Application of Multi-Dimensional Principal Component Analysis to Medical Data
Multi-dimensional principal component analysis
(PCA) is the extension of the PCA, which is used widely as the
dimensionality reduction technique in multivariate data analysis, to
handle multi-dimensional data. To calculate the PCA the singular
value decomposition (SVD) is commonly employed by the reason of
its numerical stability. The multi-dimensional PCA can be calculated
by using the higher-order SVD (HOSVD), which is proposed by
Lathauwer et al., similarly with the case of ordinary PCA. In this
paper, we apply the multi-dimensional PCA to the multi-dimensional
medical data including the functional independence measure (FIM)
score, and describe the results of experimental analysis.
[1] Lindsay I. Smith, "A tutorial on principal components analysis," www.cs.
otago.ac.nz/osc453/student_tutorials/principal_components.pdf, 2002.
[2] Hervé Abdi and Lynne J. Williams, "Principal components analysis,"
Wiley Interdisciplinary Reviews: Computational Statistics, vol.2, pp.
433-450, 2010.
[3] Naoki Yamamoto, Jun Murakami, and Chiharu Okuma, "Application of
matrix PCA to school record analysis," Proceedings of the IEICE
General Conference (in Japanese), D-15-14, 2011.
[4] Yana Mulyana, Naoki Yamamoto, Jun Murakami, and Chiharu Okuma,
"Analysis of multi-dimensional data by using multi-dimensional
principal component analysis ´╝ìapplication to Monthly Labour Survey
data," Proceedings of the 25th Technology Exchange Meeting between
Industry, Academia, and Government in Kumamoto (in Japanese),
pp.68-69, 2011.
[5] Kohei Inoue, Kenji Hara, and Kiichi Urahama, "Matrix principal
component analysis for image compression and recognition,"
Proceedings of the 1st Joint Workshop on Machine Perception and
Robotics (MPR), pp115-120, 2005.
[6] Jieping Ye, Revi Janardan, and Qi Li, "GPCA: an efficient dimension
reduction scheme for image compression and retrieval," Proceedings of
the 10th ACM SIGKDD International Conference on Knowledge
Discovery and Data Mining, pp.354-363, 2004.
[7] Rui Xu and Yen-Wei Chen, "Generalized N-dimensional principal
component analysis (GND-PCA) and its application on construction of
statistical appearance models for medical volumes with fewer samples,"
Neurocomputing, vol.72, no.10-12, pp.2276-2287, 2009.
[8] Kenneth J. Ottenbacher, Yungwen Hsu, Carl V. Granger, and Roger C.
Fiedler, "The reliability of the functional independence measure: A
quantitative review," Archives of Physical Medicine and Rehabilitation,
vol.77, pp.1226-1232, 1996.
[9] Lisbeth Claesson and Elisabeth Svensson, "Measures of order
consistency between paired ordinal data: application to the Functional
Independence Measure and Sunnaas index of ADL," Journal of
Rehabilitation Medicine, vol. 33, 2001.
[10] James W. Davis and Hui Gao, "An expressive three-mode principal
components model for gender recognition," Journal of Vision, vol.4, pp.
362-377, 2004.
[11] Lieven De Lathauwer, Bart De Moor, and Joos Vandewalle, "A
multilinear singular value decomposition," SIAM Journal on Matrix
Analysis and Applications, vol.21, no.4, pp.1253-1278, 2000.
[12] Gene H. Golub and Christian H. Reinsch, "Singular value decomposition
and least squares solution," Numerical Mathematics, vol. 14,
pp.403-420, 1970.
[13] George E. Forsythe, Michael A. Malcolm, and Cleve B. Moler, Computer
Methods for Mathematical Computations, chap.9, Englewood Cliffs,
Prentice-Hall, New Jersey, 1977.
[14] Chiharu Okuma, Jun Murakami, and Naoki Yamamoto, "Comparison
between higher-order SVD and third-order orthogonal tensor product
expansion," International Journal Electronics, Communications and
Computer Engineering, vol.1, no.2, pp.131-137, 2009.
[15] Chiharu Okuma, Naoki Yamamoto, and Jun Murakami, "An improved
algorithm for calculation of the third-order orthogonal tensor product
expansion by using singular value decomposition," International Journal
Electronics, Communications and Computer Engineering, vol.2, no.1,
pp.11-20, 2010.
[16] Tobias Heimann, Ivo Wolf, Tomos G. Williams, and Hans P. Meinzer,
"3D active shape models using gradient descent optimization of
description length," in Proceedings of the IPMI, pp.566-567, Springer,
2005.
[17] Michael E. Wall, Andreas Rechtsteiner, and Luis M. Rocha, "Singular
value decomposition and principal component analysis, " in A Practical
Approach to Microarray Data Analysis (D. P. Berrar, W. Dubitzky, M.
Granzow eds.), Kluwer: Norwell, Massachusetts, pp.91-109, 2003.
[1] Lindsay I. Smith, "A tutorial on principal components analysis," www.cs.
otago.ac.nz/osc453/student_tutorials/principal_components.pdf, 2002.
