# 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 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 ...
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 ...
573 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 ...
978 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 ...
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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 ...
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 ...
590 views

### Visualization of canonical correlation analysis results

What is a good way to visualize the results of canonical correlation analysis (CCA)?
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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 ...
180 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 ...
184 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 ...
264 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 ...
3k views

### 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, ...
254 views

### Is it valid to include binary or categorical variables in redundancy analysis (RDA)?

I have a mix of continuous and categorical explanatory variables I would like to enter into a canonical redundancy analysis (RDA), but I'm not sure whether it is valid to use discontinuous variables ...
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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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### Algebraic derivation of canonical correlations

In a paper from 1936, Harold Hotelling (access on JSTOR) defined the concepts of canonical correlations and canonical variates for two sets of variates. In pages 327 and 328, he precisely derives ...
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### Connection between canonical correlation and distribution of roots of characteristic equation

I'm trying to make sense of the following sentence from introduction "Multiple discoveries: Distribution of roots of determinantal equations" http://statweb.stanford.edu/~ckirby/ted/papers/...
845 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 ...
962 views

### 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 ...
605 views

### How to understand that MANOVA and discriminant analysis are special cases of canonical correlation analysis?

I am reading a statistical book which writes, Canonical correlation represents one way in which we can examine the relationship between multiple dependent variables ($\bf{Y}$) and multiple ...
207 views

### 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 ...
271 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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### Canonical correlation and prediction

Is it possible to predict values of variables in a matrix Y from values of variables in a matrix X, ie. using canonical correlations since some variables are correlated among these two matrix? X and ...
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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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### 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 ...
458 views

### 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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### 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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### Can CCA be used to replace expensive data with available data?

I have two sets of variables in the same dataset. Say DATA_free and DATA_exp. DATA_exp, however, consists of variables which are very expensive/difficult to obtain whereas DATA_free are always ...
82 views

### Is there a solution for Canonical Correlation Analysis on large sparse matrices?

I'm trying to run CCA over two views which are sparse matrices. The two views are very high dimensional (e.g. 300k, 400k) with 1m samples. CCA needs the input views to be zero mean but I won't be ...
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 ...
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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 ...
25 views

### Test dependency/correlation between genetic sketch and description sketch

How can I test is there a dependency/correlation between genetic sketch and description sketch ? Lets say I've got data like this: ...
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### Number of significant canonical correlations as “complexity measure” (CCA)

I want to study the association between 3 sets of variables A, B, C with about 15 variables each. For that i use canonical correlation analysis. Now i have 4 significant canonical correlation ...
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### Regularized canonical correlation analysis using the SVD approach

I am trying to implement the canonical correlation analysis algorithm of Golub and Zha (described here), but am running into a well known issue with canonical correlation analysis in that I repeatedly ...
200 views

### how do I measure similarity with canonical correlation analysis?

With canonical correlation analysis for two random vectors $X$ and $Y$, we do SVD on $$(C_XX)^{-1/2} C_XY C_{YY}^{-1/2}$$ to get $U$ and $V$ from the singular vector decomposition, and then define ...
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### How to interpret the results from regularized canonical analysis?

I am analyzing two sets of data (X, Y), which each has 19 samples and 26 variables (columns). Now I am looking for the correlations between the same columns of X and Y, ...
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### choosing the best set of variables to describe different groups

That is likely to be a very dummy question, but I'm stuck here... I have three groups (10 samples each) and 23 evaluated variables. I'm trying to pick up the subset of variables that best separate ...
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### Implementing Canonical Correlation Analysis in practice

I'm trying to implement Canonical Correlation Analysis using the Eigen template header c++ library to better my understanding of both the library and the particular statistical technique. So far, the ...
531 views

### Canonical correlation analysis: taking into account the negatieve correlations?

I've got two data sets on the same observations: one with 4000 variables, one with 5000 variables. I've calculated the first 30 canonical correlations between these two data sets and I look at which ...
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### Using Canonical Correlation Analysis (instead of EFA/PCA) to reduce the dimensionality of two sets of variables prior to clustering/classification

I have two sets of paired continuous data obtained from two tests. My goal is to answer the following research questions: Q1. To what extent can results on one test be used to predict the results on ...
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### Canonical Correlation Definitions

Suppose that we have two sets of variables $\textbf{X}$ and $\textbf{Y}$. Let $$\textbf{X} = \begin{pmatrix} X_1 \\ X_2\\ \vdots \\X_p \end{pmatrix}$$ and  \textbf{Y} = \begin{pmatrix} Y_1 \\ Y_2\\ ...
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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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### 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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### 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 ...
22 views

### 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 ...
29 views

### 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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### 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 ...