Jun Murakami

A novel nonnegative decomposition method and its application to 2-D digital filter design

In designing two-dimensional (2-D) digital filters in the frequency domain, an efficient technique is to first decompose the given 2-D frequency domain design specifications into one-dimensional (1-D) ones, and then approximate the resulting 1-D magnitude specifications using the well-developed 1-D filter design techniques. Finally, by interconnecting the designed 1-D filters one can obtain a 2-D digital filter. However, since the magnitude responses of digital filters must be nonnegative, it is required that the decomposition of 2-D magnitude specifications result in nonnegative 1-D magnitude specifications. We call such a decomposition the nonnegative decomposition. This paper proposes a nonnegative decomposition method for decomposing the given 2-D magnitude specifications into 1-D ones, and then transforms the problem of designing a 2-D digital filter into that of designing 1-D filters. Consequently, the original problem of designing a 2-D filter is significantly simplified.

Analysis of Rehabilitation Data by Multi-Dimensional Principal Component Analysis Method Using the Statistical Software R

The multi-dimensional principal component analysis (MPCA), which is an extension of the well-known principal component analysis (PCA), is proposed to reduce the dimension and to extract the feature of the multi-dimensional data. We have analyzed the rehabilitation data, which is known as the Functional Independence Measure (FIM), routinely measured from inpatients of a hospital by using MPCA. This time, we implemented the MPCA program by the statistical software R, and carried out the analysis of that data with changed configuration from the previous works in the environment of the R statistical system. From the results, the usefulness and the effectiveness of MPCA analysis in the R environment are confirmed.

Analysis of Relationships Between Amount of Physical Activity of Patients in Rehabilitation and Their ADL Scores Using Multidimensional PCA

This paper investigates relationships between the ADL evaluations of convalescent stroke patients in rehabilitation and their physical activity amounts measured by an accelerometer. A previous study performed a correlation analysis between the activity amount and two FIM items (i.e., motor FIM and cognitive FIM), which is one of the ADL evaluations, and showed the existence of a significant correlation between both of them. In this paper, we performed a correlation analysis and also did a multidimensional PCA (MPCA) of data matrix and tensors, respectively, constructed from more detailed FIM items than above. As the results of the correlation analysis, we showed that the correlation coefficients of the activity amount of walking when compared the motor and cognitive FIM were relatively large, and that the similar tendency to the result of the previous study was obtained. By considering the detailed FIM items, we noticed that correlation coefficients of the locomotion subscale of FIM compared with the walking calories and the number of walking steps were the largest. Furthermore, from the results of performing MPCA, we found several pairs of principal component scores with higher correlation coefficients. The above-mentioned results suggest that the use of accelerometer is considered to be effective in grasping patients’ FIM scores.

Calculation of Fourth-Order Tensor Product Expansion by Power Method and Comparison of it with Higher-Order Singular Value Decomposition

Higher-order singular value decomposition (HOSVD) is known as an effective technique to reduce the dimension of multidimensional data. We have proposed a method to perform third-order tensor product expansion (3OTPE) by using the power method for the same purpose as HOSVD, and showed that our method had a better accuracy property than HOSVD, and furthermore, required fewer computation time than that. Since our method could not be applied to the tensors of fourth-order (or more) in spite of having those useful properties, we extend our algorithm of 3OTPE calculation to forth-order tensors in this paper. The results of newly developed method are compared to those obtained by HOSVD. We show that the results follow the same trend as the case of 3OTPE.