# Fast SVD and PCA

Version 1.3.0.0 (3.35 KB) by
Fast truncated SVD and PCA rectangular matrices
Updated 7 Jul 2014

Truncated Singular Value Decomposition (SVD) and Principal Component Analysis (PCA) that are much faster compared to using the Matlab svd and svds functions for rectangular matrices.
svdecon is a faster alternative to svd(X,'econ') for long or thin matrices.
svdsecon is a faster alternative to svds(X,k) for dense long or thin matrices where k << size(X,1) and size(X,2).
PCA versions of the two svd functions are also implemented.
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function [U,S,V] = svdecon(X)
function [U,S,V] = svdecon(X,k)

Input:
X : m x n matrix
k : gets the first k singular values (if k not given then k = min(m,n))

Output:
X = U*S*V'
U : m x k
S : k x k
V : n x k

Description:
svdecon(X) is equivalent to svd(X,'econ')
svdecon(X,k) is equivalent to svds(X,k) where k < min(m,n)
This is faster than svdsecon when k is not much smaller than min(m,n)

---

function [U,S,V] = svdsecon(X,k)

Input:
X : m x n matrix
k : gets the first k singular values, k << min(m,n)

Output:
X = U*S*V' approximately (up to k)
U : m x k
S : k x k
V : n x k

Description:
svdsecon(X,k) is equivalent to svds(X,k) where k < min(m,n)
This function is useful if k << min(m,n) (see doc eigs)

---

function [U,T,mu] = pcaecon(X,k)

Input:
X : m x n matrix
Each column of X is a feature vector
k : extracts the first k principal components

Output:
X = U*T approximately (up to k)
T = U'*X
U : m x k
T : k x n

Description:
Principal Component Analysis (PCA)
Requires that k < min(m,n)

---

function [U,T,mu] = pcasecon(X,k)

Input:
X : m x n matrix
Each column of X is a feature vector
k : extracts the first k principal components, k << min(m,n)

Output:
X = U*T approximately (up to k)
T = U'*X
U : m x k
T : k x n

Description:
Principal Component Analysis (PCA)
Requires that k < min(m,n)
This function is useful if k << min(m,n) (see doc eigs)

### Cite As

Vipin Vijayan (2024). Fast SVD and PCA (https://www.mathworks.com/matlabcentral/fileexchange/47132-fast-svd-and-pca), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2013a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux
##### Categories
Find more on Dimensionality Reduction and Feature Extraction in Help Center and MATLAB Answers

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Version Published Release Notes
1.3.0.0

Uses less memory now

1.2.0.0

Truncated

1.1.0.0

Title change

1.0.0.0