ProjectionBasedClustering (version 1.2.1)

CCA: Curvilinear Component Analysis (CCA)

Description

CCA Projects data vectors using Curvilinear Component Analysis [Demartines/Herault, 1995],[Demartines/Herault, 1997].

Unknown values (NaN's) in the data: projections of vectors with unknown components tend to drift towards the center of the projection distribution. Projections of totally unknown vectors are set to unknown (NaN).

Usage

CCA(DataOrDistances,Epochs,OutputDimension=2,method='euclidean',
alpha0 = 0.5, lambda0,PlotIt=FALSE,Cls)

Value

A n by OutputDimension matrix containing coordinates of the projected points.

Arguments

DataOrDistances

Numerical matrix defined as either

Data, i.e., [1:n,1:d], nonsymmetric, and consists of n cases of d-dimensional data points with every case having d attributes, variables or features,

or

Distances, i.e.,[1:n,1:n], symmetric and consists of n cases, e.g., as.matrix(dist(Data,method))

Epochs

Number of eppochs (scalar), i.e, training length

OutputDimension

Number of dimensions in the Outputspace, default=2

method

method specified by distance string. One of: 'euclidean','cityblock=manhatten','cosine','chebychev','jaccard','minkowski','manhattan','binary'

alpha0

(scalar) initial step size, 0.5 by default

lambda0

(scalar) initial radius of influence, 3*max(std(D)) by default

PlotIt

Default: FALSE, If TRUE: Plots the projection as a 2d visualization. OutputDimension>2: only the first two dimensions will be shown

Cls

[1:n,1] Optional,: only relevant if PlotIt=TRUE. Numeric vector, given Classification in numbers: every element is the cluster number of a certain corresponding element of data.

Author

Florian Lerch

Details

An short overview of different types of projection methods can be found in [Thrun, 2018, p.42, Fig. 4.1] (tools:::Rd_expr_doi("10.1007/978-3-658-20540-9")).

References

[Demartines/Herault, 1997] Demartines, P., & Herault, J.: Curvilinear component analysis: A self-organizing neural network for nonlinear mapping of data sets, IEEE Transactions on Neural Networks, Vol. 8(1), pp. 148-154. 1997.

[Demartines/Herault, 1995] Demartines, P., & Herault, J.: CCA:" Curvilinear component analysis", Proc. 15 Colloque sur le traitement du signal et des images, Vol. 199, GRETSI, Groupe d'Etudes du Traitement du Signal et des Images, France 18-21 September, 1995.

Examples

data('Hepta')
Data=Hepta$Data

Proj=CCA(Data,Epochs=20)

if (FALSE) {
PlotProjectedPoints(Proj$ProjectedPoints,Hepta$Cls)
}