# 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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### What is the difference between correlation and a general linear model?

What is the difference between correlation and a general linear model? I expected the linear regression to be included in the general linear model. but how about correlation? I knew that correlation ...
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### What is the difference between a PCA, RDA and CCA analysis?

I am trying to understand the difference between a PCA, RDA and CCA analysis. Here is an example of a CCA triplot. It seems that a PCA + RDA = CCA plot. Here it's a CCA triplot, which incorporates one ...
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### Finding the vectors/modes "maximally responsible" for the fluctutation of a quantity?

I have a question which I fear might be simple but i am completely unable to figure out. Lets say we have a time-series of a vector of coordinates which define a molecule ( column vector of x,y,z) ...
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### Canonical Correlation Analysis Significance Test for non-normal data distribution

I am running a number of Canonical Correlation Analysis methods on some time series data on variables that are not normally distributed. Some of the methods I intend to apply are: Classical CCA ...
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### Moderation of relation of two datasets

I have one dataset regarding soil microbial community (20 PLFA markers) and another regarding soil nutrients (NO3, NH4, P, K, etc.). I would like to see if the correlation between these sets is less ...
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### Relation of Canonical Loadings to Canonical Variate

I am new to Canonical Correlation Analysis (CCA), I have understood until now that Canonical Loadings indicate how the original variables contribute to the overall correlation between the two sets of ...
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### Getting sample/individual values from sparse CCA using PMA package

I have a dataset of 100 samples in which two sets of data were collected, 24950 features for one and 15 features in the other. I would like to apply sparse CCA to find correlations between these two ...
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### Canonical Correlation Analysis CCA dimensionality reduction in R

I want to conduct dimensionality reduction using CCA. Let's suppose that $X$ is a matrix of $p$ predictors, $n$ samples and $y$ is a binary vector of $0$ and $1$, i.e. ...
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### inverse of canonical correlation

The canonical correlation obtains the most correlative pairs of components across two matrices. However, the inverse is not commonly known but could be useful for obtaining the most different ...
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### CCA in feature selection [R]

I'm trying to conduct feature selection based on the Canonical Correlation Analysis (CCA). As far as I know, for two given datasets $X$ and $Y$ CCA looks for the linear projections of $X$ and $Y$ such ...
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### Self-Study: Score Statistic of a Poisson

I have been attempting a question on Generalised Linear Models. I thought I understood it but doing exercises myself now, proves otherwise. I have attached an image of the question here, struggling ...
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### Canonical Correlation Analysis and Incorporating New Data

For some context, I am trying to follow this neuroscience paper (https://www.nature.com/articles/nm.4246?TB_iframe=true&width=921.6&height=921.6) Regarding my data, I have 2 datasets, one as a ...
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### Spread of species and site scores in R (vegan) DCA ordination

I have performed a Detrended Correspondence Analysis on social survey answers, aiming to see the spread of answers to 25 interview questions and how they related to the three farmer types (n =45) we ...
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### Multiview CCA with one source set and multiple independent target sets

I have 5 datasets from the same subjects that can be interpreted as different data modalities for these subjects. 4 of these datasets describe brain-related data and the last one contains behavioral ...
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### Meaning of Canonical Correlation Analysis Orthogonal Constraint

Hello Folks - I'm trying to understand canonical correlation analysis (CCA). I found that it's useful for finding linear projections such that the projection results are maximally correlated. However, ...
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### Canonical Correlation Analysis to combine two vector spaces

I have the following problem: I have two completely different vector spaces (namely word embedding vectors) from two different models. They do not have the same length since their vocabulary is ...
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### How to train a model to maximize the difference of correlations?

I have two labeled datasets, $A$ and $B$: $(X_A, y_A)$ and $(X_B, y_B)$. $X_A, X_A \in \mathbb{R}^{m \times n}$ and $y_A, y_B \in \mathbb{R}^n$. $m$ is the number of features, $n$ is the number of ...
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### Cannot manually reproduce CCA loadings

For my current project I am using sklearn.cross_decomposition.CCA. On several wepages (e.g. https://stats.idre.ucla.edu/r/dae/canonical-correlation-analysis/ or ...
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### Why the correlation in CCA can be greater than 1? [closed]

I am working with the following paper https://home.ttic.edu/~klivescu/papers/andrew_icml2013.pdf where they use DCCA and in the results they present they show correlations between different sets of ...
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### Why is the first canonical direction equal to the left singular vector i.e. why is $w_1 = a = u_1$ in CCA (Canonical Correlation Analysis)?

I want to understand why the canonical direction $a$ is equal to the left singular value of $M = \Sigma^{-1/2}_X \Sigma_{X, Y} \Sigma^{-1/2}_Y$ and not $a = \sigma_1 u_1$. My calculation tell me that ...
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### Maximization of correlation coefficient. The canonical correlation

The idea of the Canonical correlation is to maximize the correlation between two vectors $(Y,X)$ using 2 vector of weights $(\alpha,\beta)$. My problem is that I have a dependent variable $Y$ and a ...
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### What's wrong with my solution to canonical correlation analysis (CCA) using the SVD? [duplicate]

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 ...