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Locally linear discriminate embedding for face recognition. (English) Zbl 1184.94009
Summary: A novel method based on the local nonlinear mapping is presented in this research. The method is called Locally Linear Discriminate Embedding (LLDE). LLDE preserves a local linear structure of a high-dimensional space and obtains a compact data representation as accurately as possible in embedding space (low dimensional) before recognition. For computational simplicity and fast processing, Radial Basis Function (RBF) classifier is integrated with the LLDE. RBF classifier is carried out onto low-dimensional embedding with reference to the variance of the data. To validate the proposed method, CMU-PIE database has been used and experiments conducted in this research revealed the efficiency of the proposed methods in face recognition, as compared to the linear and non-linear approaches.
MSC:
94A08Image processing (compression, reconstruction, etc.)
68T10Pattern recognition, speech recognition
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Full Text: DOI EuDML
References:
[1] J. W. Sammon, “A non-linear mapping for data structure analysis,” IEEE Transactions on Computers, vol. 18, no. 5, pp. 401-409, 1996.
[2] J. H. Friedman and J. W. Tukey, “A projection pursuit algorithm for exploratory data analysis,” IEEE Transactions on Computers, vol. 23, pp. 881-890, 1974. · Zbl 0284.68079 · doi:10.1109/T-C.1974.224051
[3] J. H. Friedman and W. Stuetzle, “Projection pursuit regression,” Journal of the American Statistical Association, vol. 76, no. 376, pp. 817-823, 1981. · doi:10.2307/2287576
[4] T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer Series in Statistics, Springer, New York, NY, USA, 2001. · Zbl 0973.62007
[5] T. Hastie and W. Stuetzle, “Principal curves,” Journal of the American Statistical Association, vol. 84, no. 406, pp. 502-516, 1989. · Zbl 0679.62048 · doi:10.2307/2289936
[6] B. Kégl, A. Krzyzak, T. Linder, and K. Zeger, “Learning and design of principal curves,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 3, pp. 281-297, 2000. · doi:10.1109/34.841759
[7] A. J. Smola, S. Mika, B. Schölkopf, and R. C. Williamson, “Regularized principal manifolds,” Journal of Machine Learning Research, vol. 1, no. 3, pp. 179-209, 2001. · Zbl 1005.68137 · doi:10.1162/15324430152748227
[8] R. Tibshirani, “Principal curves revisited,” Statistics and Computing, vol. 2, no. 4, pp. 183-190, 1992. · doi:10.1007/BF01889678
[9] P. Baldi and K. Hornik, “Neural networks and principal component analysis: learning from examples without local minima,” Neural Networks, vol. 2, no. 1, pp. 53-58, 1989. · doi:10.1016/0893-6080(89)90014-2
[10] D. DeMers and G. Cottrell, “Non-linear dimensionality reduction,” in Advances in Neural Information Processing Systems, vol. 5, pp. 580-587, MIT Press, Cambridge, Mass, USA, 1993.
[11] C. M. Bishop, M. Svensén, and C. K. I. Williams, “GTM: the generative topographic mapping,” Neural Computation, vol. 10, no. 1, pp. 215-234, 1998. · Zbl 0936.68091 · doi:10.1162/089976698300017953
[12] J. Mao and A. K. Jain, “Artificial neural networks for feature extraction and multivariate data projection,” IEEE Transactions on Neural Networks, vol. 6, no. 2, pp. 296-317, 1995. · doi:10.1109/72.363467
[13] A. Hadid, O. Kouropteva, and M. Pietikainen, “Unsupervised learning using locally linear embedding: experiments in face pose analysis,” in Proceedings of the 16th International Conference on Pattern Recognition (ICPR /02), pp. 111-114, 2002.
[14] S. Z. Li, X. Lv, and H. Zhang, “View-subspace analysis of multi-view face patterns,” in Proceedings of the IEEE ICCV Workshop on Recognition, Analysis, and Tracking of Faces and Gestures in Real-Time Systems (RATFG-RTS /01), pp. 125-132, IEEE Computer Society, Washington, DC, USA, 2001.
[15] C. Bouveyron, S. Girard, and C. Schmid, “High-dimensional discriminant analysis,” Communications in Statistics: Theory and Methods, vol. 36, no. 13-16, pp. 2607-2623, 2007. · Zbl 1128.62072 · doi:10.1080/03610920701271095
[16] M.-H. Yang, “Face recognition using extended isomap,” in Proceedings of the IEEE International Conference on Image Processing, vol. 2, pp. 117-120, 2002.
[17] J. Zhang, S. Z. Li, and J. Wang, “Nearest manifold approach for face recognition,” in Proceedings of the 6th IEEE International Conference on Automatic Face and Gesture Recognition, pp. 223-228, Seoul, Korea, 2004.
[18] E. E. Abusham, D. Ngo, and A. Teoh, “Fusion of locally linear embedding and principal component analysis for face recognition (FLLEPCA),” in Proceedings of the 3rd International Conference on Advances in Patten Recognition (ICAPR /05), vol. 3687 of Lecture Notes in Computer Science, pp. 326-333, 2005.
[19] Y. Chang, C. Hu, and M. Turk, “Probabilistic expression analysis on manifolds,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 520-527, 2004.
[20] A. Elgammal and C.-S. Lee, “Inferring 3D body pose from silhouettes using activity manifold learning,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 681-688, 2004.
[21] O. C. Jenkins and M. J. Matarić, “A spatio-temporal extension to isomap nonlinear dimension reduction,” in Proceedings of the 21st International Conference on Machine Learning (ICML /04), pp. 441-448, 2004.
[22] A. Elgammal and C.-S. Lee, “Separating style and content on a nonlinear manifold,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 478-485, 2004.
[23] A. Brun, H. J. Park, H. Knutsson, and C. F. Westin, “Colouring of DT-MRI fiber traces using Laplacian eigenmaps,” in Proceedings of the 9th International Conference on Computer Aided Systems Theory, vol. 9, pp. 48-51, 2003.
[24] M. Niskanen and O. Silvén, “Comparison of dimensionality reduction methods for wood surface inspection,” in Proceedings of the 6th International Conference on Quality Control by Artificial Vision, pp. 178-188, 2003. · doi:10.1117/12.514959
[25] T. Sim, S. Baker, and M. Bsat, “The CMU pose, illumination, and expression (PIE) database,” in Proceedings of the International Conference on Automatic Face and Gesture Recognition, pp. 53-58, Washington, DC, USA, 2002.
[26] J. Yang, A. F. Frangi, J.-Y. Yang, D. Zhang, and Z. Jin, “KPCA plus LDA: a complete kernel fisher discriminant framework for feature extraction and recognition,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 2, pp. 230-244, 2005. · doi:10.1109/TPAMI.2005.33
[27] G. Baudat and F. Anouar, “Generalized discriminant analysis using a kernel approach,” Neural Computation, vol. 12, no. 10, pp. 2385-2404, 2000. · doi:10.1162/089976600300014980