ProjectionBasedClustering (version 1.2.1)

Isomap: Isomap

Description

Isomap procetion as introduced in 2000 by Tenenbaum, de Silva and Langford

Even with a manifold structure, the sampling must be even and dense so that dissimilarities along a manifold are shorter than across the folds. If data do not have such a manifold structure, the results are very sensitive to parameter values.

Usage

Isomap(Distances,k,OutputDimension=2,PlotIt=FALSE,Cls)

Value

ProjectedPoints[1:n,OutputDimension] n by OutputDimension matrix containing coordinates of the Projection: A matrix of the fitted configuration..

Arguments

Distances

Symmetric [1:n,1:n] distance matrix, e.g. as.matrix(dist(Data,method))

k

number of k nearest neighbors, if the data is fragmented choose an higher k

OutputDimension

Number of dimensions in the output space, default = 2

PlotIt

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

Cls

Optional and 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

Michael Thrun

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")).

Examples

data('Hepta')
Data=Hepta$Data

Proj=Isomap(as.matrix(dist(Data)),k=7)

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