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Dimensionality Reduction

PCA, factor analysis, nonnegative matrix factorization, sequential feature selection, 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.


FeatureSelectionNCAClassification Feature selection using NCA for classification
FeatureSelectionNCARegression Feature selection for regression using neighborhood component analysis (NCA)


fscnca Feature selection using neighborhood component analysis for classification
fsrnca Feature selection using neighborhood component analysis for regression
sequentialfs Sequential feature selection
relieff Importance of attributes (predictors) using ReliefF algorithm
barttest Bartlett's test
canoncorr Canonical correlation
pca Principal component analysis of raw data
pcacov Principal component analysis on covariance matrix
pcares Residuals from principal component analysis
ppca Probabilistic principal component analysis
factoran Factor analysis
rotatefactors Rotate factor loadings
nnmf Nonnegative matrix factorization
cmdscale Classical multidimensional scaling
mahal Mahalanobis distance
mdscale Nonclassical multidimensional scaling
pdist Pairwise distance between pairs of objects
squareform Format distance matrix
procrustes Procrustes analysis

Examples and How To

Robust Feature Selection Using NCA for Regression

Perform feature selection that is robust to outliers using a custom robust loss function in NCA.

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.

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 Nonnegative Matrix Factorization

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

Classical Multidimensional Scaling

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

Nonclassical and Nonmetric Multidimensional Scaling

Perform nonclassical multidimensional scaling using mdscale.

Compare Handwritten Shapes Using Procrustes Analysis

Use Procrustes analysis to compare two handwritten numerals.


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.

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.

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.

Nonnegative Matrix Factorization

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

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.

Procrustes Analysis

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

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