A unifying review of linear Gaussian models
Neural Computation
Mixtures of probabilistic principal component analyzers
Neural Computation
An Introduction to Variational Methods for Graphical Models
Machine Learning
On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors
SIAM Journal on Matrix Analysis and Applications
Orthogonal Tensor Decompositions
SIAM Journal on Matrix Analysis and Applications
Multilinear Analysis of Image Ensembles: TensorFaces
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Two-Dimensional PCA: A New Approach to Appearance-Based Face Representation and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Out-of-core tensor approximation of multi-dimensional matrices of visual data
ACM SIGGRAPH 2005 Papers
Generalized Low Rank Approximations of Matrices
Machine Learning
Beyond streams and graphs: dynamic tensor analysis
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Equivalence of Non-Iterative Algorithms for Simultaneous Low Rank Approximations of Matrices
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Multilinear Principal Component Analysis of Tensor Objects for Recognition
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 02
MPCA: Multilinear Principal Component Analysis of Tensor Objects
IEEE Transactions on Neural Networks
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Feature extraction from two-dimensional or higher-order data, such as face images and surveillance videos, have recently been an active research area. There have been several 2D or higher-order PCA-style dimensionality reduction algorithms, but they mostly lack probabilistic interpretations and are difficult to apply with, e.g., incomplete data. It is also hard to extend these algorithms for applications where a certain region of the data point needs special focus in the dimensionality reduction process (e.g., the facial region in a face image). In this paper we propose a probabilistic dimensionality reduction framework for 2D and higher-order data. It specifies a particular generative process for this type of data, and leads to better understanding of some 2D and higher-order PCA-style algorithms. In particular, we show it actually takes several existing algorithms as its (non-probabilistic) special cases. We develop efficient iterative learning algorithms within this framework and study the theoretical properties of the stationary points. The model can be easily extended to handle special regions in the high-order data. Empirical studies on several benchmark data and real-world cardiac ultrasound images demonstrate the strength of this framework.