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
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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 ...
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 ...
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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 ...
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. ...
15
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2answers
2k views

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 ...
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 $Y$...
9
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1answer
520 views

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 $X=Y$?
8
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1answer
935 views

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 ...
7
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1answer
3k views

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 ...
7
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1answer
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 ...
7
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1answer
1k views

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,...
6
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2answers
895 views

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 ...
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....
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 ...
5
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1answer
5k views

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, ...
5
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1answer
1k views

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 ...
5
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1answer
377 views

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 ...
5
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0answers
2k views

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 ...
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
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 ...
4
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1answer
942 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 ...
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 ...
4
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2answers
93 views

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 ...
4
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1answer
715 views

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 ...
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 ...
4
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1answer
111 views

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 ...
4
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0answers
572 views

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 ...
4
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0answers
971 views

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 ...
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,...
3
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1answer
77 views

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 ...
3
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2answers
944 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 ...
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
64 views

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{...
3
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2answers
249 views

intuitive interpretation of canonical parameterization of beta distribution

For exponential family, e.g. Beta distirbution, someone argues that the canonical parameterization is better than the traditional $Beta(\alpha,\beta)$ way. The canonical parameters are defined as $n^...
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. ...
3
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3answers
232 views

How can I find the correlation between groups of *attributes*?

Assume I have data where multiple attributes are measured for countries and the attributes can be divided into dimensions. For example one dimension can be 'Education' and have 5 attributes associated ...
3
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1answer
338 views

Transforming data for canonical correlation analysis

Okay, I'm a stats newbie so I'll try to be as specific and clear as possible. I have a set of predictor variables (2 predictor variables) and a set of response variables (7 response variables). I am ...
3
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1answer
2k views

Canonical correlation analysis with continuous and binary data

I came across interesting article on application of canonical correlation analysis (CCA). Authors apply classical CCA on a mixed variables dataset (both independent and dependent sets include ...
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 ...
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
589 views

Visualization of canonical correlation analysis results

What is a good way to visualize the results of canonical correlation analysis (CCA)?
2
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2answers
597 views

What is an analogue of PCA in the regression context?

I'm writing code to approximate a function $y=f(\vec{x})$ where $y\in\mathbb{R}$ and $\vec{x}\in\mathbb{R}^N$ for medium-sized $N$ ($N$ between 20 and 50, approx.). I have a ton of examples, however, ...
2
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1answer
232 views

How to know if Canonical Correlation analysis is overfitting?

I have X = (21,15) -> 21 observations, 15 variables; Y = (21,6) -> 21 observations, 6 variables. When I do CCA on X and Y, I get correlation coefficients of 1, but I know that it shouldnt happen for ...
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 ...
2
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1answer
643 views

Statistical modeling of land use - 3 types of variables

I am struggling at the moment with how to determine links between different sets of variables. I have data on land use/cover changes in a number of regions in a period of 20 years. They are all ...
2
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0answers
82 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 ...
2
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0answers
171 views

Difficulty interpreting/understanding canonical correlation analysis

I have read many posts on the topic (e.g. this or this) and have gone through a few introductions/tutorials, however, while I do understand the mathematical description, I still have a lot of ...
2
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0answers
31 views

How is canonical correlation analysis related to multivariate regression? [duplicate]

Given a $m\times p$ matrix $Y$ on the left, and a $m\times q$ matrix $X$ on the right, CCA tries to find 2 sets of mapping coefficients such that $Y\beta_{l}$ and $X\beta_{r}$ have the highest ...
2
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1answer
182 views

Statistical significance test for comparing two canonical correlation analyses

I have a colleague who is comparing several different treatments of data via canonical correlation analysis. In other words, given some time-varying signal, $a(t)$, he extracting some vector of ...
2
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0answers
261 views

What's wrong with my solution to canonical correlation analysis (CCA) using the SVD

I am working through the derivations for solving CCA in A Tutorial on Canonical Correlation Methods. Right now, I am trying to solve CCA using SVD (bottom of page 95:7). For completeness, I include ...