  We analyze extremes of traffic flow profiles composed of traffic counts over
a day. The data is essentially curves and determining which trajectory should
be classified as extreme is not straight forward. To assess the extremes of the
traffic flow curves in a coherent way, we use a directional definition of
extremeness and apply the dimension reduction technique called principal
component analysis (PCA) in an asymmetric norm. In the classical PCA one
reduces the dimensions of the data by projecting it in the direction of the
largest variation of the projection around its mean. In the PCA in an
asymmetric norm one chooses the projection directions, such that the
asymmetrically weighted variation around a tail index -- an expectile -- of the
data is the largest possible. Expectiles are tail measures that generalize the
mean in a similar manner as quantiles generalize the median. Focusing on the
asymmetrically weighted variation around an expectile of the data, we find the
appropriate projection directions and the low dimensional representation of the
traffic flow profiles that uncover different patterns in their extremes. Using
the traffic flow data from the roundabout on Ernst-Reuter-Platz in the city
center of Berlin, Germany, we estimate, visualize and interpret the resulting
principal expectile components. The corresponding directional extremes of the
traffic flow profiles are simple to identify and to connect to their location-
and time-related specifics. Their shapes are driven by their scores on each
principal expectile component which is useful for extracting and analyzing
traffic patterns. Our approach to dimensionality reduction towards the
directional extremes of traffic flow extends the related methodological basis
and gives promising results for subsequent analysis, prediction and control of
traffic flow patterns.
