2021 Volume 20 Issue 2 Pages 60-70
Fisher Discriminant Orthogonal Decomposition (FDOD) is a discriminant analysis method incorporating regularization coefficient and orthogonal decomposition into ordinary Fisher Discriminant Analysis (FDA). This method makes it possible to avoid overfitting in discriminant analyses of multivariate data and to obtain discriminant axes whose number is greater than that of groups. However, FDOD requires long calculation time and large memory. To solve these problems, a novel technique, Fast Fisher Discriminant Orthogonal Decomposition (FFDOD), has been developed. FFDOD saves calculation time and memory by singular value decomposition of the data to be analyzed to remove redundant data. When FFDOD was applied to 275 infrared spectra of 6 types of cellulosic fibers each of which consists of data at 7054 wavenumbers, the calculation time was reduced to 1/84 of that when using FDOD. If the time required for the singular value decomposition is not considered, a remarkable speedup to about 1/290 was realized. The calculation accuracy of FFDOD has been found equivalent with that of FDOD by comparing the results by FFDOD and FDOD.
