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Dimensionality Reduction and Feature Extraction

PCA, factor analysis, feature selection, feature extraction, and more

Feature transformation techniques reduce the dimensionality in the data by transforming data into new features. Feature selection techniques are preferable when transformation of variables is not possible, e.g., when there are categorical variables in the data. For a feature selection technique that is specifically suitable for least-squares fitting, see Stepwise Regression.


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fscncaFeature selection using neighborhood component analysis for classification
fsrncaFeature selection using neighborhood component analysis for regression
sequentialfsSequential feature selection
relieffRank importance of predictors using ReliefF or RReliefF algorithm
ricaFeature extraction by using reconstruction ICA
sparsefiltFeature extraction by using sparse filtering
transformTransform predictors into extracted features
tsnet-Distributed Stochastic Neighbor Embedding
barttestBartlett’s test
canoncorrCanonical correlation
pcaPrincipal component analysis of raw data
pcacovPrincipal component analysis on covariance matrix
pcaresResiduals from principal component analysis
ppcaProbabilistic principal component analysis
factoranFactor analysis
rotatefactorsRotate factor loadings
nnmfNonnegative matrix factorization
cmdscaleClassical multidimensional scaling
mahalMahalanobis distance
mdscaleNonclassical multidimensional scaling
pdistPairwise distance between pairs of observations
squareformFormat distance matrix
procrustesProcrustes analysis


FeatureSelectionNCAClassificationFeature selection for classification using neighborhood component analysis (NCA)
FeatureSelectionNCARegressionFeature selection for regression using neighborhood component analysis (NCA)


ReconstructionICAFeature extraction by reconstruction ICA
SparseFilteringFeature extraction by sparse filtering


Feature Selection

Feature Selection

Learn about feature selection algorithms, such as sequential feature selection.

Neighborhood Component Analysis (NCA) Feature Selection

Neighborhood component analysis (NCA) is a non-parametric and embedded method for selecting features with the goal of maximizing prediction accuracy of regression and classification algorithms.

Selecting Features for Classifying High-dimensional Data

This example shows how to select features for classifying high-dimensional data.

Feature Extraction

Feature Extraction

Feature extraction is a set of methods to extract high-level features from data.

Feature Extraction Workflow

This example shows a complete workflow for feature extraction from image data.

Extract Mixed Signals

This example shows how to use rica to disentangle mixed audio signals.

t-SNE Multidimensional Visualization


t-SNE is a method for visualizing high-dimensional data by nonlinear reduction to two or three dimensions, while preserving some features of the original data.

Visualize High-Dimensional Data Using t-SNE

This example shows how t-SNE creates a useful low-dimensional embedding of high-dimensional data.

tsne Settings

This example shows the effects of various tsne settings.

t-SNE Output Function

Output function description and example for t-SNE.

PCA and Canonical Correlation

Principal Component Analysis (PCA)

Principal Component Analysis reduces the dimensionality of data by replacing several correlated variables with a new set of variables that are linear combinations of the original variables.

Analyze Quality of Life in U.S. Cities Using PCA

Perform a weighted principal components analysis and interpret the results.

Partial Least Squares Regression and Principal Components Regression

This example shows how to apply Partial Least Squares Regression (PLSR) and Principal Components Regression (PCR), and discusses the effectiveness of the two methods.

Fitting an Orthogonal Regression Using Principal Components Analysis

This example shows how to use Principal Components Analysis (PCA) to fit a linear regression.

Factor Analysis

Factor Analysis

Factor analysis is a way to fit a model to multivariate data to estimate interdependence of measured variables on a smaller number of unobserved (latent) factors.

Analyze Stock Prices Using Factor Analysis

Use factor analysis to investigate whether companies within the same sector experience similar week-to-week changes in stock prices.

Perform Factor Analysis on Exam Grades

This example shows how to perform factor analysis using Statistics and Machine Learning Toolbox™.

Nonnegative Matrix Factorization

Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a dimension-reduction technique based on a low-rank approximation of the feature space.

Perform Nonnegative Matrix Factorization

Perform nonnegative matrix factorization using the multiplicative and alternating least-squares algorithms.

Multidimensional Scaling

Multidimensional Scaling

Multidimensional scaling allows you to visualize how near points are to each other for many kinds of distance or dissimilarity metrics and can produce a representation of data in a small number of dimensions.

Classical Multidimensional Scaling

Use cmdscale to perform classical (metric) multidimensional scaling, also known as principal coordinates analysis.

Classical Multidimensional Scaling Applied to Nonspatial Distances

This example shows how to perform classical multidimensional scaling using the cmdscale function in Statistics and Machine Learning Toolbox™.

Nonclassical Multidimensional Scaling

This example shows how to visualize dissimilarity data using nonclassical forms of multidimensional scaling (MDS).

Nonclassical and Nonmetric Multidimensional Scaling

Perform nonclassical multidimensional scaling using mdscale.

Procrustes Analysis

Procrustes Analysis

Procrustes analysis minimizes the differences in location between compared landmark data using the best shape-preserving Euclidian transformations

Compare Handwritten Shapes Using Procrustes Analysis

Use Procrustes analysis to compare two handwritten numerals.