icp.torus {ClusTorus}  R Documentation 
Conformity score for inductive prediction sets
Description
icp.torus
prepares all values
for computing the conformity score for specified methods.
plot.icp.torus
plots icp.torus
object with some options.
Usage
icp.torus(
data,
split.id = NULL,
model = c("kmeans", "kde", "mixture"),
mixturefitmethod = c("axisaligned", "circular", "general"),
kmeansfitmethod = c("general", "homogeneouscircular", "heterogeneouscircular",
"ellipsoids"),
init = c("hierarchical", "kmeans"),
d = NULL,
additional.condition = TRUE,
J = 4,
concentration = 25,
kmax = 500,
THRESHOLD = 1e10,
maxiter = 200,
verbose = TRUE,
...
)
## S3 method for class 'icp.torus'
logLik(object, ...)
## S3 method for class 'icp.torus'
predict(object, newdata, ...)
## S3 method for class 'icp.torus'
plot(
x,
data = NULL,
level = 0.1,
ellipse = TRUE,
out = FALSE,
type = NULL,
...
)
Arguments
data 
n x d matrix of toroidal data on 
split.id 
a ndimensional vector consisting of values 1 (estimation) and 2(evaluation) 
model 
A string. One of "kde", "mixture", and "kmeans" which
determines the model or estimation methods. If "kde", the model is based
on the kernel density estimates. It supports the kdebased conformity score
only. If "mixture", the model is based on the von Mises mixture, fitted
with an EM algorithm. It supports the von Mises mixture and its variants
based conformity scores. If "kmeans", the model is also based on the von
Mises mixture, but the parameter estimation is implemented with the
elliptical kmeans algorithm illustrated in Appendix. It supports the
logmaxmixture based conformity score only. If the
dimension of data space is greater than 2, only "kmeans" is supported.
Default is 
mixturefitmethod 
A string. One of "circular", "axisaligned", and
"general" which determines the constraint of the EM fitting. Default is
"axisaligned". This argument only works for 
kmeansfitmethod 
A string. One of "general", ellipsoids",
"heterogeneouscircular" or "homogeneouscircular". If "general", the
elliptical kmeans algorithm with no constraint is used. If "ellipsoids",
only the one iteration of the algorithm is used. If"heterogeneouscircular",
the same as above, but with the constraint that ellipsoids must be spheres.
If "homogeneouscircular", the same as above but the radii of the spheres are
identical. Default is "general". This argument only works for 
init 
Methods for choosing initial values of "kmeans" fitting.
Must be "hierarchical" or "kmeans". If "hierarchical", the initial
parameters are obtained with hierarchical clustering method.
If "kmeans", the initial parameters are obtained with extrinsic kmeans method.
Additional arguments for kmeans clustering and hierarchical clustering can be designated
via argument 
d 
pairwise distance matrix( 
additional.condition 
boolean index.
If 
J 
A scalar or numeric vector for the number(s) of components for 
concentration 
A scalar or numeric vector for the concentration parameter(s) for 
kmax 
the maximal number of kappa. If estimated kappa is
larger than 
THRESHOLD 
number for difference between updating and updated parameters. Default is 1e10. 
maxiter 
the maximal number of iteration. Default is 200. 
verbose 
boolean index, which indicates whether display
additional details as to what the algorithm is doing or
how many loops are done. Moreover, if 
... 
additional parameters. For plotting icp.torus, these parameters are for ggplot2::ggplot(). 
object 

newdata 
n x d matrix of toroidal data on 
x 

level 
either a numeric scalar or a vector in 
ellipse 
A boolean index which determines whether plotting ellipses from
mixture models. Default is 
out 
An option for returning the ggplot object. Default is 
type 
A string. One of "mix", "max" or "e". This argument is only available if 
Value
icp.torus
returns an icp.torus
object, containing all values
to compute the conformity score (if J
or concentration
is a
single value). if J
or concentration
is a vector containing
multiple values, then icp.torus
returns a list of icp.torus
objects
References
Jung, S., Park, K., & Kim, B. (2021). Clustering on the torus by conformal prediction. The Annals of Applied Statistics, 15(4), 15831603.
Mardia, K. V., Kent, J. T., Zhang, Z., Taylor, C. C., & Hamelryck, T. (2012). Mixtures of concentrated multivariate sine distributions with applications to bioinformatics. Journal of Applied Statistics, 39(11), 24752492.
Di Marzio, M., Panzera, A., & Taylor, C. C. (2011). Kernel density estimation on the torus. Journal of Statistical Planning and Inference, 141(6), 21562173.
Shin, J., Rinaldo, A., & Wasserman, L. (2019). Predictive clustering. arXiv preprint arXiv:1903.08125.
Examples
data < toydata1[, 1:2]
icp.torus < icp.torus(data, model = "kmeans",
kmeansfitmethod = "general",
J = 4, concentration = 25)