[1]
|
Donoho, D.L. (2000) High-Dimensional Data Analysis: The Curses and Blessings of Dimensionality. Lecture Delivered at the “Mathematical Challenges of the 21st Century” Conference of the American Math. Society, Los Angeles. http://www-stat.stanford.edu/donoho/Lectures/AMS2000/AMS2000.html
|
[2]
|
Diamantaras, K.I. and Kung, S.Y. (1996) Principal Component Neural Networks: Theory and Applications. John Wiley, NY.
|
[3]
|
Person, K. (1901) On Lines and Planes of Closest Fit to System of Points in Space. Philiosophical Magazine, 2, 559-572. http://dx.doi.org/10.1080/14786440109462720
|
[4]
|
Jenkins, O.C. and Mataric, M.J. (2002) Deriving Acion and Behavior Primitives from Human Motion Data. International Conference n Robots and Systems, 3, 2551-2556.
|
[5]
|
Jain, A.K. and Dubes, R.C. (1962) Algorithms for Clastering Data. Prentice Hall, Upper Saddle River.
|
[6]
|
Mardia, K.V., Kent, J.T. and Bibby, J.M. (1995) Multivariate Analysis Probability and Mathematical Statistics. Academic Press, Waltham.
|
[7]
|
(2002) Francesco Camastra Data Dimensionality Estimation Methods, a Survey INFM-DISI, University of Genova, Genova.
|
[8]
|
Fukunaga, K. (1982) Intrinsic Dimensionality Extraction, in Classification, Pattern Recognition and Reduction of Dimensionality, Vol. 2 of Handbook of Statistics, North Holland, 347-362.
|
[9]
|
Torgerson, W.S. (1952) Multidimenmsional Scaling I: Theory and Methode. Psychometrika, 17, 401-419. http://dx.doi.org/10.1007/BF02288916
|
[10]
|
Teng, L., Li, H., Fu, X., Chen, W. and Shen, I-F. (2005) Dimension Reduction of Microarrey Data Based on Local Tangent Space Aligment. Proceedings of the 4th IEEE international Conference on Cogenitive Informatics, 154-159.
|
[11]
|
Williams, C.K.I. (2002) On a Connection between Kernel PCA and Metric Multidimensional Scaling. Machine Learning, 46, 11-19. http://dx.doi.org/10.1023/A:1012485807823
|
[12]
|
Chatfield, C. and Collins, A.J. (1980) Introduction to Multivariate Analysis. Chapman and Hill. http://dx.doi.org/10.1007/978-1-4899-3184-9
|
[13]
|
Platt, J.C. (2005) FastMap, MetricMap, and Landmark MDS are all Nystrom algorithms. Proceddings of the 10th International Workshop on Artificial Intelligence and Statistics, 15, 261-268.
|
[14]
|
Roweis, S.T. (1997) EM Algorithms for PCA and SPCA. Advances in Neural Information Processing Systems, 10, 626-632.
|
[15]
|
Lawrence, N.D. (2005) Probabilistic Non-Linear Proncipal Component Analysis with Gaussian Process Latent Variable Models. Journal of Machine Learning Research, 6, 1783-1816.
|
[16]
|
Welling, M., Rosen-Zvi, M. and Hinton, G. (2004) Exponential Family Harmoniums with an Application to Information Retrieval. Advances in Neural Information Processing Systems, 17, 1481-1488.
|
[17]
|
Turk, M.A. and Pentland, A.P. (1991) Face Recognition Using Eigenfaces. Proceedings of the Computer Vision and Pattern Recognition 1991, Maui, 586-591. http://dx.doi.org/10.1109/CVPR.1991.139758
|
[18]
|
Huber, R., Ramoser, H., Mayer, K., Penz, H. and Rubik, M. (2005) Classification of Coins Using an Eigenspace Approach. Pattern Recognition Letters, 26, 61-75. http://dx.doi.org/10.1016/j.patrec.2004.09.006
|
[19]
|
Posadas, A.M., Vidal, F., de Miguel, F., Alguacil, G., Pena, J., Ibanez, J.M. and Morales, J. (1993) Spatialtemporal Analysis of a Seismic Series Using the Principal Components Method. Journal of Geophysical Research, 98, 1923-1932. http://dx.doi.org/10.1029/92JB02297
|
[20]
|
Partridge, M. and Calvo, R. (1997) Fast Dimensionality Reduction and Simple PCA. Intelligent Data Analysis, 2, 292-298.
