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Volumn 34, Issue 6, 2012, Pages 1041-1055

A least-squares framework for component analysis

Author keywords

Canonical correlation analysis; Dimensionality reduction; K means; Kernel methods; Linear discriminant analysis; Principal component analysis; Reduced rank regression; Spectral clustering

Indexed keywords

CANONICAL CORRELATION ANALYSIS; DIMENSIONALITY REDUCTION; K-MEANS; KERNEL METHODS; LINEAR DISCRIMINANT ANALYSIS; REDUCED RANK REGRESSION; SPECTRAL CLUSTERING;

EID: 84860257221     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2011.184     Document Type: Article
Times cited : (163)

References (115)
  • 3
    • 58149421595 scopus 로고
    • Analysis of a complex of statistical variables into principal components
    • H. Hotelling, "Analysis of a Complex of Statistical Variables into Principal Components," J. Educational Psychology, vol. 24, no. 6, pp. 417-441, 1933.
    • (1933) J. Educational Psychology , vol.24 , Issue.6 , pp. 417-441
    • Hotelling, H.1
  • 4
    • 0001474381 scopus 로고
    • The statistical utilization of multiple measurements
    • R.A. Fisher, "The Statistical Utilization of Multiple Measurements," Annals of Eugenics, vol. 8, pp. 376-386, 1938.
    • (1938) Annals of Eugenics , vol.8 , pp. 376-386
    • Fisher, R.A.1
  • 5
    • 0000764772 scopus 로고
    • The use of multiple measurements in taxonomic problems
    • R.A. Fisher, "The Use of Multiple Measurements in Taxonomic Problems," Annals of Eugenics, vol. 7, pp. 179-188, 1936.
    • (1936) Annals of Eugenics , vol.7 , pp. 179-188
    • Fisher, R.A.1
  • 6
    • 0000107975 scopus 로고
    • Relations between two sets of variates
    • H. Hotelling, "Relations between Two Sets of Variates," Biometrika, vol. 28, pp. 321-377, 1936.
    • (1936) Biometrika , vol.28 , pp. 321-377
    • Hotelling, H.1
  • 7
    • 0042378381 scopus 로고    scopus 로고
    • Laplacian eigenmaps for dimensionality reduction and data representation
    • DOI 10.1162/089976603321780317
    • M. Belkin and P. Niyogi, "Laplacian Eigenmaps for Dimensionality Reduction and Data Representation," Neural Computation, vol. 15, no. 6, pp. 1373-1396, 2003. (Pubitemid 37049796)
    • (2003) Neural Computation , vol.15 , Issue.6 , pp. 1373-1396
    • Belkin, M.1    Niyogi, P.2
  • 13
    • 0033556862 scopus 로고    scopus 로고
    • A unifying review of linear gaussian models
    • S. Roweis and Z. Ghahramani, "A Unifying Review of Linear Gaussian Models," Neural Computation, vol. 11, no. 2, pp. 305-345, 1999.
    • (1999) Neural Computation , vol.11 , Issue.2 , pp. 305-345
    • Roweis, S.1    Ghahramani, Z.2
  • 16
    • 0001497505 scopus 로고
    • Estimating linear restrictions on regression coefficients for multivariate normal distributions
    • T.W. Anderson, "Estimating Linear Restrictions on Regression Coefficients for Multivariate Normal Distributions," Annals of Math. Statistics, vol. 12, pp. 327-351, 1951.
    • (1951) Annals of Math. Statistics , vol.12 , pp. 327-351
    • Anderson, T.W.1
  • 19
    • 0026260103 scopus 로고    scopus 로고
    • The SVD and reduced rank signal processing
    • L. Scharf, "The SVD and Reduced Rank Signal Processing," Signal Processing, vol. 25, no. 2, pp. 113-133, 2002.
    • (2002) Signal Processing , vol.25 , Issue.2 , pp. 113-133
    • Scharf, L.1
  • 22
    • 0024774330 scopus 로고
    • Neural networks and principal component analysis: Learning from examples without local minima
    • P. Baldi and K. Hornik, "Neural Networks and Principal Component Analysis: Learning from Examples without Local Minima," Neural Networks, vol. 2, pp. 53-58, 1989.
