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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72
votes
4answers
22k views

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 ...
24
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4answers
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 ...
4
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1answer
3k views

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 ...
20
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1answer
11k views

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. ...
28
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1answer
7k views

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 ...
3
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1answer
1k views

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,...
5
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1answer
3k views

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 ...
4
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1answer
9k views

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 ...
7
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1answer
372 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 ...
3
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3answers
235 views

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 ...
3
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1answer
252 views

Relationship between coupled matrix factorization and CCA

Canonical Correlation Analysis (CCA) computes a low-dimensional shared embedding of two set of variables $X$ and $Y$ such that the correlations among the variables between the two sets is maximized. ...
2
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1answer
2k views

Interpreting Canonical Correspondence Analysis (CCA) Inertia - in Vegan

I am wanting to know if I can use the ratio of Constrained/Total Inertia in my CCA to describe 'The variability explained by my constraining variables'. I am asking because I've seen different ...
9
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1answer
2k views

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 $Y$...
5
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1answer
2k views

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....
4
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4answers
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 ...
4
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1answer
943 views

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 ...
3
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2answers
946 views

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 ...
4
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2answers
190 views

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 ...
3
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0answers
63 views

What is the test of significance for kernel canonical correlations?

I am trying to conduct a test of independence between two multivariate datasets. For canonical correlation, I have used Wilk’s lambda test. What should be the test statistics for kernel CCA. I believe ...
3
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0answers
76 views

Are there random matrix results like Marcenko-Pastur, but for CCA?

The Marcenko-Pastur law is about asymptotic distributions of eigenvalues. It starts from a simple null model (iid zero-mean Gaussian entries) and derives a distribution for the spectrum. In PCA, this ...
2
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0answers
83 views

how to explain canonical correlation to laymen?

Given two sets of variables and the objective of finding correlations among the variables in the two sets, is there any simple examples or explanation, for a group of biologists knowing only basic ...
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0answers
96 views

Least square formulation of CCA

I am trying to understand how CCA can be formulated as a least-squares problem in the binary class case. I understood how CCA and Least square problem works. But not getting how we can formulate a ...