computeElasticPrincipalCircle: Conscruct a princial elastic circle
In Albluca/ElPiGraph.R: Elastic principal graph construction

Description Usage Arguments Value Examples

This function is a wrapper to the computeElasticPrincipalGraph function that construct the appropriate initial graph and grammars when constructing a circle

computeElasticPrincipalCircle(X, NumNodes, NumEdges = Inf, InitNodes = 3,
  Lambda = 0.01, Mu = 0.1, MaxNumberOfIterations = 10,
  TrimmingRadius = Inf, eps = 0.01, Do_PCA = TRUE,
  InitNodePositions = NULL, InitEdges = NULL, ElasticMatrix = NULL,
  AdjustVect = NULL, CenterData = TRUE, ComputeMSEP = TRUE,
  verbose = FALSE, ShowTimer = FALSE, ReduceDimension = NULL,
  drawAccuracyComplexity = TRUE, drawPCAView = TRUE, drawEnergy = TRUE,
  n.cores = 1, MinParOP = 20, ClusType = "Sock", nReps = 1,
  Subsets = list(), ProbPoint = 1, Mode = 1, FinalEnergy = "Base",
  alpha = 0, beta = 0, FastSolve = FALSE, ICOver = NULL,
  DensityRadius = NULL, AvoidSolitary = FALSE, EmbPointProb = 1,
  ParallelRep = FALSE, SampleIC = TRUE, AvoidResampling = FALSE,
  AdjustElasticMatrix = NULL, AdjustElasticMatrix.Initial = NULL,
  Lambda.Initial = NULL, Mu.Initial = NULL, ...)

`X`	numerical 2D matrix, the n-by-m matrix with the position of n m-dimensional points
`NumNodes`	integer, the number of nodes of the principal graph
`NumEdges`	integer, the maximum nulber of edges
`InitNodes`	integer, number of points to include in the initial graph
`Lambda`	real, the lambda parameter used the compute the elastic energy
`Mu`	real, the lambda parameter used the compute the elastic energy
`MaxNumberOfIterations`	integer, maximum number of steps to embed the nodes in the data
`TrimmingRadius`	real, maximal distance of point from a node to affect its embedment
`eps`	real, minimal relative change in the position of the nodes to stop embedment
`Do_PCA`	boolean, should data and initial node positions be PCA trnasformed?
`InitNodePositions`	numerical 2D matrix, the k-by-m matrix with k m-dimensional positions of the nodes in the initial step
`InitEdges`	numerical 2D matrix, the e-by-2 matrix with e end-points of the edges connecting the nodes
`ElasticMatrix`	numerical 2D matrix, the k-by-k elastic matrix
`AdjustVect`	boolean vector keeping track of the nodes for which the elasticity parameters have been adjusted. When true for a node its elasticity parameters will not be adjusted.
`CenterData`	boolean, should data and initial node positions be centered?
`ComputeMSEP`	boolean, should MSEP be computed when building the report?
`verbose`	boolean, should debugging information be reported?
`ShowTimer`	boolean, should the time to construct the graph be computed and reported for each step?
`ReduceDimension`	integer vector, vector of principal components to retain when performing dimensionality reduction. If NULL all the components will be used
`drawAccuracyComplexity`	boolean, should the accuracy VS complexity plot be reported?
`drawPCAView`	boolean, should a 2D plot of the points and pricipal curve be dranw for the final configuration?
`drawEnergy`	boolean, should changes of evergy VS the number of nodes be reported?
`n.cores`	either an integer (indicating the number of cores to used for the creation of a cluster) or cluster structure returned, e.g., by makeCluster. If a cluster structure is used, all the nodes must contains X (this is done using clusterExport)
`MinParOP`	integer, the minimum number of operations to use parallel computation
`ClusType`	string, the type of cluster to use. It can gbe either "Sock" or "Fork". Currently fork clustering only works in Linux
`nReps`	integer, number of replica of the construction
`Subsets`	list of column names (or column number). When specified a principal circle will be computed for each of the subsets specified.
`ProbPoint`	real between 0 and 1, probability of inclusing of a single point for each computation
`Mode`	integer, the energy computation mode
`FinalEnergy`	string indicating the final elastic emergy associated with the configuration. Currently it can be "Base" or "Penalized"
`alpha`	positive numeric, the value of the alpha parameter of the penalized elastic energy
`beta`	positive numeric, the value of the beta parameter of the penalized elastic energy
`FastSolve`	boolean, should FastSolve be used when fitting the points to the data?
`ICOver`	string, initial condition overlap mode. This can be used to alter the default behaviour for the initial configuration of the principal circle
`DensityRadius`	numeric, the radius used to estimate local density. This need to be set when ICOver is equal to "Density"
`AvoidSolitary`	boolean, should configurations with "solitary nodes", i.e., nodes without associted points be discarded?
`EmbPointProb`	numeric between 0 and 1. If less than 1 point will be sampled at each iteration. EmbPointProb indicates the probability of using each points. This is an experimental feature, which may helps speeding up the computation if a large number of points is present.
`ParallelRep`	boolean, should parallel execution be performed on the sampling instead of the the grammar evaluations?
`SampleIC`	boolean, should the initial configuration be considered on the sampled points when applicable?
`AvoidResampling`	booleand, should the sampling of initial conditions avoid reselecting the same points (or points neighbors if DensityRadius is specified)?
`AdjustElasticMatrix`	a penalization function to adjust the elastic matrices after a configuration has been chosen (e.g., AdjustByConstant). If NULL (the default), no penalization will be used.
`AdjustElasticMatrix.Initial`	a penalization function to adjust the elastic matrices of the initial configuration (e.g., AdjustByConstant). If NULL (the default), no penalization will be used.
`Lambda.Initial`	real, the lambda parameter used the construct the elastic matrix associted with ther initial configuration if needed. If NULL, the value of Lambda will be used.
`Mu.Initial`	real, the mu parameter used the construct the elastic matrix associted with ther initial configuration if needed. If NULL, the value of Mu will be used.
`...`	optional parameter that will be passed to the AdjustElasticMatrix function

A named list

Elastic circle with different parameters
PG <- computeElasticPrincipalCircle(X = circle_data, NumNodes = 30, InitNodes = 3, verbose = TRUE)
PG <- computeElasticPrincipalCircle(X = circle_data, NumNodes = 30, InitNodes = 3, verbose = TRUE, Mu = 1, Lambda = .001)

Bootstrapping the construction of the circle
PG <- computeElasticPrincipalCircle(X = circle_data, NumNodes = 40, InitNodes = 3,
drawAccuracyComplexity = FALSE, drawPCAView = FALSE, drawEnergy = FALSE,
verbose = FALSE, nReps = 50, ProbPoint = .8)

PlotPG(X = circle_data, TargetPG = PG[[length(PG)]], BootPG = PG[1:(length(PG)-1)])