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2014 | 24 | 1 | 123-131
Tytuł artykułu

An efficient eigenspace updating scheme for high-dimensional systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Systems based on principal component analysis have developed from exploratory data analysis in the past to current data processing applications which encode and decode vectors of data using a changing projection space (eigenspace). Linear systems, which need to be solved to obtain a constantly updated eigenspace, have increased significantly in their dimensions during this evolution. The basic scheme used for updating the eigenspace, however, has remained basically the same: (re)computing the eigenspace whenever the error exceeds a predefined threshold. In this paper we propose a computationally efficient eigenspace updating scheme, which specifically supports high-dimensional systems from any domain. The key principle is a prior selection of the vectors used to update the eigenspace in combination with an optimized eigenspace computation. The presented theoretical analysis proves the superior reconstruction capability of the introduced scheme, and further provides an estimate of the achievable compression ratios.
Rocznik
Tom
24
Numer
1
Strony
123-131
Opis fizyczny
Daty
wydano
2014
otrzymano
2013-06-27
poprawiono
2013-11-06
poprawiono
2013-11-22
Twórcy
autor
  • Faculty of Electrical Engineering and Computer Science, University of Maribor, Smetanova ulica 17, 2000 Maribor, Slovenia
autor
  • Faculty of Electrical Engineering and Computer Science, University of Maribor, Smetanova ulica 17, 2000 Maribor, Slovenia
autor
  • Faculty of Electrical Engineering and Computer Science, University of Maribor, Smetanova ulica 17, 2000 Maribor, Slovenia
Bibliografia
  • Chandrasekaran, S., Manjunath, B., Wang, Y., Winkeler, J. and Zhang, H. (1997). An eigenspace update algorithm for image analysis, Graphical Models and Image Processing 59(5): 321-332.
  • Gangl, S. and Žalik, B. (2011). Partially lossless compression of dicom image sets, Anales del Congreso Argentino de Informatica y Salud, C´ordoba, Argentina, pp. 131-136.
  • Han, X. (2010). Nonnegative principal component analysis for cancer molecular pattern discovery, IEEE/ACM Transactions on Computational Biology and Bioinformatics 7(3): 537-549.
  • ITU (2007). ITU-T Recommendation H.264: Advanced video coding for generic audiovisual services.
  • Jin, X.-Q. and Wei, Y.-M. (2007). A short note on singular values of optimal and superoptimal preconditioned matrices, International Journal of Computer Mathematics 84(8): 1261-1263.
  • Jolliffe, I.T. (1986). Principal Component Analysis, 1st Edn., Springer, New York, NY.
  • Lenz, R. and Bui, T.H. (2004). Recognition of non-negative patterns, Proceedings of the 17th International Conference on Pattern Recognition ICPR 2004, Cambridge, UK, Vol. 3, pp. 498-501.
  • Liu, X., Chen, T. and Thornton, S.M. (2003). Eigenspace updating for non-stationary process and its application to face recognition, Pattern Recognition 36(9): 1945-1959.
  • Lo, S.-C. B., Li, H. and Freedman, M.T. (2003). Optimization of wavelet decomposition for image compression and feature preservation, IEEE Transactions on Medical Imaging 22(9): 1141-1151.
  • Meyer, C.D. (2000). Matrix Analysis and Applied Linear Algebra, Society for Industrial and Applied Mathematics, Philadelphia, PA.
  • Nie, Y.Y., Li, Z. and Han, J.D. (2008). Origin-shifted algorithm for matrix eigenvalues, International Journal of Computer Mathematics 85(9): 1397-1411.
  • Perez-Iglesias, H., Dapena, A. and Castedo, L. (2005). A novel video coding scheme based on principal component analysis, 2005 IEEE Workshop on Machine Learning for Signal Processing, Mystic, CT, USA, pp. 361-366.
  • Richardson, I. (2003). H.264 and MPEG-4 Video Compression: Video Coding for Next-generation Multimedia, Wiley, Chichester.
  • Siwek, K., Osowski, S. and Szupiluk, R. (2009). Ensemble neural network approach for accurate load forecasting in a power system, International Journal of Applied Mathematics and Computer Science 19(2): 303-315, DOI: 10.2478/v10006-009-0026-2.
  • Skraban, J., Dzeroski, S., Zenko, B., Mongus, D., Gangl, S. and Rupnik, M. (2013). Gut microbiota patterns associated with colonization of different Clostridium difficile ribotypes, PLoS ONE 8(2): e58008.
  • Söderström, U. and Li, H. (2005). Very low bitrate full-frame facial video coding based on principal component analysis, Proceedings of the Signal and Image Processing Conference, Honolulu, HI, USA, pp. 127-132.
  • Söderström, U. and Li, H. (2007). Principal component video coding for simple decoding on mobile devices, Proceedings of the Swedish Symposium on Image Analysis, Linköping, Sweden, no. 47, pp. 149-152.
  • Spiegel, S., Gaebler, J., Lommatzsch, A., De Luca, E. and Albayrak, S. (2011). Pattern recognition and classification for multivariate time series, Proceedings of the 5th International Workshop on Knowledge Discovery from Sensor Data, Sensor KDDM'11, San Diego, CA, USA, pp. 34-42.
  • Sumi, S.M., Zaman, M.F. and Hirose, H. (2012). A rainfall forecasting method using machine learning models and its application to the Fukuoka city case, International Journal of Applied Mathematics and Computer Science 22(4): 841-854, DOI: 10.2478/v10006-012-0062-1.
  • Taubman, D.S. and Marcellin, M.W. (2002). JPEG2000: Image Compression Fundamentals, Standards and Practice, Kluwer Academic Publishers, Boston, MA.
  • Turk, M. and Pentland, A. (1991). Eigenfaces for recognition, Journal of Cognitive Neuroscience 3(1): 71-86.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv24i1p123bwm
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