Rdimtools (version 1.0.0)

Rdimtools: Dimension Reduction and Estimation Methods

Description

Rdimtools is an R suite of a number of dimension reduction and estimation methods implemented using RcppArmadillo for efficient computations. Please see the section below for the complete composition of this package and what we can provide in a unifying interface across many methods.

Composition of the package

The package consists of following families of functions whose names start with do., est., and aux. for performing dimension reduction/manifold learning, estimating intrinsic dimension, and some efficient implementations of other useful methods respectively.

(1) <code>do.</code> family for dimension reduction algorithms

do. functions are for dimension reduction (or, manifold learning) methods. A simple taxonomy of the methods would be to categorize based on the linearity of embedding mappings. In the table below, TYPE represents whether it is supervised (S), semisupervised (SS), or unsupervised (U).

For linear methods, we have

FUNCTION	TYPE	ALGORITHM
do.adr	U	Adaptive Dimension Reduction
do.ammc	S	Adaptive Maximum Margin Criterion
do.anmm	S	Average Neighborhood Margin Maximization
do.asi	U	Adaptive Subspace Iteration
do.bpca	U	Bayesian Principal Component Analysis
do.cca	S	Canonical Correlation Analysis
do.cnpe	U	Complete Neighborhood Preserving Embedding
do.crp	U	Collaborative Representation-based Projection
do.cscore	S	Constraint Score
do.cscoreg	S	Constraint Score using Spectral Graph
do.dagdne	S	Double-Adjacency Graphs-based Discriminant Neighborhood Embedding
do.dne	S	Discriminant Neighborhood Embedding
do.disr	U	Diversity-Induced Self-Representation
do.dspp	S	Discriminative Sparsity Preserving Projection
do.elde	S	Exponential Local Discriminant Embedding
do.elpp2	U	Enhanced Locality Preserving Projection (2013)
do.enet	S	Elastic Net Regularization
do.eslpp	S	Extended Supervised Locality Preserving Projection
do.extlpp	U	Extended Locality Preserving Projection
do.fa	U	(Exploratory) Factor Analysis
do.fscore	S	Fisher Score
do.fssem	U	Feature Subset Selection using Expectation-Maximization
do.ica	U	Independent Component Analysis
do.isoproj	U	Isometric Projection
do.kmvp	S	Kernel-Weighted Maximum Variance Projection
do.kudp	U	Kernel-Weighted Unsupervised Discriminant Projection
do.lasso	S	Least Absolute Shrinkage and Selection Operator
do.lda	S	Linear Discriminant Analysis
do.ldakm	U	Combination of LDA and K-means
do.lde	S	Local Discriminant Embedding
do.ldp	S	Locally Discriminating Projection
do.lea	U	Locally Linear Embedded Eigenspace Analysis
do.lfda	S	Local Fisher Discriminant Analysis
do.llp	U	Local Learning Projections
do.lltsa	U	Linear Local Tangent Space Alignment
do.lmds	U	Landmark Multidimensional Scaling
do.lpca	U	Locally Principal Component Analysis
do.lpe	U	Locality Pursuit Embedding
do.lpfda	S	Locality Preserving Fisher Discriminant Analysis
do.lpmip	U	Locality-Preserved Maximum Information Projection
do.lpp	U	Locality Preserving Projection
do.lqmi	S	Linear Quadratic Mutual Information
do.lscore	U	Laplacian Score
do.lsda	S	Locality Sensitive Discriminant Analysis
do.lsdf	SS	Locality Sensitive Discriminant Feature
do.lsir	S	Localized Sliced Inverse Regression
do.lspe	U	Locality and Similarity Preserving Embedding
do.lspp	S	Local Similarity Preserving Projection
do.mcfs	U	Multi-Cluster Feature Selection
do.mds	U	(Metric) Multidimensional Scaling
do.mfa	S	Marginal Fisher Analysis
do.mlie	S	Maximal Local Interclass Embedding
do.mmc	S	Maximum Margin Criterion
do.mmp	SS	Maximum Margin Projection
do.mmsd	S	Multiple Maximum Scatter Difference
do.modp	S	Modified Orthogonal Discriminant Projection
do.msd	S	Maximum Scatter Difference
do.mvp	S	Maximum Variance Projection
do.nolpp	U	Nonnegative Orthogonal Locality Preserving Projection
do.nonpp	U	Nonnegative Orthogonal Neighborhood Preserving Projections
do.npca	U	Nonnegative Principal Component Analysis
do.npe	U	Neighborhood Preserving Embedding
do.nrsr	U	Non-convex Regularized Self-Representation
do.odp	S	Orthogonal Discriminant Projection
do.olda	S	Orthogonal Linear Discriminant Analysis
do.olpp	U	Orthogonal Locality Preserving Projection
do.onpp	U	Orthogonal Neighborhood Preserving Projections
do.opls	S	Orthogonal Partial Least Squares
do.pca	U	Principal Component Analysis
do.pflpp	U	Parameter-Free Locality Preserving Projection
do.pls	S	Partial Least Squares
do.ppca	U	Probabilistic Principal Component Analysis
do.rlda	S	Regularized Linear Discriminant Analysis
do.rndproj	U	Random Projection
do.rpcag	U	Robust Principal Component Analysis via Geometric Median
do.rsir	S	Regularized Sliced Inverse Regression
do.rsr	U	Regularized Self-Representation
do.sammc	SS	Semi-Supervised Adaptive Maximum Margin Criterion
do.save	S	Sliced Average Variance Estimation
do.sda	SS	Semi-Supervised Discriminant Analysis
do.sdlpp	U	Sample-Dependent Locality Preserving Projection
do.sir	S	Sliced Inverse Regression
do.slpe	S	Supervised Locality Pursuit Embedding
do.slpp	S	Supervised Locality Preserving Projection
do.spc	S	Supervised Principal Component Analysis
do.spca	U	Sparse Principal Component Analysis
do.specs	S	Supervised Spectral Feature Selection
do.specu	U	Unsupervised Spectral Feature Selection
do.spp	U	Sparsity Preserving Projection
do.spufs	U	Structure Preserving Unsupervised Feature Selection
do.ssldp	SS	Semi-Supervised Locally Discriminant Projection
do.udfs	U	Unsupervised Discriminative Features Selection
do.udp	U	Unsupervised Discriminant Projection

