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 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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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 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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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 ...
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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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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 ...
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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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Compare canonical loadings across groups

Is it possible to statistically compare the factor loadings or canonical coefficients coming from a canonical correlation analysis run within each of two groups across both groups? e.g. statistically ...
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CCA on feature maps: Gradient w.r.t to Jacobian

Assume I have two neural networks, abstracted as two feature maps, parametrized by $\theta_x,\theta_y$ respectively. $\phi_x(x;\theta_x) \in \mathbb{R}^{h_1}$, $\phi_y(x;\theta_y) \in \mathbb{R}^{h_2}$...
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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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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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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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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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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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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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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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1answer
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RDA and CCA output- unconstrained inertia 0.00 rank 0

I get an ouput for RDA and for CCA that says that my unconstrained inertia is 0, rank 0. I thought that would be a good thing in the meaning that all the variance in the data is explained by my (...
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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 ...
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202 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 ...
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158 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 ...
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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 ...
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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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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 ...
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49 views

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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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^...
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2k 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, ...
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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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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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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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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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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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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 ...
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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 ...
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Interpreting canonical correlation plots

I have learnt (from another answer) that CCA will find pairs of vectors ($w$,$v$) such that projections $X_w$ and $Y_v$ have maximal possible correlations (the pairs will be ordered in the order ...
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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. ...
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Orthogonal linear combinations of x that have highest correlation with y

I am reading about canonical correlation analysis (CCA), and I understand that it is a technique to find linear combinations of a set of variables X that have the highest correlations with linear ...
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107 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 ...
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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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315 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 ...
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Can CCA model any linear transformation?

I have recently been looking into canonical correlation analysis (CCA) as a way to map between different spaces. As I understand it, CCA maps data from both distinct spaces to a common (possibly ...
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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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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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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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Different eigenvalues in R and SPSS

I'm trying to understand some canonical correlation outputs, and I found differences between eigenvalues results for R and SPSS. Some code: ...