(1) Dimension Estimation

Intrinsic dimension estimation algorithms try to estimate the rank/dimension of low-dimensional structure that is embedded in high-dimensional space.

est.Ustat()

ID Estimation with Convergence Rate of U-statistic on Manifold

est.boxcount()

Box-counting Dimension

est.clustering()

Intrinsic Dimension Estimation via Clustering

est.correlation()

Correlation Dimension

est.danco()

Intrinsic Dimensionality Estimation with DANCo

est.gdistnn()

Intrinsic Dimension Estimation based on Manifold Assumption and Graph Distance

est.incisingball()

Intrinsic Dimension Estimation with Incising Ball

est.made()

Manifold-Adaptive Dimension Estimation

est.mindkl()

MiNDkl

est.mindml()

MINDml

est.mle1()

Maximum Likelihood Esimation with Poisson Process

est.mle2()

Maximum Likelihood Esimation with Poisson Process and Bias Correction

est.nearneighbor1()

Intrinsic Dimension Estimation with Near-Neighbor Information

est.nearneighbor2()

Near-Neighbor Information with Bias Correction

est.packing()

Intrinsic Dimension Estimation using Packing Numbers

est.pcathr()

PCA Thresholding with Accumulated Variance

est.twonn()

Intrinsic Dimension Estimation by a Minimal Neighborhood Information

(2) Linear Embedding

Although all linear methods are designed to find explicit projection matrix for embedding, we divide this part into two categories; feature selection to select a subset of variables to extract information at their own best measurements, and dimension reduction type to denote the rest.

(2-1) Feature Selection

do.cscore()

Constraint Score

do.cscoreg()

Constraint Score using Spectral Graph

do.disr()

Diversity-Induced Self-Representation

do.enet()

Elastic Net Regularization

do.fscore()

Fisher Score

do.lasso()

Least Absolute Shrinkage and Selection Operator

do.lscore()

Laplacian Score

do.lsdf()

Locality Sensitive Discriminant Feature

do.lsls()

Locality Sensitive Laplacian Score

do.lspe()

Locality and Similarity Preserving Embedding

do.mcfs()

Multi-Cluster Feature Selection

do.mifs()

Mutual Information for Selecting Features

do.nrsr()

Non-convex Regularized Self-Representation

do.procrustes()

Feature Selection using PCA and Procrustes Analysis

do.rsr()

Regularized Self-Representation

do.specs()

Supervised Spectral Feature Selection

do.specu()

Unsupervised Spectral Feature Selection

do.spufs()

Structure Preserving Unsupervised Feature Selection

do.udfs()

Unsupervised Discriminative Features Selection

do.ugfs()

Unsupervised Graph-based Feature Selection

do.uwdfs()

Uncorrelated Worst-Case Discriminative Feature Selection

do.wdfs()

Worst-Case Discriminative Feature Selection

(2-2) Linear Projection

do.adr()

Adaptive Dimension Reduction

do.ammc()

Adaptive Maximum Margin Criterion

do.anmm()

Average Neighborhood Margin Maximization

do.asi()

Adaptive Subspace Iteration

do.bpca()

Bayesian Principal Component Analysis

do.cca()

Canonical Correlation Analysis

do.cnpe()

Complete Neighborhood Preserving Embedding

do.crp()

Collaborative Representation-based Projection

do.dagdne()

Double-Adjacency Graphs-based Discriminant Neighborhood Embedding

do.dne()

Discriminant Neighborhood Embedding

do.dspp()

Discriminative Sparsity Preserving Projection

do.elde()

Exponential Local Discriminant Embedding

do.elpp2()

Enhanced Locality Preserving Projection (2013)

do.eslpp()

Extended Supervised Locality Preserving Projection

do.extlpp()

Extended Locality Preserving Projection

do.fa()

Exploratory Factor Analysis

do.fssem()

Feature Subset Selection using Expectation-Maximization

do.ica()

Independent Component Analysis

do.isoproj()

Isometric Projection

do.kmvp()

Kernel-Weighted Maximum Variance Projection

do.kudp()

Kernel-Weighted Unsupervised Discriminant Projection

do.lda()

Linear Discriminant Analysis

do.ldakm()

Combination of LDA and K-means

do.lde()

Local Discriminant Embedding

do.ldp()

Locally Discriminating Projection

do.lea()

Locally Linear Embedded Eigenspace Analysis

do.lfda()

Local Fisher Discriminant Analysis

do.llp()

Local Learning Projections

do.lltsa()

Linear Local Tangent Space Alignment

do.lmds()

Landmark Multidimensional Scaling

do.lpca2006()

Locally Principal Component Analysis by Yang et al. (2006)

do.lpe()

Locality Pursuit Embedding

do.lpfda()

Locality Preserving Fisher Discriminant Analysis

do.lpmip()

Locality-Preserved Maximum Information Projection

do.lpp()

Locality Preserving Projection

do.lqmi()

Linear Quadratic Mutual Information

do.lsda()

Locality Sensitive Discriminant Analysis

do.lsir()

Localized Sliced Inverse Regression

do.lspp()

