ProjectionPursuitClustering: Cluster Identification using Projection Pursuit as described...

In FCPS: Fundamental Clustering Problems Suite

Cluster Identification using Projection Pursuit as described in [Hofmeyr/Pavlidis, 2019].

Description

Summarizes recent projection pursuit methods for clustering based on [Hofmeyr/Pavlidis, 2015], [Hofmeyr, 2016] and [Pavlidis et al., 2016] .

Usage

ProjectionPursuitClustering(Data,ClusterNo,Type="MinimumDensity",

PlotIt=FALSE,PlotSolution=FALSE,...)

Arguments

Data	[1:n,1:d] matrix of dataset to be clustered. It consists of n cases of d-dimensional data points. Every case has d attributes, variables or features.
ClusterNo	A number k which defines k different clusters to be built by the algorithm.
Type	Either MinimumDensity[Pavlidis et al., 2016] MaximumClusterbility[Hofmeyr/Pavlidis, 2015]], or NormalisedCut [Hofmeyr, 2016] or KernelPCA [Hofmeyr/Pavlidis, 2019].
PlotIt	Default: FALSE, if TRUE plots the first three dimensions of the dataset with colored three-dimensional data points defined by the clustering stored in Cls
PlotSolution	Plots the partioning solution as a tree as described in
...	Further arguments to be set for the clustering algorithm, if not set, default arguments are used.

Details

The details of the options for projection pursuit and partioning of data are defined in [Hofmeyr/Pavlidis, 2019].

"KernelPCA" uses additionally the package kernlab and is implemented as given in the fifth example on page 21, section "extension" of [Hofmeyr/Pavlidis, 2019].

The first idea of using non-PCA projections for clustering was published by [Bock, 1987] as an definition. However, to the knowledge of the author it was not applied to any data. The first systematic comparison to Projection-Pursuit Methods ProjectionPursuitClustering and AutomaticProjectionBasedClustering can be found in [Thrun/Ultsch, 2018]. For PCA-based clustering methods please see TandemClustering

Value

List of

Cls	[1:n] numerical vector with n numbers defining the classification as the main output of the clustering algorithm. It has k unique numbers representing the arbitrary labels of the clustering. Points which cannot be assigned to a cluster will be reported with 0.
Object	Object defined by clustering algorithm as the other output of this algorithm

Author(s)

Michael Thrun

References

[Hofmeyr/Pavlidis, 2015] Hofmeyr, D., & Pavlidis, N.: Maximum clusterability divisive clustering, Proc. 2015 IEEE Symposium Series on Computational Intelligence, pp. 780-786, IEEE, 2015.

[Hofmeyr/Pavlidis, 2019] Hofmeyr, D., & Pavlidis, N.: PPCI: an R Package for Cluster Identification using Projection Pursuit, The R Journal, 2019.

[Hofmeyr, 2016] Hofmeyr, D. P.: Clustering by minimum cut hyperplanes, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 39(8), pp. 1547-1560. 2016.

[Pavlidis et al., 2016] Pavlidis, N. G., Hofmeyr, D. P., & Tasoulis, S. K.: Minimum density hyperplanes, The Journal of Machine Learning Research, Vol. 17(1), pp. 5414-5446. 2016.

[Thrun/Ultsch, 2018] Thrun, M. C., & Ultsch, A.: Using Projection based Clustering to Find Distance and Density based Clusters in High-Dimensional Data, Journal of Classification, Vol. in revision, 2018.

[Bock, 1987] Bock, H.: On the interface between cluster analysis, principal component analysis, and multidimensional scaling, Multivariate statistical modeling and data analysis, (pp. 17-34), Springer, 1987.

Examples

data('Hepta')
out=ProjectionPursuitClustering(Hepta$Data,ClusterNo=7,PlotIt=FALSE)

FCPS documentation built on Oct. 19, 2023, 5:06 p.m.