    • (1989) Neural Networks , vol.2 , pp. 53-58
    • Baldi, P.1    Hornik, K.2
  • 23
    • 0029220876 scopus 로고
    • Visual learning and recognition of 3D objects from appearance
    • H. Murase and S.K. Nayar, "Visual Learning and Recognition of 3D Objects from Appearance," Int'l J. Computer Vision, vol. 1, no. 14, pp. 5-24, 1995.
    • (1995) Int'l J. Computer Vision , vol.1 , Issue.14 , pp. 5-24
    • Murase, H.1    Nayar, S.K.2
  • 26
    • 0141742284 scopus 로고    scopus 로고
    • A framework for robust subspace learning
    • F. De la Torre and M.J. Black, "A Framework for Robust Subspace Learning," Int'l J. Computer Vision, vol. 54, pp. 117-142, 2003.
    • (2003) Int'l J. Computer Vision , vol.54 , pp. 117-142
    • De La Torre, F.1    Black, M.J.2
  • 29
    • 0020464111 scopus 로고
    • A simplified neuron model as a principal component analyzer
    • DOI 10.1007/BF00275687
    • E. Oja, "A Simplified Neuron Model as Principal Component Analyzer," J. Math. Biology, vol. 15, pp. 267-273, 1982. (Pubitemid 13209700)
    • (1982) Journal of Mathematical Biology , vol.15 , Issue.3 , pp. 267-273
    • Oja, E.1
  • 31
    • 0018546040 scopus 로고
    • Lower rank approximation of matrices by least squares with any choice of weights
    • K.R. Gabriel and S. Zamir, "Lower Rank Approximation of Matrices by Least Squares with Any Choice of Weights," Technometrics, vol. 21, pp. 489-498, 1979. (Pubitemid 10427363)
    • (1979) Technometrics , vol.21 , Issue.4 , pp. 489-498
    • Gabriel K.Ruben1    Zamir, S.2
  • 32
    • 0029373923 scopus 로고
    • Principal component analysis with missing data and its application to polyhedral object modeling
    • Sept.
    • H. Shum, K. Ikeuchi, and R. Reddy, "Principal Component Analysis with Missing Data and Its Application to Polyhedral Object Modeling," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 9, pp. 855-867, Sept. 1995.
    • (1995) IEEE Trans. Pattern Analysis and Machine Intelligence , vol.17 , Issue.9 , pp. 855-867
    • Shum, H.1    Ikeuchi, K.2    Reddy, R.3
  • 33
    • 0038959172 scopus 로고    scopus 로고
    • Probabilistic principal component analysis
    • M. Tipping and C.M. Bishop, "Probabilistic Principal Component Analysis," J. Royal Statistical Soc. B, vol. 61, pp. 611-622, 1999.
    • (1999) J. Royal Statistical Soc. B , vol.61 , pp. 611-622
    • Tipping, M.1    Bishop, C.M.2
  • 34
    • 0347243182 scopus 로고    scopus 로고
    • Nonlinear Component Analysis as a Kernel Eigenvalue Problem
    • B. Schölkopf, A.J. Smola, and K.-R. Müller, "Nonlinear Component Analysis as a Kernel Eigenvalue Problem," Neural Computation, vol. 10, no. 5, pp. 1299-1319, 1998. (Pubitemid 128463674)
    • (1998) Neural Computation , vol.10 , Issue.5 , pp. 1299-1319
    • Scholkopf, B.1    Smola, A.2    Muller, K.-R.3
  • 42
    • 0001565436 scopus 로고
    • The utilization of multiple measurements in problems of biological classification
    • C. Rao, "The Utilization of Multiple Measurements in Problems of Biological Classification," J. Royal Statistical Soc.-Series B, vol. 10, no. 2, pp. 159-203, 1948.
    • (1948) J. Royal Statistical Soc.-Series B , vol.10 , Issue.2 , pp. 159-203
    • Rao, C.1
  • 46
    • 21844447839 scopus 로고    scopus 로고
    • Characterization of a family of algorithms for generalized discriminant analysis on undersampled problems
    • Sept.
    • J. Ye, "Characterization of a Family of Algorithms for Generalized Discriminant Analysis on Undersampled Problems," J. Machine Learning Research, vol. 6, no. 1, pp. 483-502, Sept. 2005.
    • (2005) J. Machine Learning Research , vol.6 , Issue.1 , pp. 483-502
    • Ye, J.1
  • 47
    • 36048970830 scopus 로고    scopus 로고
    • Discriminant subspace analysis: A fukunaga-koontz approach
    • Oct.
