CCA {ProjectionBasedClustering}

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)

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.

Details

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

Value

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

Note

Only Transfered from matlab to R. Matlabversion: Contributed to SOM Toolbox 2.0, February 2nd, 2000 by Juha Vesanto.

You can use the standard Sheparddiagram or the better approach through the ShepardDensityScatter of the CRAN package DataVisualizations.

Author(s)

Florian Lerch

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)

## Not run: 
PlotProjectedPoints(Proj$ProjectedPoints,Hepta$Cls)

## End(Not run)