop on the Advances of Information Technology, Budapest, Hungary, pp. 187-195.

[035] Wang, Y., Jiang, H., Drew, M.S., Li, Z.-N. and Mori, G. (2006). Unsupervised discovery of action classes, IEEE Conference on Computer Vision and Pattern Recognition, New York, NY, USA, pp. 1645-1661.

[036] Wu, C. (2013). Towards linear-time incremental structure from motion, International Conference on 3D Vision, Seattle, WA, USA, pp. 127-134.

[037] Yang, M.-H. and Ahuja, N. (2001). Face detection using multimodal density models, International Series in Video Computing 1(1): 97-122. | Zbl 1033.68614

[038] Yang, M. and Yuan, X.-M. (2009). Structured semi-supervised discriminant analysis, International Conference on Wavelet Analysis and Pattern Recognition, Baoding, China, pp. 148-153.

[039] Yasuoka, S., Kang, Y., Morooka, K. and Nagahashi, H. (2004). Texture classification using hierarchical discriminant analysis, IEEE Conference on Systems, Man and Cybernetics, The Hague, The Netherlands, pp. 6395-6400.

[040] Zhu, M. and Martinez, A.M. (2006). Subclass discriminant analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence 28(8): 1274-1286.