caa a22 4500 445871369 CHVBK 20180317145512.0 cr unu---uuuuu 170323e20110501xx s 000 0 eng 10.1007/s10618-010-0183-9 doi (NATIONALLICENCE)springer-10.1007/s10618-010-0183-9 Matrix-variate and higher-order probabilistic projections [Elektronische Daten] [Shipeng Yu, Jinbo Bi, Jieping Ye] 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. The Author(s), 2010 Dimensionality reduction nationallicence Higher-order principle component analysis nationallicence Low-rank matrix factorization nationallicence Probabilistic projection nationallicence Yu Shipeng Siemens Medical Solutions USA, Malvern, PA, USA aut Bi Jinbo Department of Computer Science and Engineering, University of Connecticut, 06269, Storrs, CT, USA aut Ye Jieping Arizona State University, Tempe, AZ, USA aut Data Mining and Knowledge Discovery Springer US; http://www.springer-ny.com 22/3(2011-05-01), 372-392 1384-5810 22:3<372 2011 22 10618 https://doi.org/10.1007/s10618-010-0183-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10618-010-0183-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Yu Shipeng Siemens Medical Solutions USA, Malvern, PA, USA aut NATIONALLICENCE 700 1- Bi Jinbo Department of Computer Science and Engineering, University of Connecticut, 06269, Storrs, CT, USA aut NATIONALLICENCE 700 1- Ye Jieping Arizona State University, Tempe, AZ, USA aut NATIONALLICENCE 773 0- Data Mining and Knowledge Discovery Springer US; http://www.springer-ny.com 22/3(2011-05-01), 372-392 1384-5810 22:3<372 2011 22 10618 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer