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., {"references":["Lindsay I. Smith, \"A tutorial on principal components analysis,\" www.cs.\notago.ac.nz/osc453/student_tutorials/principal_components.pdf, 2002.","Hervé Abdi and Lynne J. Williams, \"Principal components analysis,\"\nWiley Interdisciplinary Reviews: Computational Statistics, vol.2, pp.\n433-450, 2010.","Naoki Yamamoto, Jun Murakami, and Chiharu Okuma, \"Application of\nmatrix PCA to school record analysis,\" Proceedings of the IEICE\nGeneral Conference (in Japanese), D-15-14, 2011.","Yana Mulyana, Naoki Yamamoto, Jun Murakami, and Chiharu Okuma,\n\"Analysis of multi-dimensional data by using multi-dimensional\nprincipal component analysis ´╝ìapplication to Monthly Labour Survey\ndata,\" Proceedings of the 25th Technology Exchange Meeting between\nIndustry, Academia, and Government in Kumamoto (in Japanese),\npp.68-69, 2011.","Kohei Inoue, Kenji Hara, and Kiichi Urahama, \"Matrix principal\ncomponent analysis for image compression and recognition,\"\nProceedings of the 1st Joint Workshop on Machine Perception and\nRobotics (MPR), pp115-120, 2005.","Jieping Ye, Revi Janardan, and Qi Li, \"GPCA: an efficient dimension\nreduction scheme for image compression and retrieval,\" Proceedings of\nthe 10th ACM SIGKDD International Conference on Knowledge\nDiscovery and Data Mining, pp.354-363, 2004.","Rui Xu and Yen-Wei Chen, \"Generalized N-dimensional principal\ncomponent analysis (GND-PCA) and its application on construction of\nstatistical appearance models for medical volumes with fewer samples,\"\nNeurocomputing, vol.72, no.10-12, pp.2276-2287, 2009.","Kenneth J. Ottenbacher, Yungwen Hsu, Carl V. Granger, and Roger C.\nFiedler, \"The reliability of the functional independence measure: A\nquantitative review,\" Archives of Physical Medicine and Rehabilitation,\nvol.77, pp.1226-1232, 1996.","Lisbeth Claesson and Elisabeth Svensson, \"Measures of order\nconsistency between paired ordinal data: application to the Functional\nIndependence Measure and Sunnaas index of ADL,\" Journal of\nRehabilitation Medicine, vol. 33, 2001.\n[10] James W. Davis and Hui Gao, \"An expressive three-mode principal\ncomponents model for gender recognition,\" Journal of Vision, vol.4, pp.\n362-377, 2004.\n[11] Lieven De Lathauwer, Bart De Moor, and Joos Vandewalle, \"A\nmultilinear singular value decomposition,\" SIAM Journal on Matrix\nAnalysis and Applications, vol.21, no.4, pp.1253-1278, 2000.\n[12] Gene H. Golub and Christian H. Reinsch, \"Singular value decomposition\nand least squares solution,\" Numerical Mathematics, vol. 14,\npp.403-420, 1970.\n[13] George E. Forsythe, Michael A. Malcolm, and Cleve B. Moler, Computer\nMethods for Mathematical Computations, chap.9, Englewood Cliffs,\nPrentice-Hall, New Jersey, 1977.\n[14] Chiharu Okuma, Jun Murakami, and Naoki Yamamoto, \"Comparison\nbetween higher-order SVD and third-order orthogonal tensor product\nexpansion,\" International Journal Electronics, Communications and\nComputer Engineering, vol.1, no.2, pp.131-137, 2009.\n[15] Chiharu Okuma, Naoki Yamamoto, and Jun Murakami, \"An improved\nalgorithm for calculation of the third-order orthogonal tensor product\nexpansion by using singular value decomposition,\" International Journal\nElectronics, Communications and Computer Engineering, vol.2, no.1,\npp.11-20, 2010.\n[16] Tobias Heimann, Ivo Wolf, Tomos G. Williams, and Hans P. Meinzer,\n\"3D active shape models using gradient descent optimization of\ndescription length,\" in Proceedings of the IPMI, pp.566-567, Springer,\n2005.\n[17] Michael E. Wall, Andreas Rechtsteiner, and Luis M. Rocha, \"Singular\nvalue decomposition and principal component analysis, \" in A Practical\nApproach to Microarray Data Analysis (D. P. Berrar, W. Dubitzky, M.\nGranzow eds.), Kluwer: Norwell, Massachusetts, pp.91-109, 2003."]}