sumppdistnet | R Documentation |
Based on the shortest-path metric in a network, determine the TT-p-distances (or RTT-p-distances)
between a single point pattern zeta
and a collection of point patterns. Then
compute the sum of q-th powers of these distances. The point patterns are
specified by vectors of indices referring to the vertices in the network.
sumppdistnet( dmat, zeta, ppmatrix, penalty = 1, type = c("tt", "rtt", "TT", "RTT"), p = 1, q = 1 )
dmat |
the distance matrix of a network containing all shortest-path distances between its vertices. |
zeta |
a vector specifying the vertex-indices of zeta. |
ppmatrix |
a matrix specifying in its columns the vertex-indices of the point patterns in the collection. A virtual index that is one greater than the maximum vertex-index in the network can be used to fill up columns so that they all have the same length. |
penalty |
a positive number. The penalty for adding/deleting points. |
type |
either |
p |
a number >0. Matchings between |
q |
a number >0. |
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, ..., 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.
A nonnegative number, the q
-th order sum of the TT-p- or RTT-p-distances
between the patterns represented by zeta
and ppmatrix
. This number has an attribute
distances
that contains the individual distances.
Raoul Müller raoul.mueller@uni-goettingen.de
Dominic Schuhmacher schuhmacher@math.uni-goettingen.de
kmeansbarynet
, sumppdist
# See examples for kmeansbarynet
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