deletions | additions       diff --git a/Methodology Complementary Data.tex b/Methodology Complementary Data.tex  index 1ba1b33..93f65a4 100644  --- a/Methodology Complementary Data.tex  +++ b/Methodology Complementary Data.tex 
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\begin{equation} \label{eqn:coordinate-transform} (x,y)\to(l,S,\gamma). \end{equation}  where a point located at ($x$,$y$) in cartesian Cartesian  space is snapped to the nearest position on the nearest alignment $l$, and is represented by the curvilinear distance coordinate  $S$ along this alignment from its begining and the offset \( \gamma \), orthogonal to this alignment, measuring the distance between the original point and it's its position  snapped position. to the alignment.  These coordinates are useful for measuring following behaviour, lane changes, and lane deflection. Many approaches exist to trajectory clustering, some methods are supervised, many more are unsupervised (e.g. k-means \cite{MacQueen_1967}). Supervised trajectory clustering is labour intensive and potentially a source of bias, but allows for tight control of scenery description and analysis oversight. Unsupervised clustering is systematic but naive as this form of clustering can only make use of trajectory data to infer spatial relationship. Supervised clustering along a series of splines, called alignments, is chosen for its simple implementation and tight control over interpretation. A hybrid approach, which refines spatial positioning of manually defined alignments through traditional unsupervised clustering approaches, is proposed as future work.