Citation Relationships

Chang KY, Ghosh J (2001) A Unified Model for Probabilistic Principal Surfaces IEEE Transactions on Pattern Analysis and Machine Intelligence 23:22-41

   Method of probabilistic principle surfaces (PPS) (Chang and Ghosh 2001)

References and models cited by this paper

References and models that cite this paper

Attias H (1999) Independent factor analysis. Neural Comput 11:803-51 [PubMed]

Banfield JD, Raftery AE (1992) Ice Floe Identification in Satellite Images Using Mathematical Morphology and Clustering about Principal Curves J Am Stat Assoc 87:7-16

Bishop C (1995) Neural Networks For Pattern Recognition

Bishop CM, Svensen M, Williams CKI (1998) GTM: The Generative Topographic Mapping Neural Comput 10:215-235

Bishop CM, Svensn M (1997) GTM: The Generative Topographic Mapping Technical Report NCRG-96-015

Bishop CM, Svensn M, Williams CKI (1998) Developments of the Generative Topographic Mapping Neurocomput 21:203-224

Bishop CM, Tipping ME (1998) A Hierarchical Latent Variable Model for Data Visualization IEEE Trans Pattern Analysis And Machine Intelligence 20:281-293

Blake CL, Merz CJ (1998) UCI Repository of Machine Learning Databases

Bourlard H, Kamp Y (1988) Auto-association by multilayer perceptrons and singular value decomposition. Biol Cybern 59:291-4 [PubMed]

Chang KY (1994) Image and Signal Processing Using Neural Networks

Chang KY (2000) Nonlinear Dimensionality Reduction Using Probabilistic Principal Surfaces PhD Thesis

Chang KY, Ghosh J (1998) Principal Curves for Nonlinear Feature Extraction and Classification SPIE: Applications Of Artificial Neural Networks In Image Processing III 3307:120-129

Chang KY, Ghosh J (1999) Proc Intl Joint Conf Neural Networks :605

Chang KY, Ghosh J (2000) Three-Dimensional Model-Based Object Recognition and Pose Estimation Using Probabilistic Principal Surfaces SPIE: Applications of Artificial Neural Networks in Image Processing V :192-203

Cleveland W, Devlin S (1988) Locally Weighted Regression: An Approach to Regression Analysis by Local Fitting J Am Stat Assoc 83:596-610

Cottrell GW, Munroe P, Zipser D (1987) Image Compression by Back Propagation: An Example of Extensional Programming Technical Report ICS 8702

de_boor C (1978) A Practical Guide to Splines

Delicado P (1998) Principal Curves and Principal Oriented Points Technical Report 309, Departament dEconomia Empresa

Delicado P (1999) Another Look at Principal Curves and Surfaces Unpublished

Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc B 39:1-38

Dong D, Mcavoy TJ (1996) Nonlinear Principal Component Analysis-Based on Principal Curves and Neural Networks Computers And Chemical Eng 20:65-78

Duchamp T, Stuetzle W (1996) Extremal Properties of Principal Curves in the Plane Ann Stat 24:1511-1520

Duda RO, Hart PE (1973) Pattern Classification and Scene Analysis

Erwin E, Obermayer K, Schulten K (1992) Self-organizing maps: ordering, convergence properties and energy functions. Biol Cybern 67:47-55 [PubMed]

Fahrmeir L, Tutz G (1994) Multivariate Statistical Modelling Based on Generalized Linear Models

Fisher R (1936) The Case of Multiple Measurements in Taxonomic Problems Ann Eugen 7:179-188

Friedman JH (1987) Exploratory Projection Pursuit J Am Stat Assoc 82:249-266

Friedman JH (1991) Multivariate Adaptive Regression Splines Ann Stat 19:1-141

Friedman JH (1994) An Overview of Predictive Learning and Function Approximation From Statistics to Neural Networks, Cherkassky V:Friedman JH:Wechsler H, ed. pp.1

Hastie T (1984) Principal Curves and Surfaces PhD Thesis

Hastie T, Stuetzle W (1988) Principal Curves J Am Stat Assoc 84:502-516

Hertz J, Krogh A, Palmer RG (1991) Introduction to the Theory of Neural Computation.

Hyvarinen A (1999) Survey on Independent Component Analysis Neural Computing Surveys 2:94-128

Johnson RA, Wichern DW (1982) Applied Multivariate Statistical Analysis

Karhunen J, Oja E, Wang L, Vigario R, Joutsensalo J (1997) A class of neural networks for independent component analysis. IEEE Trans Neural Netw 8:486-504 [Journal] [PubMed]

Kegl B, Krzyzak A, Linder T, Zeger K (1998) Principal Curves: Learning and Convergence Proc IEEE Intl Symp Information Theory 387:387

Kegl B, Krzyzak A, Linder T, Zeger K (1998) A Polygonal Line Algorithm for Constructing Principal Curves Neural Information Processing Systems 11:501-507

Kegl B, Krzyzak A, Linder T, Zeger K (2000) Learning and Design of Principal Curves IEEE Trans Pattern Analysis And Machine Intelligence 22:281-297

Kohonen T (1995) Self-organizing Maps

Kramer MA (1991) Nonlinear Principal Component Analysis Using Autoassociative Neural Networks Am Inst Chemical Eng J 2:233-243

Leblanc M, Tibshirani R (1994) Adaptive Principal Surfaces J Am Stat Assoc 89:53-64

Magnus JR, Neudecker H (1988) Matrix Differential Calculus with Applications in Statistics and Econometrics

Malthouse EC (1998) Limitations of Nonlinear PCA as Performed with Generic Neural Networks IEEE Trans Neural Networks 1:165-173

Moon TK (1996) The Expectation-Maximization Algorithm IEEE Signal Processing Magazine :47-60

Mulier F, Cherkassky V (1995) Self-organization as an iterative kernel smoothing process. Neural Comput 7:1165-77 [PubMed]

Ritter H, Martinetz T, Schulten K (1992) Neural Computation and Self-Organizing Maps: An Introduction.

Svensn M (1998) GTM: The Generative Topographic Mapping PhD Thesis

Tan S, Mavrovouniotis ML (1995) Reducing Data Dimensionality through Optimizing Neural Network Inputs Am Inst Chemical Eng J 41:1471-1480

Tibshirani R (1992) Principal Curves Revisited Stat Comput 2:183-190

Tipping ME, Bishop CM (1997) Mixtures of Probabilistic Principal Component Analysers Technical Report NCRG-97-003

Wu CFJ (1983) On the Convergence Properties of the EM Algorithm Ann Stat 11:95-103

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