[2] Hervé Abdi and Lynne J. Williams, "Principal components analysis,"
Wiley Interdisciplinary Reviews: Computational Statistics, vol.2, pp.
433-450, 2010.
[3] Naoki Yamamoto, Jun Murakami, and Chiharu Okuma, "Application of
matrix PCA to school record analysis," Proceedings of the IEICE
General Conference (in Japanese), D-15-14, 2011.
[4] Yana Mulyana, Naoki Yamamoto, Jun Murakami, and Chiharu Okuma,
"Analysis of multi-dimensional data by using multi-dimensional
principal component analysis ´╝ìapplication to Monthly Labour Survey
data," Proceedings of the 25th Technology Exchange Meeting between
Industry, Academia, and Government in Kumamoto (in Japanese),
pp.68-69, 2011.
[5] Kohei Inoue, Kenji Hara, and Kiichi Urahama, "Matrix principal
component analysis for image compression and recognition,"
Proceedings of the 1st Joint Workshop on Machine Perception and
Robotics (MPR), pp115-120, 2005.
[6] Jieping Ye, Revi Janardan, and Qi Li, "GPCA: an efficient dimension
reduction scheme for image compression and retrieval," Proceedings of
the 10th ACM SIGKDD International Conference on Knowledge
Discovery and Data Mining, pp.354-363, 2004.
[7] Rui Xu and Yen-Wei Chen, "Generalized N-dimensional principal
component analysis (GND-PCA) and its application on construction of
statistical appearance models for medical volumes with fewer samples,"
Neurocomputing, vol.72, no.10-12, pp.2276-2287, 2009.
[8] Kenneth J. Ottenbacher, Yungwen Hsu, Carl V. Granger, and Roger C.
Fiedler, "The reliability of the functional independence measure: A
quantitative review," Archives of Physical Medicine and Rehabilitation,
vol.77, pp.1226-1232, 1996.
[9] Lisbeth Claesson and Elisabeth Svensson, "Measures of order
consistency between paired ordinal data: application to the Functional
Independence Measure and Sunnaas index of ADL," Journal of
Rehabilitation Medicine, vol. 33, 2001.
[10] James W. Davis and Hui Gao, "An expressive three-mode principal
components model for gender recognition," Journal of Vision, vol.4, pp.
362-377, 2004.
[11] Lieven De Lathauwer, Bart De Moor, and Joos Vandewalle, "A
multilinear singular value decomposition," SIAM Journal on Matrix
Analysis and Applications, vol.21, no.4, pp.1253-1278, 2000.
[12] Gene H. Golub and Christian H. Reinsch, "Singular value decomposition
and least squares solution," Numerical Mathematics, vol. 14,
pp.403-420, 1970.
[13] George E. Forsythe, Michael A. Malcolm, and Cleve B. Moler, Computer
Methods for Mathematical Computations, chap.9, Englewood Cliffs,
Prentice-Hall, New Jersey, 1977.
[14] Chiharu Okuma, Jun Murakami, and Naoki Yamamoto, "Comparison
between higher-order SVD and third-order orthogonal tensor product
expansion," International Journal Electronics, Communications and
Computer Engineering, vol.1, no.2, pp.131-137, 2009.
[15] Chiharu Okuma, Naoki Yamamoto, and Jun Murakami, "An improved
algorithm for calculation of the third-order orthogonal tensor product
expansion by using singular value decomposition," International Journal
Electronics, Communications and Computer Engineering, vol.2, no.1,
pp.11-20, 2010.
[16] Tobias Heimann, Ivo Wolf, Tomos G. Williams, and Hans P. Meinzer,
"3D active shape models using gradient descent optimization of
description length," in Proceedings of the IPMI, pp.566-567, Springer,
2005.
[17] Michael E. Wall, Andreas Rechtsteiner, and Luis M. Rocha, "Singular
value decomposition and principal component analysis, " in A Practical
Approach to Microarray Data Analysis (D. P. Berrar, W. Dubitzky, M.
Granzow eds.), Kluwer: Norwell, Massachusetts, pp.91-109, 2003.
@article{"International Journal of Information, Control and Computer Sciences:54696", author = "Naoki Yamamoto and Jun Murakami and Chiharu Okuma and Yutaro Shigeto and Satoko Saito and Takashi Izumi and Nozomi Hayashida", title = "Application of Multi-Dimensional Principal Component Analysis to Medical Data", abstract = "Multi-dimensional principal component analysis
(PCA) is the extension of the PCA, which is used widely as the
dimensionality reduction technique in multivariate data analysis, to
handle multi-dimensional data. To calculate the PCA the singular
value decomposition (SVD) is commonly employed by the reason of
its numerical stability. The multi-dimensional PCA can be calculated
by using the higher-order SVD (HOSVD), which is proposed by
Lathauwer et al., similarly with the case of ordinary PCA. In this
paper, we apply the multi-dimensional PCA to the multi-dimensional
medical data including the functional independence measure (FIM)
score, and describe the results of experimental analysis.", keywords = "multi-dimensional principal component analysis,
higher-order SVD (HOSVD), functional independence measure (FIM),
medical data, tensor decomposition", volume = "6", number = "3", pages = "315-7", }