    • S. Zhang and T. Sim, "Discriminant Subspace Analysis: A Fukunaga-Koontz Approach," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 10, pp. 1732-1745, Oct. 2007.
    • (2007) IEEE Trans. Pattern Analysis and Machine Intelligence , vol.29 , Issue.10 , pp. 1732-1745
    • Zhang, S.1    Sim, T.2
  • 49
    • 0025746876 scopus 로고
    • On the relations between discriminant analysis and multilayer perceptrons
    • DOI 10.1016/0893-6080(91)90071-C
    • P. Gallinari, S. Thiria, F. Badran, and F. Fogelman-Soulie, "On the Relations between Discriminant Analysis and Multilayer Perceptrons," Neural Networks, vol. 4, pp. 349-360, 1991. (Pubitemid 21682552)
    • (1991) Neural Networks , vol.4 , Issue.3 , pp. 349-360
    • Gallinari, P.1    Thiria, S.2    Badran, F.3    Fogelman-Soulie, F.4
  • 51
  • 53
    • 0343503881 scopus 로고
    • Canonical variables as optimal predictors
    • V.J. Yohai and M.S. Garcia, "Canonical Variables as Optimal Predictors," The Annals of Statistics, vol. 8, no. 4, pp. 865-869, 1980.
    • (1980) The Annals of Statistics , vol.8 , Issue.4 , pp. 865-869
    • Yohai, V.J.1    Garcia, M.S.2
  • 54
    • 0000807171 scopus 로고
    • Reduced-rank regression and canonical analysis
    • M. Tso, "Reduced-Rank Regression and Canonical Analysis," J. Royal Statistical Soc., Series B, vol. 43, no. 2, pp. 183-189, 1981.
    • (1981) J. Royal Statistical Soc., Series B , vol.43 , Issue.2 , pp. 183-189
    • Tso, M.1
  • 56
    • 0034704229 scopus 로고    scopus 로고
    • A global geometric framework for nonlinear dimensionality reduction
    • DOI 10.1126/science.290.5500.2319
    • J.B. Tenenbaum, V. de Silva, and J.C. Langford, "A Global Geometric Framework for Nonlinear Dimensionality Reduction," Science, vol. 5500, no. 290, pp. 2319-2323, 2000. (Pubitemid 32041577)
    • (2000) Science , vol.290 , Issue.5500 , pp. 2319-2323
    • Tenenbaum, J.B.1    De Silva, V.2    Langford, J.C.3
  • 57
    • 0034704222 scopus 로고    scopus 로고
    • Nonlinear dimensionality reduction by locally linear embedding
    • DOI 10.1126/science.290.5500.2323
    • S. Roweis and L. Saul, "Nonlinear Dimensionality Reduction by Locally Linear Embedding," Science, vol. 290, no. 5500, pp. 2323-2326, 2000. (Pubitemid 32041578)
    • (2000) Science , vol.290 , Issue.5500 , pp. 2323-2326
    • Roweis, S.T.1    Saul, L.K.2
  • 59
    • 4344599431 scopus 로고    scopus 로고
    • Learning eigenfunctions links spectral embedding and kernel PCA
    • DOI 10.1162/0899766041732396
    • Y. Bengio, P. Vincent, J. Paiement, P. Vincent, and M. Ouimet, "Learning Eigenfunctions Links Spectral Embedding and Kernel PCA," Neural Computation, vol. 16, pp. 2197-2219, 2004. (Pubitemid 39137820)
    • (2004) Neural Computation , vol.16 , Issue.10 , pp. 2197-2219
    • Bengio, Y.1    Delalleau, O.2    Le Roux, N.3    Paiement, J.-F.4    Vincent, P.5    Ouimet, M.6
  • 69
    • 0003882879 scopus 로고    scopus 로고
    • Spectral graph theory. Providence: CBMS regional conference series in mathematics
    • F.K. Chung, Spectral Graph Theory. Providence: CBMS Regional Conference Series in Mathematics, vol. 92, Am. Math. Soc., 1997.
    • (1997) Am. Math. Soc. , vol.92
    • Chung, F.K.1
  • 73
    • 77952345425 scopus 로고    scopus 로고
    • Techncial Report CMU-RI-TR-06-44, Robotics Inst., Carnegie Mellon Univ Aug.