|
[21]
|
Scholkopf, B., Smola, A. and Müller, K.R. (1998) Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural Computation, 10, 1299-1319.
|
[22]
|
Shawe-Taylor, J. and Christianini, N. (2004) Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge.
|
[23]
|
Tipping, M.E. (2000) Sparse Kernel Principal Component Analysis. Advances in Neural Information Processing Systems, 13, 633-639.
|
[24]
|
Kim, K.I., Jung, K. and Kim, H.J. (2002) Face Recognition Using Kernel Principal Component Analysis. IEEE Signal Processing Letters, 9, 40-42. http://dx.doi.org/10.1109/97.991133
|
[25]
|
Hoffmann. H. (2007) Kernel PCA for Novelty Detection. Pattern Recognition, 40, 863-874. http://dx.doi.org/10.1016/j.patcog.2006.07.009
|
[26]
|
Lima, A., Zen, H. Nankaku, Y. Miyajima, C. Tokuda, K. and Kitamura. T. (2004) On the Use of Kernel PCA for Feature Extraction in Speech Recognition. IEICE Transactions on Information Systems, E87-D, 2802-2811.
|
[27]
|
Duda, R.O., Hart, P.E. and Stork, D.G. (2001) Pattern Classification, Wiley Interscience, New York.
|
[28]
|
Shin, Y.J. and Park, C.H. (2011) Analysis of Correlation Based Dimension Reduction Methods. International Journal of Applied Mathematics and Computer Science, 21, 549-558.
|
[29]
|
Fukunaga, K. (1990) Introduction to Statistical Pattern Recognition. 2nd Edition, Academic Press, San Diego.
|
[30]
|
Hotelling, H. (1936) Relations between Two Sets of Vertices. Biometrika, 28, 321-377.
|
[31]
|
Sun, Q., Zeng, S., Liu, Y., Heng, P. and Xia, D. (2005) A New Methode of Feature Fusion and Its Application in Image Recognition. Pattern Recognition, 38, 2437-2448. http://dx.doi.org/10.1016/j.patcog.2004.12.013
|
[32]
|
Hastie, T. and Stuezle, W. (1989) Principal Curves. Journal of the American Statistical Association, 84, 502-516.
|
[33]
|
Kegl, B. and Linder, T. (2000) Learning and Design of Principal Curves. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22, 281-297.
|
[34]
|
Ozertem, U. and Erdogmus, D. (2011) Locally Defined Principal Curves and Surfaces. Journal of Machine Learning Research, 12, 1249-1286.
|
[35]
|
Malthouse, E. (1996) Some Theoretical Results on Nonlinear Principal Component Analysis. citeseer.nj.net.com/malthouse96some.html
|
[36]
|
Carreira-Perpinan, M.A. (1997) A Review of Dimension Reduction Tecniques. Technical Report CS-96-09. Department of Computer Science, University of Sheffield, Sheffield.
|
[37]
|
Tibshirani, R. (1992) Principal Curves Revisited. Statistics and Computing, 2,183-190. http://dx.doi.org/10.1007/BF01889678
|
[38]
|
Bishop, C.M. (1995) Neural Networks for Pattern Recognition. Oxford University Press, New York.
|
[39]
|
Ripley, B.D. (1996) Pattern Recognition and Neural Networks. Cambridge University Press, Cambridge.
|
[40]
|
Spierenburg, J.A. (1997) Dimension Reduction of Images Using Neural Networks. Master’s Thesis, Leiden University, Leiden.
|
[41]
|
Kramer, M.A. (1991) Non-Linear Principal Component Analysis Using Associative Neural Networks. AIChE Journal, 37, 233-243. http://dx.doi.org/10.1002/aic.690370209
|
[42]
|
Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vettering, W.T. (1992) Numerical Recips in C: The Art of Scientific Computing. 2nd Edition, Cambridge University Press, Cambridge.
|
[43]
|
Fowlkers, C., Belongie, S., Chung, F. and Malik, J. (2004) Specral Grouping Using the Nysroem Method. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26, 214-225.
|
[44]
|
Marida, K.V., Kent, J.T. and Bibby, J.M. (1995) Multivariate Analysis. Probability and Mathematical Statistics. Academic Press, Waltham.
|
[45]
|
Faloutsos, C. and Lin, K.I. (1995) FastMap: A Fast Algorithm for Indexing, Data-Mining and Visualization of Traditional and Multimedia Datasets. In: Carey, M.J. and Schneider, D.A., Eds., Proceedings of the 1995 ACM SIGMOD International Conference on Management of Data, San Jose, 163-174. http://dx.doi.org/10.1145/223784.223812
|
[46]
|
Fodor, I.K. (2002) A Survey of Dimension Reduction Techniques. Center for Applied Scientific Computing, Livermore National Laborary, Livermore.
