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correlation: Review

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Manos Katsomallos
2021-08-04 01:07:03 +03:00
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text/preliminaries/correlation.tex
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The most prominent types of correlation might be: The most prominent types of correlation might be:
\begin{itemize} \begin{itemize}
\item \emph{temporal}~\cite{wei2006time}---appearing in observations (i.e.,~values) of the same object over time. \item \emph{Temporal}~\cite{wei2006time}---appearing in observations (i.e.,~values) of the same object over time.
\item \emph{Spatial}~\cite{legendre1993spatial, anselin1995local}---denoted by the degree of similarity of nearby data points in space, and indicating if and how phenomena relate to the (broader) area where they take place. \item \emph{Spatial}~\cite{legendre1993spatial, anselin1995local}---denoted by the degree of similarity of nearby data points in space, and indicating if and how phenomena relate to the (broader) area where they take place.
\item \emph{Spatiotemporal}---a combination of the previous categories, appearing when processing time series or sequences of human activities with geolocation characteristics, e.g.,~\cite{ghinita2009preventing}. \item \emph{Spatiotemporal}---a combination of the previous categories, appearing when processing time series or sequences of human activities with geolocation characteristics, e.g.,~\cite{ghinita2009preventing}.
\end{itemize} \end{itemize}
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\subsection{Extraction of correlation} \subsection{Extraction of correlation}
\label{subsec:cor-ext} \label{subsec:cor-ext}
A common practice for extracting data dependence from continuous data, is by expressing the data as a \emph{stochastic} or \emph{random process}. A common practice for extracting correlation from continuous data with dependence, is by expressing the data as a \emph{stochastic} or \emph{random process}.
A random process is a collection of \emph{random variables} or \emph{bivariate data}, indexed by some set, e.g.,~a series of timestamps, a Cartesian plane $\mathbb{R}^2$, an $n$-dimensional Euclidean space, etc.~\cite{skorokhod2005basic}. A random process is a collection of \emph{random variables} or \emph{bivariate data}, indexed by some set, e.g.,~a series of timestamps, a Cartesian plane $\mathbb{R}^2$, an $n$-dimensional Euclidean space, etc.~\cite{skorokhod2005basic}.
The values a random variable can take are outcomes of an unpredictable process, while bivariate data are pairs of data values with a possible association between them. The values a random variable can take are outcomes of an unpredictable process, while bivariate data are pairs of data values with a possible association between them.
Expressing data as stochastic processes allows their modeling depending on their properties, and thereafter the discovery of relevant data dependence. Expressing data as stochastic processes allows their modeling depending on their properties, and thereafter the discovery of relevant data dependence.