Description Usage Arguments Value Examples
This function is a wrapper to the computeElasticPrincipalGraph function that construct the appropriate initial graph and grammars when increasing the nume number around the branching point
1 2 3 4 5 6 7 8 9 10 11 12 13 14  GrowLeaves(X, NumNodes, NumEdges = Inf, InitNodes = 2, Lambda = 0.01,
Mu = 0.1, InitNodePositions, InitEdges = NULL, ElasticMatrix = NULL,
MaxSteps = 100, MaxNumberOfIterations = 10, TrimmingRadius = Inf,
eps = 0.01, Do_PCA = TRUE, 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, AdjustElasticMatrix = NULL,
AdjustElasticMatrix.Initial = NULL, Lambda.Initial = NULL,
Mu.Initial = NULL, ...)

X 
numerical 2D matrix, the nbym matrix with the position of n mdimensional 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 
InitNodePositions 
numerical 2D matrix, the kbym matrix with k mdimensional positions of the nodes in the initial step 
InitEdges 
numerical 2D matrix, the eby2 matrix with e endpoints of the edges connecting the nodes 
ElasticMatrix 
numerical 2D matrix, the kbyk elastic matrix 
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? 
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 curve 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 curve. 
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 

SampleIC 
boolean, should the initial configuration be considered on the sampled points when applicable? 
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 list of principal graph strucutures containing the curves constructed during the different replica of the algorithm. If the number of replicas is larger than 1. The the final element of the list is the "average curve", which is constructed by fitting the coordinates of the nodes of the reconstructed curves
1 2 3 4 5 6 7 8 9 10 11 12 13 14  Elastic curve with different parameters
PG < computeElasticPrincipalCurve(X = tree_data, NumNodes = 30, InitNodes = 2, verbose = TRUE)
PG < computeElasticPrincipalCurve(X = circle_data, NumNodes = 30, InitNodes = 2, verbose = TRUE)
PG < computeElasticPrincipalCurve(X = tree_data, NumNodes = 30, InitNodes = 2, verbose = TRUE, Mu = 1, Lambda = .001)
PG < computeElasticPrincipalCurve(X = circle_data, NumNodes = 30, InitNodes = 2, verbose = TRUE, Mu = 1, Lambda = .001)
Bootstrapping the construction of the curve
PG < computeElasticPrincipalCurve(X = tree_data, NumNodes = 40, InitNodes = 2,
drawAccuracyComplexity = FALSE, drawPCAView = FALSE, drawEnergy = FALSE,
verbose = FALSE, nReps = 50, ProbPoint = .8)
PlotPG(X = tree_data, TargetPG = PG[[length(PG)]], BootPG = PG[1:(length(PG)1)])

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