Also, we have nonlinear methods implemented

FUNCTION	TYPE	ALGORITHM
do.bmds	U	Bayesian Multidimensional Scaling
do.cge	SS	Constrained Graph Embedding
do.cisomap	U	Conformal Isometric Feature Mapping
do.crca	U	Curvilinear Component Analysis
do.crda	U	Curvilinear Distance Analysis
do.dm	U	Diffusion Maps
do.dve	U	Distinguishing Variance Embedding
do.fastmap	U	FastMap
do.idmap	U	Interactive Document Map
do.iltsa	U	Improved Local Tangent Space Alignment
do.isomap	U	Isometric Feature Mapping
do.ispe	U	Isometric Stochastic Proximity Embedding
do.keca	U	Kernel Entropy Component Analysis
do.klde	S	Kernel Local Discriminant Embedding
do.klfda	S	Kernel Local Fisher Discriminant Analysis
do.klsda	S	Kernel Locality Sensitive Discriminant Analysis
do.kmfa	S	Kernel Marginal Fisher Analysis
do.kmmc	S	Kernel Maximium Margin Criterion
do.kpca	U	Kernel Principal Component Analysis
do.kqmi	S	Kernel Quadratic Mutual Information
do.ksda	SS	Kernel Semi-Supervised Discriminant Analysis
do.lamp	U	Local Affine Multidimensional Scaling
do.lapeig	U	Laplacian Eigenmaps
do.lisomap	U	Landmark Isometric Feature Mapping
do.lle	U	Locally Linear Embedding
do.llle	U	Local Linear Laplacian Eigenmaps
do.ltsa	U	Local Tangent Space Alignment
do.mve	U	Minimum Volume Embedding
do.mvu	U	Maximum Variance Unfolding / Semidefinite Embedding
do.nnp	U	Nearest Neighbor Projection
do.plp	U	Piecewise Laplacian Projection
do.ree	U	Robust Euclidean Embedding
do.rpca	U	Robust Principal Component Analysis
do.sammon	U	Sammon Mapping
do.sne	U	Stochastic Neighbor Embedding
do.spe	U	Stochastic Proximity Embedding
do.splapeig	S	Supervised Laplacian Eigenmaps
do.spmds	U	Spectral Multidimensional Scaling

(2) <code>est.</code> family for intrinsic dimension estimation algorithms

est. family of functions include,

FUNCTION	TYPE	ALGORITHM
est.boxcount	G	Box-Counting Dimension
est.clustering	G	Clustering-based Estimation
est.correlation	G	Correlation Dimension
est.danco	G	Dimensionality from Angle and Norm Concentration
est.made	G/P	Manifold-Adaptive Dimension Estimation
est.gdistnn	G/P	Graph Distance based on Manifold Assummption
est.mindkl	G	Minimum Neighbor Distance with Kullback Leibler Divergence
est.mindml	G	Minimum Neighbor Distance with Maximum Likelihood
est.mle1	G	MLE using Poisson Process
est.mle2	G	MLE using Poisson Process with Bias Correction
est.nearneighbor1	G	Near-Neighbor Information
est.nearneighbor2	G	Near-Neighbor Information with Bias Correction
est.incisingball	G	Estimation using Incising Ball
est.packing	G	Estimation using Packing Numbers
est.pcathr	G	PCA Thresholding with Accumulated Variance
est.twonn	G	Minimal Neighborhood Information

where the taxonomy is of global(G) or pointwise(P). Global methods return a single estimated dimension of the data manifold, whereas Pointwise methods return locally estimated intrinsic dimension at each point.

(3) <code>oos.</code> family for out-of-sample predictions

If the original dimension reduction method was linear-type, then you could use oos.linear function.

FUNCTION

ALGORITHM

Regardless of the types of previous manifold learning methods, belows are general out-of-sample methods.

FUNCTION

ALGORITHM

(4) <code>aux.</code> functions

Some auxiliary functions (aux.) are also provided,

FUNCTION	DESCRIPTION
aux.gensamples	generates samples from predefined shapes
aux.graphnbd	builds a neighborhood graph given certain criteria
aux.kernelcov	computes a centered gram matrix with 20 kernels supported
aux.preprocess	performs preprocessing of centering, decorrelating, or whitening
aux.shortestpath	Floyd-Warshall algorithm (it's Fast!)