# Questions tagged [canonical-correlation]

Canonical correlation analysis (CCA) is a method to analyze correlations between two sets of variables. It finds linear combinations of variables in each set such that their correlation is maximal.

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### How to visualize what canonical correlation analysis does (in comparison to what principal component analysis does)?

Canonical correlation analysis (CCA) is a technique related to principal component analysis (PCA). While it is easy to teach PCA or linear regression using a scatter plot (see a few thousand examples ...
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### PCA, LDA, CCA, and PLS

How are PCA, LDA, CCA, and PLS related? They all seem "spectral" and linear algebraic and very well understood (say 50+ years of theory built around them). They are used for very different things (PCA ...
20k views

### What is the relationship between regression and linear discriminant analysis (LDA)?

Is there a relationship between regression and linear discriminant analysis (LDA)? What are their similarities and differences? Does it make any difference if there are two classes or more than two ...
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### How LDA, a classification technique, also serves as dimensionality reduction technique like PCA

In this article , the author links linear discriminant analysis (LDA) to principal component analysis (PCA). With my limited knowledge, I am not able to follow how LDA can be somewhat similar to PCA. ...
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### Canonical correlation analysis with rank correlation

Canonical correlation analysis (CCA) aims to maximize the usual Pearson product-moment correlation (i.e. linear correlation coefficient) of the linear combinations of the two data sets. Now, consider ...
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### Doing CCA vs. building a dependent variable with PCA and then doing regression

Given two multidimensional datasets, $X$ and $Y$, some people perform multivariable analysis by building a surrogate dependent variable using principal component analysis (PCA). That is, run PCA on $Y$...
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### Is CCA between two identical datasets equivalent to PCA on this dataset?

Reading Wikipedia about canonical correlation analysis (CCA) for two random vectors $X$ and $Y$, I was wondering if principal component anslysis (PCA) is the same as CCA when $X=Y$?
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### PCA is to CCA as ICA is to?

PCA looks for factors in data that maximize explained variance. Canonical correlation analysis (CCA), as far as I understand, is like an PCA but looks for a factors that maximize cross covariance ...
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### Difference between canonical correpondence analysis and canonical correlation analysis

I am bit confused between two terms Canonical Correpondence Analysis and Canonical Correlation Analysis. Are the two some how related or they are entirely different techniques? Do they point to ...
371 views

### Probabilistic models for partial least squares, reduced rank regression, and canonical correlation analysis?

This question results from the discussion following a previous question: What is the connection between partial least squares, reduced rank regression, and principal component regression? For ...
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### Correlation between principal components

I have two matrices a, b of dimensions (100x500), (100x15000) and I am trying to find associations between sets of variables in both matrices. When I perform principal component analysis on matrix a,...
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### CCA/KCCA for more than two views

Canonical Correlation Analysis (CCA) (and its kernel equivalent (KCCA)) can be used to find linear (nonlinear) relationships between two aligned multivariate datasets (or views). Is there a way to ...
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### How does CCA find a low-dimensional common subspace?

According to Wikipedia, canonical correlation analysis (CCA) finds pairs of canonical variables. CCA has also been used in many cases as dimensionality reduction tool to find low-dimensional subspaces....
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### Statistical significance in canonical correlation analysis

I do canonical correlation analysis between two multivariate datasets $X$ and $Y$. For each pair of canonical variates (x-y pair) I get the canonical correlation coefficient. How can I test its ...
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### Differences between linear and canonical discriminant analyses (LDA and CDA)

I'm using R to try and compare the results of variable chemical compositions, following on from an article I've read. In it, the authors used CDA to do something very similar to what I want to do, ...
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### Canonical Correlation Analysis for different data types

I have to do canonical correlation analysis between two multivariate datasets X and Y. One dataset contain numerical data and the other binary data. I would like to know what features are highly ...
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### How does Canonical Time Warping help in time alignment?