    • D. Tolliver, "Spectral Rounding and Image Segmentation," Techncial Report CMU-RI-TR-06-44, Robotics Inst., Carnegie Mellon Univ., Aug. 2006.
    • (2006) Spectral Rounding and Image Segmentation
    • Tolliver, D.1
  • 74
    • 34548025132 scopus 로고    scopus 로고
    • A survey of kernel and spectral methods for clustering
    • DOI 10.1016/j.patcog.2007.05.018, PII S0031320307002580
    • M. Filippone, F. Camastra, F. Masulli, and S. Rovetta, "A Survey of Kernel and Spectral Methods for Clustering," Pattern Recognition, vol. 41, no. 1, pp. 176-190, 2008. (Pubitemid 47284212)
    • (2008) Pattern Recognition , vol.41 , Issue.1 , pp. 176-190
    • Filippone, M.1    Camastra, F.2    Masulli, F.3    Rovetta, S.4
  • 75
    • 34548748711 scopus 로고    scopus 로고
    • Weighted graph cuts without eigenvectors a multilevel approach
    • DOI 10.1109/TPAMI.2007.1115
    • I.S. Dhillon, Y. Guan, and B. Kulis, "Weighted Graph Cuts without Eigenvectors: A Multilevel Approach," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 11, pp. 1944-1957, Nov. 2007. (Pubitemid 47430448)
    • (2007) IEEE Transactions on Pattern Analysis and Machine Intelligence , vol.29 , Issue.11 , pp. 1944-1957
    • Dhillon, I.S.1    Guan, Y.2    Kulis, B.3
  • 78
    • 34547965335 scopus 로고    scopus 로고
    • Adaptive dimension reduction using discriminant analysis and k-means clustering
    • C. Ding and T. Li, "Adaptive Dimension Reduction Using Discriminant Analysis and K-Means Clustering," Proc. Int'l Conf. Machine Learning, 2007.
    • (2007) Proc. Int'l Conf. Machine Learning
    • Ding, C.1    Li, T.2
  • 81
    • 33749255098 scopus 로고    scopus 로고
    • On the equivalence of nonnegative matrix factorization and spectral clustering
    • C. Ding, X. He, and H. Simon, "On the Equivalence of Nonnegative Matrix Factorization and Spectral Clustering," Proc. SIAM Int'l Conf. Data Mining, 2005.
    • (2005) Proc. SIAM Int'l Conf. Data Mining
    • Ding, C.1    He, X.2    Simon, H.3
  • 83
    • 72249110121 scopus 로고
    • Self modeling curve resolution
    • W.H. Lawton and E.A. Sylvestre, "Self Modeling Curve Resolution," Technometrics, vol. 13, no. 3, pp. 617-633, 1971.
    • (1971) Technometrics , vol.13 , Issue.3 , pp. 617-633
    • Lawton, W.H.1    Sylvestre, E.A.2
  • 84
    • 0028561099 scopus 로고
    • Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values
    • P. Paatero and U. Tapper, "Positive Matrix Factorization: A Non-Negative Factor Model with Optimal Utilization of Error Estimates of Data Values," Envirometrics, vol. 5, pp. 111-126, 1994.
    • (1994) Envirometrics , vol.5 , pp. 111-126
    • Paatero, P.1    Tapper, U.2
  • 85
    • 0024801666 scopus 로고
    • A receptor model using a specific non-negative transformation technique for ambient aerosol
    • J. Shena and G. Israela, "A Receptor Model Using a Specific Non-Negative Transformation Technique for Ambient Aerosol," Atmospheric Environment, vol. 23, no. 10, pp. 2289-2298, 1989.
    • (1989) Atmospheric Environment , vol.23 , Issue.10 , pp. 2289-2298
    • Shena, J.1    Israela, G.2
  • 93
  • 94
  • 95
    • 0141637236 scopus 로고    scopus 로고
    • Robust parameterized component analysis: Theory and applications to 2d facial appearance models
    • F. De la Torre and M.J. Black, "Robust Parameterized Component Analysis: Theory and Applications to 2D Facial Appearance Models," Computer Vision and Image Understanding, vol. 91, pp. 53-71, 2003.
