Statistical analysis with missing data
Statistical analysis with missing data
Classification by minimum-message-length inference
ICCI'90 Proceedings of the international conference on Advances in computing and information
Keeping the neural networks simple by minimizing the description length of the weights
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Principal component neural networks: theory and applications
Principal component neural networks: theory and applications
EM algorithms for PCA and SPCA
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
A view of the EM algorithm that justifies incremental, sparse, and other variants
Learning in graphical models
Accelerating Cyclic Update Algorithms for Parameter Estimation by Pattern Searches
Neural Processing Letters
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Learning from Incomplete Data
Latent semantic models for collaborative filtering
ACM Transactions on Information Systems (TOIS)
On the Effect of the Form of the Posterior Approximation in Variational Learning of ICA Models
Neural Processing Letters
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Building Blocks for Variational Bayesian Learning of Latent Variable Models
The Journal of Machine Learning Research
Restricted Boltzmann machines for collaborative filtering
Proceedings of the 24th international conference on Machine learning
Bayesian probabilistic matrix factorization using Markov chain Monte Carlo
Proceedings of the 25th international conference on Machine learning
Principal Component Analysis for Large Scale Problems with Lots of Missing Values
ECML '07 Proceedings of the 18th European conference on Machine Learning
Principal Component Analysis for Sparse High-Dimensional Data
Neural Information Processing
Scalable Collaborative Filtering with Jointly Derived Neighborhood Interpolation Weights
ICDM '07 Proceedings of the 2007 Seventh IEEE International Conference on Data Mining
Multiple imputation in principal component analysis
Advances in Data Analysis and Classification
Neural Processing Letters
Eigen combination of colour and texture informations for image segmentation
ICISP'12 Proceedings of the 5th international conference on Image and Signal Processing
Bayesian Robust PCA of Incomplete Data
Neural Processing Letters
Hybrid bilinear and trilinear models for exploratory analysis of three-way poisson counts
ICANN'12 Proceedings of the 22nd international conference on Artificial Neural Networks and Machine Learning - Volume Part II
Document categorization based on minimum loss of reconstruction information
MICAI'12 Proceedings of the 11th Mexican international conference on Advances in Computational Intelligence - Volume Part II
Global analytic solution of fully-observed variational Bayesian matrix factorization
The Journal of Machine Learning Research
Bayesian Canonical correlation analysis
The Journal of Machine Learning Research
Minimizer of the Reconstruction Error for multi-class document categorization
Expert Systems with Applications: An International Journal
Hi-index | 0.01 |
Principal component analysis (PCA) is a classical data analysis technique that finds linear transformations of data that retain the maximal amount of variance. We study a case where some of the data values are missing, and show that this problem has many features which are usually associated with nonlinear models, such as overfitting and bad locally optimal solutions. A probabilistic formulation of PCA provides a good foundation for handling missing values, and we provide formulas for doing that. In case of high dimensional and very sparse data, overfitting becomes a severe problem and traditional algorithms for PCA are very slow. We introduce a novel fast algorithm and extend it to variational Bayesian learning. Different versions of PCA are compared in artificial experiments, demonstrating the effects of regularization and modeling of posterior variance. The scalability of the proposed algorithm is demonstrated by applying it to the Netflix problem.