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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how to understand the implications of the SVD matrix of the covariance $C_{XY} = X Y^T$

Given an $m \times n$ data matrix $X$, the SVD of its covariance matrix $$C = XX^T = ULU^T$$ provides the orthogonal unit vectors that maximize the variance in these directions. In the case of an $m \...
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Canonical Correlation Analysis coefficient interpretation

I´m performing some CCA in R for two sets of variables. Clinical and physiological. For one of the models I get this ...
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canonical correlation analysis explained variance interpretation

I´m performing a canonical correlation analysis (cca) between two sets of variables, let´s call them physiological and clinical. ...
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Run a CCA eliminating the influence of a third variable

I performed a Canonical Correlation Analysis between two variates, one being clinical traits, and the other one being physiological measures. This yields significant results, however, it is known that ...
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Relationship n_components and Y array dimension - Canonical Correlation Analysis (CCA)

Background My system tries to classify among three classes. At first, my labeling for CCA had a single dimension {1, 2, 4}, but then I found out that to get more ...
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Link between CCA and PCA

I have two datasets, $X$ and $Y$. I calculate the PCA components of $X$ and also perform CCA on $X$ and $Y$. If I create a model with all the PCA components of $X$, and another model with all the CCA ...
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Canonical correlation (matrices/vectors): where did $C = P \Upsilon Q^T$ come from? Are the singular values $\upsilon$ eigenvalues?

I am given the following description of the Canonical Correlation Matrix: Consider a random vector $\mathbf{X}$ and assume we split this into two parts $\mathbf{X}^{[1]}$ with the first $d_1$ ...
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How to get from CCA to PCA?

Saw this question in a applied scientist tech interview. How do you get to CCA objective function from PCA? I really wouldnt know where to start with this.
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Penalized Canonical Correlation in R with PMA Module

I am trying to use sparse canonical correlation analysis as implemented in the R PMA package. I'm finding that the correlations output by the package seem slightly inconsistent with the ones you would ...
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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 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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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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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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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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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, meaning that all the variance in the data is explained by my (constrained)...
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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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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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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? [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 ...