|
[47]
|
Chung, F.R.K. (1997) Spectral Graph Theory. American Mathematical Society. CBMS Regional Conference Series in Mathematics in American Mathematical Society, 212, 92.
|
[48]
|
Belkin, M. and Niyogi, P. (2003) Laplacian Eigenmaps for Dimensionality Reduction and Data Representation. Neural Computation, 15, 1373-1396. http://dx.doi.org/10.1162/089976603321780317
|
[49]
|
Rivest, R., Cormen, T., Leiserson, C. and Stein, C. (2001) Introduction to Algorithms. MIT Press, Cambridge.
|
[50]
|
Kumar, V., Grama, A., Gupta, A. and Karypis, G. (1994) Introduction to Parallel Computing. Benjamin-Cummings, Redwood City.
|
[51]
|
Donoho, D. and Grimes, C. Hessian Eigenmaps: Locally Linear Embedding Techniques for High-Dimensional Data. Proceedings of National Academy of Sciences, 100.
|
[52]
|
Ye, Q. and Zhi, W.F. (2003) Discrete Hessian Eigenmaps Method for Dimensionality Reduction.
|
[53]
|
Kamhaltla, N. and Leen, T.K. (1994) Fast Non-Linear Dimension Reduction. In: Advances in Neural Information Processing Systems, Morgan Kaufmann Publishers, Inc., Burlington, 152-159.
|
[54]
|
Goldberg, D.E. (1989) Genetic Algorithms in Search, Optimization and Machin Learning. Addisn Wesley, Reading.
|
[55]
|
Raymer, M.L., Goodman, E.D., Kuhn, L.A. and Jain, A.K. (2000) Dimensionality Reduction Using Genetic Algorithms. IEEE Transactions on Evolutionary Computation, 4, 164-171. http://dx.doi.org/10.1109/4235.850656
|
[56]
|
Jones, G. (2002) Published Online: 15 APR. University of Sheffield, Sheffield.
|
[57]
|
Kohavi, R. and John, G. (1998) The Wrapper Approach. In: Liu, H. and Motoda, H., Eds., Feature Extraction, Construction and Selection: A Data Mining Perspective, Springer Verlag, Berlin, 33-50. http://dx.doi.org/10.1007/978-1-4615-5725-8_3
|
[58]
|
Huber, P.J. (1985) Projection Persuit. Annals of Statistics, 13, 435-475. http://dx.doi.org/10.1214/aos/1176349519
|
[59]
|
McCullagh, P. and Nelder, J.A. (1989) Generalized Linear Models. Chapman and Hall, Boca Raton. http://dx.doi.org/10.1007/978-1-4899-3242-6
|
[60]
|
Dobson, A.J. (1990) An Introduction to Generalized Linear Models. Chapman and Hall, London. http://dx.doi.org/10.1007/978-1-4899-7252-1
|
[61]
|
Leathwick, J.R. Elith, J. and Hastie, T. (2006) Comparative Performance of Generalized Additive Models and Multivariate Adaptive Regression Splines for Statistical Modelling of Species Distributions. Ecological Modelling, 188-196. http://www.stanford.edu/~hastie/Papers/Ecology/leathwick_etal_2006_mars_ecolmod.pdf
|
[62]
|
Li, K.C. (2000) High Dimensional Data Analysis via SIR/PHD Approach. Lecture Note in Progress. http://www.stat.ucla.edu/kcli/
|
[63]
|
Dennis Cook, R. and Li, B. (2002) Dimension Reduction for Conditional Mean in Regression. Annals of Statistics, 30, 455-474. http://dx.doi.org/10.1214/aos/1021379861
|
[64]
|
Zhang, Z. and Zha, H. (2002) Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment. http://arxiv.org/pdf/cs.LG/0212008.pdf
|
[65]
|
Wang, H. and Xia, Y. (2008) Sliced Regression for Dimension Reduction. Peking University & National University of Singapore, Journal of the American Statistical Association, 103, 811-821.
|
[66]
|
Feng, W.K., He, X. and Shi, P. (2002) Dimension Reduction Based on Canonical Correlation. Statistica Sinica, 12, 1093-1113.
|
[67]
|
Lectures on Fractals and Dimension Theory. http://homepages.warwick.ac.uk/masdbl/dimensiontotal.pdf
|