Local Similarity Preserving Projection

do.mds()

(Classical) Multidimensional Scaling

do.mfa()

Marginal Fisher Analysis

do.mlie()

Maximal Local Interclass Embedding

do.mmc()

Maximum Margin Criterion

do.mmp()

Maximum Margin Projection

do.mmsd()

Multiple Maximum Scatter Difference

do.modp()

Modified Orthogonal Discriminant Projection

do.msd()

Maximum Scatter Difference

do.mvp()

Maximum Variance Projection

do.nolpp()

Nonnegative Orthogonal Locality Preserving Projection

do.nonpp()

Nonnegative Orthogonal Neighborhood Preserving Projections

do.npca()

Nonnegative Principal Component Analysis

do.npe()

Neighborhood Preserving Embedding

do.odp()

Orthogonal Discriminant Projection

do.olda()

Orthogonal Linear Discriminant Analysis

do.olpp()

Orthogonal Locality Preserving Projection

do.onpp()

Orthogonal Neighborhood Preserving Projections

do.opls()

Orthogonal Partial Least Squares

do.pca()

Principal Component Analysis

do.pflpp()

Parameter-Free Locality Preserving Projection

do.pls()

Partial Least Squares

do.ppca()

Probabilistic Principal Component Analysis

do.rlda()

Regularized Linear Discriminant Analysis

do.rndproj()

Random Projection

do.rpcag()

Robust Principal Component Analysis via Geometric Median

do.rsir()

Regularized Sliced Inverse Regression

do.sammc()

Semi-Supervised Adaptive Maximum Margin Criterion

do.save()

Sliced Average Variance Estimation

do.sda()

Semi-Supervised Discriminant Analysis

do.sdlpp()

Sample-Dependent Locality Preserving Projection

do.sir()

Sliced Inverse Regression

do.slpe()

Supervised Locality Pursuit Embedding

do.slpp()

Supervised Locality Preserving Projection

do.spc()

Supervised Principal Component Analysis

do.spca()

Sparse Principal Component Analysis

do.spp()

Sparsity Preserving Projection

do.ssldp()

Semi-Supervised Locally Discriminant Projection

do.udp()

Unsupervised Discriminant Projection

do.ulda()

Uncorrelated Linear Discriminant Analysis

(3) Nonlinear Embedding

do.bmds()

Bayesian Multidimensional Scaling

do.cge()

Constrained Graph Embedding

do.cisomap()

Conformal Isometric Feature Mapping

do.crca()

Curvilinear Component Analysis

do.crda()

Curvilinear Distance Analysis

do.dm()

Diffusion Maps

do.dve()

Distinguishing Variance Embedding

do.fastmap()

FastMap

do.idmap()

Interactive Document Map

do.iltsa()

Improved Local Tangent Space Alignment

do.isomap()

Isometric Feature Mapping

do.ispe()

Isometric Stochastic Proximity Embedding

do.keca()

Kernel Entropy Component Analysis

do.klde()

Kernel Local Discriminant Embedding

do.klfda()

Kernel Local Fisher Discriminant Analysis

do.klsda()

Kernel Locality Sensitive Discriminant Analysis

do.kmfa()

Kernel Marginal Fisher Analysis

do.kmmc()

Kernel Maximum Margin Criterion

do.kpca()

Kernel Principal Component Analysis

do.kqmi()

Kernel Quadratic Mutual Information

do.ksda()

Kernel Semi-Supervised Discriminant Analysis

do.lamp()

Local Affine Multidimensional Projection

do.lapeig()

Laplacian Eigenmaps

do.lisomap()

Landmark Isometric Feature Mapping

do.lle()

Locally Linear Embedding

do.llle()

Local Linear Laplacian Eigenmaps

do.ltsa()

Local Tangent Space Alignment

do.mmds()

Metric Multidimensional Scaling

do.mve()

Minimum Volume Embedding

do.mvu()

Maximum Variance Unfolding / Semidefinite Embedding

do.nnp()

Nearest Neighbor Projection

do.phate()

Potential of Heat Diffusion for Affinity-based Transition Embedding

do.plp()

Piecewise Laplacian-based Projection (PLP)

do.ree()

Robust Euclidean Embedding

do.rpca()

Robust Principal Component Analysis

do.sammon()

Sammon Mapping

do.sne()

Stochastic Neighbor Embedding

do.spe()

Stochastic Proximity Embedding

do.splapeig()

Supervised Laplacian Eigenmaps

do.spmds()

Spectral Multidimensional Scaling

do.tsne()

t-distributed Stochastic Neighbor Embedding

(4) Out-of-sample Prediction

oos.linproj()

OOS : Linear Projection

(5) Auxiliary Functions

aux.gensamples()

Generate model-based samples

aux.graphnbd()

Construct Nearest-Neighborhood Graph

aux.kernelcov()

Build a centered kernel matrix K

aux.pkgstat()

Show the number of functions for Rdimtools.

aux.preprocess()

Preprocessing the data

aux.shortestpath()

Find shortest path using Floyd-Warshall algorithm

(6) Data

iris

Load Iris data

usps

Load USPS handwritten digits data