Canonical Time Warping is a state-of-the-art technique for time alignment. According to the original paper, it helps account for individual varieties when aligning sequences derived from different ...
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### Interpreting MANOVA and redundancy analysis of a canonical correlation analysis

I have done a canonical correlation analysis using the American Community Survey Dataset. The analysis is done between Ancestry and ...
510 views

### Books about model selection in ecology

I am an ecology student and have to deal with 10 or 20 field variables, including species frequencies. I need to screen out what variables are most important in the occurrence of a bird species. What ...
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### Using canonical correlation analysis (CCA) to find matches

I have a training dataset of images: X (Visual) and Y (Infrared). Each set has $300$ training examples. I extract feature ...
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### Canonical correlation analysis with a tiny example and dimensionals

I've tried reading many explanations of CCA, and I don't understand it. For example, on Wikipedia, it refers to two "vectors" $a$ and $b$ such that $\rho = \text{corr}(a^{\top} X, b^{\top} Y)$ is ...
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### Canonical Correlation analysis without raw data (algebra of CCA)

I want to run a Canonical Correlation (in R) but I don't have the original (raw) data. I have only the correlation matrix of all the variables. I have seen some ...
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### Recovering true data from many noisy samples with varying unknown amounts of noise

Input: $k$ vectors $x^1,\ldots,x^k \in \mathbb{R}^n$, where $x^i \sim \mathcal{N}(x,\mathbb{1} \cdot \sigma_i^2)$. Goal: approximate the vector $x$ as well as possible. The quality of approximation ...
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### Eigenvalues nearly all 1 in canonical correlation analysis

I ran a Canonical Correlation Analysis on about 845 cases with 1000 variables each. (It originally started with 1000 cases and 400 variables but by using a kernel I got a 1000x1000 matrix) As a ...
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### How to reduce dimensions of variable space w.r.t. single response variable? CCA?

My dataset is presence/absence (or relative abundance score) of 100 species on 5000 squares, and for each square I have ~100 environmental variables (many of them strongly correlated). I want to ...
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### Do products $AB$ and $BA$ of rectangular matrices contain the same information?

I have data measuring two events in space and in time. More precisely, I have two rectangular data matrices $A$ and $B$ which both have $20$ time rows and $1\text{M}$ space columns. I want to analyse ...
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### Help explain the “redundancy” of canonical correlation

I am reading a material about canonical correlation and it introduces a concept named "redundancy". I have been puzzled for one day but still could not get a understanding. The following is a screen ...
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### Get canonical loadings (i.e. scores) from weights in r package PMA

I want to perform regularized canonical correlation between two matrices with more variables than observations (same subjects), one of which is very large (~18000 columns). The only r package that ...
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### Objective function of canonical correlation analysis (CCA)

Given two vectors of random variables $X$ and $Y$, Canonical Correlation Analysis (CCA) finds the transformation matrices $A$ and $B$ so that $\operatorname{corr}(A_{1*} X, B_{1*} Y)$ is first maximal,...
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### correlation using a single transformation

I was presently working on Canonical Correlation Analysis which maximizes the correlation between two variables $X$ and $Y$ of two modalities in some transformed domain using transformations $T_1$ and ...
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### Dimensionality reduction technique similar to LDA when class labels are probabilistic

Given discrete class labels, say True and False, LDA (linear discriminant analysis) can be used to perform discriminant dimensionality reduction and attempt to find a subspace that best separates the ...
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### How to recognize similar environmental variables using multivariate analysis?

I am completely new to multivariate analyses and I need an advice how to get it applied to my data and which analyses to choose for which purpose. My dataset is presence/absence (or relative ...
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### Formulating Partial Least Squares as minimizing squared error

The book chapter linked below (see section 4.3.1) lists a few formulations of partial least squares (PLS). The first two make sense to me and seem standard: \underset{\mathbf{u}, \mathbf{v}}{\text{...