diff --git a/text/preliminaries/correlation.tex b/text/preliminaries/correlation.tex index 7ccad56..a33f15b 100644 --- a/text/preliminaries/correlation.tex +++ b/text/preliminaries/correlation.tex @@ -7,7 +7,7 @@ The most prominent types of correlation might be: \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{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} @@ -20,7 +20,7 @@ A positive spatial autocorrelation indicates that similar data are \emph{cluster \subsection{Extraction of correlation} \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}. 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.