講演抄録/キーワード |
講演名 |
2018-12-22 14:55
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(Tokyo Inst. Tech.)・Yuichi Kida(OHU Univ.) DE2018-29 |
抄録 |
(和) |
(まだ登録されていません) |
(英) |
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. %\
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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. |
キーワード |
(和) |
/ / / / / / / |
(英) |
signal approximation / pseudo inverse matrix / artificial intelligence / / / / / |
文献情報 |
信学技報, vol. 118, no. 377, DE2018-29, pp. 65-70, 2018年12月. |
資料番号 |
DE2018-29 |
発行日 |
2018-12-14 (DE) |
ISSN |
Online edition: ISSN 2432-6380 |
著作権に ついて |
技術研究報告に掲載された論文の著作権は電子情報通信学会に帰属します.(許諾番号:10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) |
PDFダウンロード |
DE2018-29 |
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