elpigraph.computeElasticPrincipalCurve

elpigraph.computeElasticPrincipalCurve(X, NumNodes, NumEdges=inf, InitNodes=3, Lambda=0.01, Mu=0.1, GrammarOptimization=False, MaxSteps=inf, GrammarOrder=['Grow', 'Shrink'], MaxNumberOfIterations=10, TrimmingRadius=inf, eps=0.01, Do_PCA=True, InitNodePositions=None, AdjustVect=None, ElasticMatrix=None, InitEdges=None, CenterData=True, ComputeMSEP=True, verbose=False, ShowTimer=False, ReduceDimension=None, n_cores=1, MinParOp=20, nReps=1, Subsets=[], ProbPoint=1, Mode=1, FinalEnergy='Base', alpha=0, beta=0, Configuration='Line', ICOver=None, DensityRadius=None, AvoidSolitary=False, EmbPointProb=1, PointWeights=None, SampleIC=True, AvoidResampling=True, AdjustElasticMatrix=None, AdjustElasticMatrix_Initial=None, Lambda_Initial=None, Mu_Initial=None, DisplayWarnings=False, StoreGraphEvolution=False, GPU=False, FixNodesAtPoints=[], pseudotime=None, pseudotimeLambda=0.01, label=None, labelLambda=0.01, MaxNumberOfGraphCandidatesDict={'AddNode2Node': inf, 'BisectEdge': inf, 'RemoveNode': inf, 'ShrinkEdge': inf})

Construct a principal elastic curve

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

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

Lambda: real,

the lambda parameter used the compute the elastic energy

Mu: real,

the lambda parameter used the compute the elastic energy

InitNodes: integer,

number of points to include in the initial graph

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

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 None 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

nReps: integer,

number of replica of the construction

ProbPoint: real

between 0 and 1, probability of inclusing of a single point for each computation

Subsets: list

of column names (or column number). When specified a principal curve will be computed for each of the subsets specified.

NumEdges: integer,

the maximum nulber of edges

Mode: integer,

the energy computation mode

FastSolve: boolean,

should FastSolve be used when fitting the points to the data?

ClusType: string,

the type of cluster to use. It can gbe either “Sock” or “Fork”.

Currently fork clustering only works in Linux 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?

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

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.

AdjustElasticMatrix: function

a penalization function to adjust the elastic matrices after a configuration has been chosen (e.g., AdjustByConstant). If None (the default), no penalization will be used.

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.

AdjustElasticMatrix_Initial: function

a penalization function to adjust the elastic matrices of the initial configuration (e.g., AdjustByConstant). If None (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 None, 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 None, the value of Mu will be used. boolean, should parallel execution be performed on the sampling instead of the the grammar evaluations?

AvoidResampling: booleand,

should the sampling of initial conditions avoid reselecting the same points

(or points neighbors if DensityRadius is specified)? SampleIC: boolean,

should the initial configuration be considered on the sampled points when applicable?

Returns:

• 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