From ab12c4f6c14b2958e7eb1b911c1898545f7e1fca Mon Sep 17 00:00:00 2001 From: Maxim Divilkovskiy Date: Sat, 7 Sep 2024 18:04:33 +0300 Subject: [PATCH] english version --- paper/Divilkovskiy2024SourceSpace_en.aux | 4 ++-- paper/Divilkovskiy2024SourceSpace_en.pdf | Bin 524088 -> 523878 bytes .../Divilkovskiy2024SourceSpace_en.synctex.gz | Bin 111628 -> 110821 bytes paper/Divilkovskiy2024SourceSpace_en.tex | 2 -- 4 files changed, 2 insertions(+), 4 deletions(-) diff --git a/paper/Divilkovskiy2024SourceSpace_en.aux b/paper/Divilkovskiy2024SourceSpace_en.aux index c8ec3b7..982ef27 100644 --- a/paper/Divilkovskiy2024SourceSpace_en.aux +++ b/paper/Divilkovskiy2024SourceSpace_en.aux @@ -23,9 +23,9 @@ \citation{Biosignals} \citation{boyd2017multiperiod} \citation{MulticorrelatedQuadratic} +\citation{jadon2022comprehensive} \babel@aux{english}{} \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}\protected@file@percent } -\citation{jadon2022comprehensive} \@writefile{toc}{\contentsline {section}{\numberline {2}Formulation of the problem of pointwise forecasting of a set of time series}{2}{section.2}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\numberline {3}Algorithm in case of predicting a single distance matrix}{2}{section.3}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\numberline {4}Existence of several values of a series satisfying same distance matrix}{2}{section.4}\protected@file@percent } @@ -37,7 +37,7 @@ \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {Modified functions where 3 is subtracted from the last values}}}{3}{subfigure.1.2}\protected@file@percent } \citation{puchkin2023sharper} \@writefile{toc}{\contentsline {section}{\numberline {5}Pairwise correlation between time series as the distance function}{4}{section.5}\protected@file@percent } -\newlabel{fig:fig5}{{\caption@xref {fig:fig5}{ on input line 250}}{6}{Pairwise correlation between time series as the distance function}{figure.caption.2}{}} +\newlabel{fig:fig5}{{\caption@xref {fig:fig5}{ on input line 248}}{6}{Pairwise correlation between time series as the distance function}{figure.caption.2}{}} \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Function $||\hat {\mathbf {\Sigma }}_{t+1} - \bar {\mathbf {\Sigma }}_{t+1}||_2^2$ for following series: $(1, 3)$ and $(2, 4)$. 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z(MJ+gGcwxSS%iq5)J7|qM_~1lEawu=cTyWBRYcaRp3EyGD?!?&Ak|jD@NOBm85oo! z;8gC$zp}G5V7Ln<41bL84!uUQszI9$IJvGmortt})TMi#E5c6Y$za1?30DU?u-_hDJ!<9|!`S&k1UZ5ZV=C0A<6 zc(TDSc|{Ohel0&Pv!u|GNJ0^zium!|U}wKU{y-kJm;S_x{(XhyUJudVWt!#>eZ&kB>J` z*FRlKw+h@*v$@CN`I%yr=a diff --git a/paper/Divilkovskiy2024SourceSpace_en.tex b/paper/Divilkovskiy2024SourceSpace_en.tex index 18f4e52..d39313a 100644 --- a/paper/Divilkovskiy2024SourceSpace_en.tex +++ b/paper/Divilkovskiy2024SourceSpace_en.tex @@ -90,8 +90,6 @@ \section{Introduction} Existing time series prediction methods such as LSTM \cite{LSTM}, SSA \cite{SSA} and other \cite{Biosignals}, \cite{boyd2017multiperiod} are based on predicting the value of a single series. These methods can be modified to forecast also a set of time series. For this purpose, it is sufficient to consider a set of series as one multivariate series. However, this approach does not explicitly model the dependencies between different series. In this paper, we propose to analyze the change in \textit{set} of time series. This approach explicitly uses the relationships between them as information. A similar study is carried out in the \cite{MulticorrelatedQuadratic} paper, but it emphasizes on the feature selection task. This task consists in selecting such a subset of the original time series for which it is possible to make a forecast of sufficient quality. - In this paper, forecasting is done not in the original space, but in the space of pairwise distances. The advantage of this method is that in real sets of time series (natural, physical, financial, etc.), there is often a dependence close to linear. This additional information can improve the quality of the final prediction. - Further, we consider conditions on the distance function between rows under which there is a way to recover the values of time series. The insufficiency of one matrix to recover the answer is proved. Two methods using several matrices are proposed for the case of accurate forecast and for the case of forecast with non-zero noise. Also, we propose a recovery algorithm based on two theorems about the explicit form of the response using pairwise correlation as a function of pairwise distance between rows. Mean Squared Error and Mean Absolute Error are used as quality criteria. It is shown in the article\cite{jadon2022comprehensive} that they are the most suitable for the task of time series forecasting. \section{Formulation of the problem of pointwise forecasting of a set of time series}