    • (2003) Computer Vision and Image Understanding , vol.91 , pp. 53-71
    • De La Torre, F.1    Black, M.J.2
  • 96
    • 33644857757 scopus 로고    scopus 로고
    • Data driven image models through continuous joint alignment
    • DOI 10.1109/TPAMI.2006.34
    • E.G. Learned-Miller, "Data Driven Image Models through Continuous Joint Alignment," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 2, pp. 236-250, Feb. 2006. (Pubitemid 46395291)
    • (2006) IEEE Transactions on Pattern Analysis and Machine Intelligence , vol.28 , Issue.2 , pp. 236-250
    • Learned-Miller, E.G.1
  • 98
    • 4644302314 scopus 로고    scopus 로고
    • Automatic construction of active appearance models as an image coding problem
    • Oct.
    • S. Baker, I. Matthews, and J. Schneider, "Automatic Construction of Active Appearance Models as an Image Coding Problem," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 10, pp. 1380-1384, Oct. 2004.
    • (2004) IEEE Trans. Pattern Analysis and Machine Intelligence , vol.26 , Issue.10 , pp. 1380-1384
    • Baker, S.1    Matthews, I.2    Schneider, J.3
  • 100
    • 51949111955 scopus 로고    scopus 로고
    • Parameterized kernel principal component analysis: Theory and applications to supervised and unsupervised image alignment
    • F. De la Torre and M. Nguyen, "Parameterized Kernel Principal Component Analysis: Theory and Applications to Supervised and Unsupervised Image Alignment," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2008.
    • (2008) Proc. IEEE Conf. Computer Vision and Pattern Recognition
    • De La Torre, F.1    Nguyen, M.2
  • 101
    • 0031651559 scopus 로고    scopus 로고
    • EigenTracking: Robust Matching and Tracking of Articulated Objects Using a View-Based Representation
    • M.J. Black and A.D. Jepson, "Eigentracking: Robust Matching and Tracking of Objects Using View-Based Representation," Int'l J. Computer Vision, vol. 26, no. 1, pp. 63-84, 1998. (Pubitemid 128513060)
    • (1998) International Journal of Computer Vision , vol.26 , Issue.1 , pp. 63-84
    • Black, M.J.1    Jepson, A.D.2
  • 105
    • 3042535216 scopus 로고    scopus 로고
    • Distinctive image features from scale-invariant keypoints
    • D. Lowe, "Distinctive Image Features from Scale-Invariant Keypoints," Int'l J. Computer Vision, vol. 60, no. 2, pp. 91-110, 2004.
    • (2004) Int'l J. Computer Vision , vol.60 , Issue.2 , pp. 91-110
    • Lowe, D.1
  • 107
    • 0030779611 scopus 로고    scopus 로고
    • Sparse coding with an overcomplete basis set: A strategy employed by V1?
    • DOI 10.1016/S0042-6989(97)00169-7, PII S0042698997001697
    • B. Olshausen and D. Field, "Sparse Coding with an Overcomplete Basis Set: A Strategy Employed by V1?" Vision Research, vol. 37, pp. 3311-3325, 1997. (Pubitemid 27493805)
    • (1997) Vision Research , vol.37 , Issue.23 , pp. 3311-3325
    • Olshausen, B.A.1    Field, D.J.2
  • 108
    • 84898939890 scopus 로고    scopus 로고
    • On a connection between kernel PCA and metric multidimensional scaling
    • C. Williams, "On a Connection between Kernel PCA and Metric Multidimensional Scaling," Proc. Neural Information Processing Systems, 2001.
    • (2001) Proc. Neural Information Processing Systems
    • Williams, C.1
  • 109
    • 41249089920 scopus 로고    scopus 로고
    • On the equivalence between non-negative matrix factorization and probabilistic latent semantic indexing
    • C. Ding, T. Li, and W. Peng, "On the Equivalence between Non-Negative Matrix Factorization and Probabilistic Latent Semantic Indexing," Computational Statistics and Data Analysis, vol. 52, pp. 3913-3927, 2008.
    • (2008) Computational Statistics and Data Analysis , vol.52 , pp. 3913-3927
    • Ding, C.1    Li, T.2    Peng, W.3
  • 113
    • 68649096448 scopus 로고    scopus 로고
    • Tensor decompositions and applications
    • T.G. Kolda and B.W. Bader, "Tensor Decompositions and Applications," SIAM Rev., vol. 51, pp. 455-500, 2009.
    • (2009) SIAM Rev. , vol.51 , pp. 455-500
    • Kolda, T.G.1    Bader, B.W.2


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