# 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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### Individual effect of different variables where one explaining variable depends on the other in a non linear way

I have data on native and invasive species along a height gradient. I want to know what effect the number of native species has on the number of invasive species (or the portion of invasive species). ...
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### 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 ...
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### How to interpret results from Canonical Correlation Analysis (CCA)

I am learning CCA following an example posted here: https://stats.idre.ucla.edu/r/dae/canonical-correlation-analysis/ I have questions regarding on how to interpret the canonical coefficients, ...
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### How does eigenvalues work with binary data in redundancy analysis?

I am using the vegan package in R to do a redundancy analysis (RDA, a part of canonical correlation analysis). My response data is binary and my explanatory variables contains 0, 0.5 an 1. I get quite ...
889 views

### Assumptions for Canonical Correspondence analysis

I have been trying to find the major assumptions a Canonical Correspondence Analysis makes when doing its analysis. I have had a hard time finding anything useful. I did, however, find the assumptions ...
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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 ...
279 views

### Compare the results of two canonical correlation analyses (CCA)

I have four datasets: morphological measurements for a set of species (M1), ecological measurements for the same set of species (E1), morphological measurements for a second set of species (M2), and ...
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### Using canonical correlation analysis with leave one out prediction

I am trying to use canonical correlation to predict a set of held out x variables from a multivariable set of X and Y data. In this particular case I am only interested in X. In the real data X is a ...
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### What's the relation between Canonical Correlation Analysis (CCA) and Regression?

I'm wondering if CCA is just a feature transformation method. Can I use it for predicting continuous variables like in regression methods? What I'm doing is to use CCA to transform my training and ...
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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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### 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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### how to check if makes sense to do canonical correlation?

I wanted to check if it is reasonable to do a canonical correlation analysis on my covariance matrix. I am trying to follow Wichern's book: The author says that we have to test if $\sum_{12}=0$. ...
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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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### 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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### How to solve multiple regression using canonical correlation analysis?

I've read that the results from multiple regression and canonical correlation analysis are the same, aside from scaling. No one online has shown how to prove this by hand, since most examples for ...
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### Multiple species & environment variables: how to reduce variable space (PCA, CCA, RDA?)

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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### Interpreting Canonical Correlation Analysis results in XLSTAT

I am new to CCA, one of the problems at hand is to find how much redundant information is contained in one set of data with respect to another.I tried using CCA in XLSTAT , the two datasets which were ...
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### Calculating CCA “scores” by hand in R

I'm trying to compute "by hand" the output of some popular Canonical Correlation Analysis functions in R, in order to be sure I understand the underlying math. I can produce the "canonical ...
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### What statistical analysis to use to relate multispectral seed data to other conventional tests?

I'm a PhD student at the University of São Paulo, Brazil, and I'm conducting experiments with multispectral analysis of soybean seeds. I have reflectance data for 8 different soybean seed samples, ...
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### Comparison/Visualisation of Regression Methods

This question follows this question, in particular @amoeba's clarifying answer and the plot from the SAS documentation included. I'm especially interested in knowing if $\mathbf{X}, \mathbf{Y}$ are ...
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### Recovering dimensionality of shared subspace?

Suppose I have X random variable have form $\langle x1,0,x2\rangle$ and Y random variable have form $\langle y1,y2,0\rangle$. These variables have 1 dimension in common. Is it possible to determine ...
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### How to get change of basis matrix for Canonical Correlation Analysis?

A bit of background: I am trying to create toy example of the Curds and Whey regression shrinkage algorithm in python. In a standard multivariate regression this algorithm uses canonical correlation ...
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### What is the difference between CCA and ordinary correlation analysis? [closed]

Ordinary correlation between two multidimensional variables would give similarity between these variables, whereas canonical correlation analysis (CCA) would find two linear transforms to obtain ...
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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 ...
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### Similarity between time series

Consider two sets A and B of time series, with dimensions (Txn) and (Txk) respectively and k Each time series in A is associated to one or more series in B. The association is based on some prior ...
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### Measuring mutual dependencies between variables. The most fundamental relation

One has a simple dataset of 3 independent variables, e.g., x, y, z. Now: y and z are logically connected (this is known a priori) and indeed a nice & tight correlation (small scatter) between ...
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### Do I always need to log transform my data to do a canonical correspondence analysis?

I have species relative abundance data (as percentages) and several environmental parameters- and I have done normality tests on my data and it all seems to be normally distributed, but do I need to ...
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### CCA (Canonical Correspondence Analysis) - Which version of the dataset is more adequate?

I'm currently working on a dataset of +400 samples, with 2 quantitative variables (salinity and depth) and 2 qualitative ones (sequencing method performed and nature of the sample, sediment or water) ...
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### Longitudinal canonical correlation analysis

So I have prospective data and I want to look at changes in certain variables (variate 1) being associated with changes in certain clinical variables (variate 2). Cross sectionally I know I could use ...
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### Why would CCA improve with increased noise?

I found that running Canonical Correlation Analysis (CCA) on a simple test dataset gave that the first component was as expected but the second would only be good if the system had substantial noise ...
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### How can lasso CCA be solved using LARS?

According to paper By Sun, Ji an Ye; A Least Squares Formulation for Canonical Correlation Analysis http://www.machinelearning.org/archive/icml2008/papers/270.pdf CCA can be reformulated as a least ...
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### Book about ordination in ecology

I am looking for a book that would cover a lot of different ordinations techniques (indirect gradient analysis e.g. PCA, CA, DCA, MDS, nMDS but also direct gradient analysis e.g. CCA, CCorA, RDA) with ...
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### sparse canonical correlation with PMA package in R - correlation coefficients

I'm new to canonical correlation analysis. I'm running a sparse canonical correlation analysis in R using the PMA package. My first question is why the correlation coefficients associated to the ...
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### 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 ...
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### Canonical correlation using spss

I wanted to prove the correlation between 8 variables. I used spss MANOVA MANOVA S K A E WITH D AC C AS / discrim all alpha(1) / print=sig(eigen dim). But I don't get the canonical correlation ...
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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{...
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### 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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### I'd like to do regression using canonical correlation analysis

I got two multidimensional datasets, X and Y. I thought I build the model, which explains the relationship between two datasets, using canonical correlation analysis (CCA). The first correlation ...
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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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### 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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### 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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### 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 ...
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### Canonical Correlation Analysis (CCA) - do you need to scale the input variables?

I am learning CCA and I have come across a question that I do not know how to answer. Suppose we have the following 2 sets of variables: ...
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### 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 ...
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### 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 ...
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### Which analysis to use to discriminate morphometrics measurements from different species from 2 different environment?

So I have a dataset of measurements (lengths, surface areas, volumes...) from 3 species from 2 different environments, with 3 individuals per species. Can be summarised like that: ...
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### Correlation analysis between two sets of random variables (pathway analysis)

I'm newbie to multivariate analysis and working on a project where I'm interested in the strength of association between two pathways (proteomic data). Abstractly speaking, each pathway is represented ...
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### Canonical correlation analysis when one of the matrices consists of binary data

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 ...
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 ...