Presentation	2018-12-22 Linear processing type optimum future prediction of signals applying Kida's optimum signal-approximation to multi-dimensional signals that are made by arranging known region restriction data in a row Takuro Kida, Yuichi Kida,
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Abstract(in Japanese)	(See Japanese page)
Abstract(in English)	With respect to a matrix-filterbank that the matrix analysis-filterbank ${bf H}$ and the matrix sampling-filterbank ${bf S}$ are given, it is accomplished to present the optimum matrix synthesis-filterbank ${bf Z}$ that minimizes all the worst-case measures of matrix-error-signals ${bf E}(omega)={bf F}(omega)-{bf Y}(omega)$ between the input matrix-signals ${bf F}(omega)$ and the output matrix-signals ${bf Y(omega)}$ of the matrix-filterbank, at the same time. In this analysis, we assume that a set of the one-dimensional scanned input matrix-signals ${bf f}(t)={bf f}({bf x}(t))$, $({bf x}(t)=(x_0(t), x_1(t), ldots, x_{N-1}(t))$ of the multi-dimensional input matrix-images ${bf f}({bf x})$, $({bf x}=(x_0, x_1, ldots, x_{N-1}))$, is given. We assume that ${bf f}(t)$ is band-limited with an arbitrary given band-width and is allowed to include that ${bf f}(t)$ has uniformly or non-uniformly arranged sample-values. %\ %hspace*{3mm}Based on the concept of pseudo-inverse-matrix, we prove that the optimum synthesis-filterbank ${bf Z}$ is equal to the synthesis-filterbank that minimizes the upper-limit of a given matrix-norm of the error ${bf E}(omega)={bf F}(omega)-{bf Y}(omega)$ among all the input matrix-signals ${bf F}(omega)$ contained in the set of ${bf F}(omega)$. As the consequence of this fact, it is shown that there exists a linear calculation method which gives the optimum synthesis-matrix ${bf Z}$ by solving a set of linear equations. This result shows that, among all AI approximate estimation systems including well-known deep learning systems, there exists an optimum linear approximation system based on the set of the one-dimensional scanned data of the given multi-dimensional knowledge-data that is considered as the scanned input matrix-images ${bf f}({bf x}(t))$. In the final part of this paper, we show that there exists the explicit relation between the presented optimum approximation and the artificial intelligent system based on the given past knowledge data.
Keyword(in Japanese)	(See Japanese page)
Keyword(in English)	signal approximationpseudo inverse matrixartificial intelligence
Paper #	DE2018-29
Date of Issue	2018-12-14 (DE)

Conference Information
Committee	DE / IPSJ-DBS
Conference Date	2018/12/21(2days)
Place (in Japanese)	(See Japanese page)
Place (in English)	National Institute of Informatics
Topics (in Japanese)	(See Japanese page)
Topics (in English)
Chair	Akiyo Nadamoto(Konan Univ.) / 吉川 正俊(京大)
Vice Chair	Jun Miyazaki(Tokyo Inst. of Tech.) / Shingo Otsuka(Kanagawa Inst. of Tech.)
Secretary	Jun Miyazaki(Univ. of Hyogo) / Shingo Otsuka(Univ. of Marketing and Distrbution Science) / (筑波大)
Assistant	Kazuo Goda(Univ. of Tokyo) / Hiroaki Shiokawa(Tsukuba Univ.)

Paper Information
Registration To	Technical Committee on Data Engineering / Special Interest Group on Database System
Language	ENG
Title (in Japanese)	(See Japanese page)
Sub Title (in Japanese)	(See Japanese page)
Title (in English)	Linear processing type optimum future prediction of signals applying Kida's optimum signal-approximation to multi-dimensional signals that are made by arranging known region restriction data in a row
Sub Title (in English)
Keyword(1)	signal approximationpseudo inverse matrixartificial intelligence
1st Author's Name	Takuro Kida
1st Author's Affiliation	Professor Emeritus, Tokyo Institute of Technology(Tokyo Inst. Tech.)
2nd Author's Name	Yuichi Kida
2nd Author's Affiliation	The School of Pharmaceutical Sciences, Ohu University(OHU Univ.)
Date	2018-12-22
Paper #	DE2018-29
Volume (vol)	vol.118
Number (no)	DE-377
Page	pp.pp.65-70(DE),
#Pages	6
Date of Issue	2018-12-14 (DE)