Intrinsic dimension estimation algorithms try to estimate the rank/dimension of lowdimensional structure that is embedded in highdimensional space. 


ID Estimation with Convergence Rate of Ustatistic on Manifold 

Boxcounting Dimension 

Intrinsic Dimension Estimation via Clustering 

Correlation Dimension 

Intrinsic Dimensionality Estimation with DANCo 

Intrinsic Dimension Estimation based on Manifold Assumption and Graph Distance 

Intrinsic Dimension Estimation with Incising Ball 

ManifoldAdaptive Dimension Estimation 

MiNDkl 

MINDml 

Maximum Likelihood Esimation with Poisson Process 

Maximum Likelihood Esimation with Poisson Process and Bias Correction 

Intrinsic Dimension Estimation with NearNeighbor Information 

NearNeighbor Information with Bias Correction 

Intrinsic Dimension Estimation using Packing Numbers 

PCA Thresholding with Accumulated Variance 

Intrinsic Dimension Estimation by a Minimal Neighborhood Information 

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. 

(21) Feature Selection 

Constraint Score 

Constraint Score using Spectral Graph 

DiversityInduced SelfRepresentation 

Elastic Net Regularization 

Forward Orthogonal Search by Maximizing the Overall Dependency 

Fisher Score 

Least Absolute Shrinkage and Selection Operator 

Laplacian Score 

Locality Sensitive Discriminant Feature 

Locality Sensitive Laplacian Score 

Locality and Similarity Preserving Embedding 

MultiCluster Feature Selection 

Mutual Information for Selecting Features 

Nonconvex Regularized SelfRepresentation 

Principal Feature Analysis 

Feature Selection using PCA and Procrustes Analysis 

Regularized SelfRepresentation 

Supervised Spectral Feature Selection 

Unsupervised Spectral Feature Selection 

Structure Preserving Unsupervised Feature Selection 

Unsupervised Discriminative Features Selection 

Unsupervised Graphbased Feature Selection 

Uncorrelated WorstCase Discriminative Feature Selection 

WorstCase Discriminative Feature Selection 

(22) Linear Projection 

Adaptive Dimension Reduction 

Adaptive Maximum Margin Criterion 

Average Neighborhood Margin Maximization 

Adaptive Subspace Iteration 

Bayesian Principal Component Analysis 

Canonical Correlation Analysis 

Complete Neighborhood Preserving Embedding 

Collaborative Representationbased Projection 

DoubleAdjacency Graphsbased Discriminant Neighborhood Embedding 

Discriminant Neighborhood Embedding 

Discriminative Sparsity Preserving Projection 

Exponential Local Discriminant Embedding 

Enhanced Locality Preserving Projection (2013) 

Extended Supervised Locality Preserving Projection 

Extended Locality Preserving Projection 

Exploratory Factor Analysis 

Feature Subset Selection using ExpectationMaximization 

Independent Component Analysis 

Isometric Projection 

KernelWeighted Maximum Variance Projection 

KernelWeighted Unsupervised Discriminant Projection 

Linear Discriminant Analysis 

Combination of LDA and Kmeans 

Local Discriminant Embedding 

Locally Discriminating Projection 

Locally Linear Embedded Eigenspace Analysis 

Local Fisher Discriminant Analysis 

Local Learning Projections 

Linear Local Tangent Space Alignment 

Landmark Multidimensional Scaling 

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

Locality Pursuit Embedding 

Locality Preserving Fisher Discriminant Analysis 

LocalityPreserved Maximum Information Projection 

Locality Preserving Projection 

Linear Quadratic Mutual Information 

Locality Sensitive Discriminant Analysis 

Localized Sliced Inverse Regression 

Local Similarity Preserving Projection 

(Classical) Multidimensional Scaling 

Marginal Fisher Analysis 

Maximal Local Interclass Embedding 

Maximum Margin Criterion 

Maximum Margin Projection 

Multiple Maximum Scatter Difference 

Modified Orthogonal Discriminant Projection 

Maximum Scatter Difference 

Maximum Variance Projection 

Nonnegative Orthogonal Locality Preserving Projection 

Nonnegative Orthogonal Neighborhood Preserving Projections 

Nonnegative Principal Component Analysis 

Neighborhood Preserving Embedding 

Orthogonal Discriminant Projection 

Orthogonal Linear Discriminant Analysis 

Orthogonal Locality Preserving Projection 

Orthogonal Neighborhood Preserving Projections 

Orthogonal Partial Least Squares 

Principal Component Analysis 

ParameterFree Locality Preserving Projection 

Partial Least Squares 

Probabilistic Principal Component Analysis 

Regularized Linear Discriminant Analysis 

Random Projection 

Robust Principal Component Analysis via Geometric Median 

Regularized Sliced Inverse Regression 

SemiSupervised Adaptive Maximum Margin Criterion 

Sliced Average Variance Estimation 

SemiSupervised Discriminant Analysis 

SampleDependent Locality Preserving Projection 

Sliced Inverse Regression 

Supervised Locality Pursuit Embedding 

Supervised Locality Preserving Projection 

Supervised Principal Component Analysis 

Sparse Principal Component Analysis 

Sparsity Preserving Projection 

SemiSupervised Locally Discriminant Projection 

Unsupervised Discriminant Projection 

Uncorrelated Linear Discriminant Analysis 



Bayesian Multidimensional Scaling 

Constrained Graph Embedding 

Conformal Isometric Feature Mapping 

Curvilinear Component Analysis 

Curvilinear Distance Analysis 

Diffusion Maps 

Dual Probabilistic Principal Component Analysis 

Distinguishing Variance Embedding 

FastMap 

Hyperbolic Distance Recovery and Approximation 

Interactive Document Map 

Improved Local Tangent Space Alignment 

Isometric Feature Mapping 

Isometric Stochastic Proximity Embedding 

Kernel Entropy Component Analysis 

Kernel Local Discriminant Embedding 

Kernel Local Fisher Discriminant Analysis 

Kernel Locality Sensitive Discriminant Analysis 

Kernel Marginal Fisher Analysis 

Kernel Maximum Margin Criterion 

Kernel Principal Component Analysis 

Kernel Quadratic Mutual Information 

Kernel SemiSupervised Discriminant Analysis 

Local Affine Multidimensional Projection 

Laplacian Eigenmaps 

Landmark Isometric Feature Mapping 

Locally Linear Embedding 

Local Linear Laplacian Eigenmaps 

Local Tangent Space Alignment 

Metric Multidimensional Scaling 

Minimum Volume Embedding 

Maximum Variance Unfolding / Semidefinite Embedding 

Nearest Neighbor Projection 

Potential of Heat Diffusion for Affinitybased Transition Embedding 

Piecewise Laplacianbased Projection (PLP) 

Robust Euclidean Embedding 

Robust Principal Component Analysis 

Sammon Mapping 

Stochastic Neighbor Embedding 

Stochastic Proximity Embedding 

Supervised Laplacian Eigenmaps 

Spectral Multidimensional Scaling 

tdistributed Stochastic Neighbor Embedding 



OOS : Linear Projection 



Generate modelbased samples 

Construct NearestNeighborhood Graph 

Build a centered kernel matrix K 

Show the number of functions for Rdimtools. 

Preprocessing the data 

Find shortest path using FloydWarshall algorithm 



Load Iris data 

Load USPS handwritten digits data 