Determine the Euclidean distance based TT-p-distances (or RTT-p-distances) between
a single point pattern zeta and each point pattern in a list pplist. Then
compute the sum of \(q\)-th powers of these distances.
sumppdist(
zeta,
pplist,
penalty = 1,
type = c("tt", "rtt", "TT", "RTT"),
p = 1,
q = 1
)A nonnegative number, the q-th order sum of the TT-p- or RTT-p-distances
between zeta and each pattern in pplist. This number has an attribute
distances that contains the individual distances.
an object of class ppp.
an object of class ppplist or an
object that can be coerced to this class, such as a list of ppp
objects.
a positive number. The penalty for adding/deleting points.
either "tt"/"TT" for the transport-transform metric
or "rtt"/"RTT" for the relative transport-transform metric.
a number \(>0\). Matchings between zeta and the patterns in
pplist are chosen such that the p-th order sums (\(\ell_p\)-norms)
of the Euclidean distances are minimized.
a number \(>0\).
Dominic Schuhmacher schuhmacher@math.uni-goettingen.de
The main purpose of this function is to evaluate the relative performance of approximate \(q\)-th order barycenters of point patterns. A true \(q\)-th order barycenter of the point patterns \(\xi_1,\ldots,\xi_k\) with respect to the TT-p metric \(\tau_p\) minimizes $$\sum_{j=1}^k \tau_p(\xi_j, \zeta)^q$$ in \(\zeta\).
The most common choices are p = q = 1 and p = q = 2. Other
choices have not been tested.
ppdist for computation of TT-p- and RTT-p-metrics,
kmeansbary for finding a local minimum of the above sum for p = q = 2
# See the examples for kmeansbary
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