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evaluation: Minor corrections

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Manos Katsomallos 2021-10-14 17:17:31 +02:00
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text/evaluation/details.tex
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\section{Experimental setting and data sets} \section{Setting, configurations, and data sets}
\label{sec:eval-dtl} \label{sec:eval-dtl}
In this section we list all the relevant details regarding the evaluation setting (Section~\ref{subsec:eval-setup}), and we present the real and synthetic data sets that we used (Section~\ref{subsec:eval-dat}), along with the corresponding configurations (Section~\ref{subsec:eval-conf}). In this section we list all the relevant details regarding the evaluation setting (Section~\ref{subsec:eval-setup}), and we present the real and synthetic data sets that we used (Section~\ref{subsec:eval-dat}), along with the corresponding configurations (Section~\ref{subsec:eval-conf}).
@ -123,8 +123,7 @@ For this reason, and in order to create a more controlled environment for our ex
We model the temporal correlation in the synthetic data as a \emph{stochastic matrix} $P$, using a \emph{Markov Chain}~\cite{gagniuc2017markov}. We model the temporal correlation in the synthetic data as a \emph{stochastic matrix} $P$, using a \emph{Markov Chain}~\cite{gagniuc2017markov}.
$P$ is an $n \times n$ matrix, where the element $P_{ij}$ $P$ is an $n \times n$ matrix, where the element $P_{ij}$
%at the $i$th row of the $j$th column that %at the $i$th row of the $j$th column that
represents the transition probability from a state $i$ to another state $j$. represents the transition probability from a state $i$ to another state $j$, $\forall$ $i$, $j$ $\leq$ $n$.
%, $\forall i, j \leq n$.
It holds that the elements of every row $j$ of $P$ sum up to $1$. It holds that the elements of every row $j$ of $P$ sum up to $1$.
We follow the \emph{Laplacian smoothing} technique~\cite{sorkine2004laplacian}, as utilized in~\cite{cao2018quantifying}, to generate the matrix $P$ with a degree of temporal correlation $s > 0$ equal to We follow the \emph{Laplacian smoothing} technique~\cite{sorkine2004laplacian}, as utilized in~\cite{cao2018quantifying}, to generate the matrix $P$ with a degree of temporal correlation $s > 0$ equal to
% and generate a stochastic matrix $P$ with a degree of temporal correlation $s$ by calculating each element $P_{ij}$ as follows % and generate a stochastic matrix $P$ with a degree of temporal correlation $s$ by calculating each element $P_{ij}$ as follows

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text/evaluation/theotherthing.tex
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\section{Selection of landmarks} \section{Selection of {\thethings}}
\label{sec:eval-lmdk-sel} \label{sec:eval-lmdk-sel}
In this section, we present the experiments on the methodology for the {\thething} selection presented in Section~\ref{subsec:lmdk-sel-sol}, on the real and synthetic data sets. In this section, we present the experiments on the methodology for the {\thething} selection presented in Section~\ref{subsec:lmdk-sel-sol}, on the real and synthetic data sets.
With the experiments on the synthetic data sets (Section~\ref{subsec:sel-utl}) we show the normalized Euclidean and Wasserstein distance metrics (not to be confused with the temporal distances in Figure~\ref{fig:avg-dist}) With the experiments on the synthetic data sets (Section~\ref{subsec:sel-utl}) we show the normalized Euclidean and Wasserstein distance metrics (not to be confused with the temporal distances in Figure~\ref{fig:avg-dist})