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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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scikit-learn CCA: x_loadings_x attribute

I'm doing a canonical correlation analysis using scikit-learn's CCA. After doing the usual steps and calling ca.x_loadings_, I see that I get values bigger than 1. ...
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Is there a way to perform a Hierarchical Partitioning with NMDS in R?

I performed non-metric multidimensional scaling (NMDS) on my ecological data and I was satisfied with my results, but I was told that I should use hierarchical partitioning in my analysis to check for ...
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"RV coefficient" relationship to canonical correlation

Canonical correlation addresses the following: Given matrices $X$ and $Y$, what linear combination of the columns of $X$ best correlates with what linear combination of the columns of $Y$, and what ...
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Using the jackknife method in permutation tests

We aim to employ a permutation test to evaluate the significance of the relationship between two datasets using Sparse Canonical Correlation Analysis (SCCA) for a specific level of sparsity. To ...
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What would it mean to have equal canonical coefficients (A,B) as a result of CCA?

I am using CCA to compare two matrices of n by m dimensions. ...
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Extracted variance is above 1 (CCA and redundancy analysis)

I tried to repeat the analysis from Stewart and Love 1968, to compute the Variance Extracted and redundancy index from CCA. Based on their paper (if I followed it correctly), Variance Extracted per ...
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Determining an efficient index on sample sets

Context: I have an ever-growing data set of samples. (It consists of around $500$ samples currently.) Each sample in this set is an $m \times 3$ matrix where the $m$ rows represent $m$ different ...
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Canonical correlation analysis - loadings vs coefficients

I'm trying to wrap my head around how to interpret the results of CCA. I've got a fairly deep understanding of OLS regression, and I've read a lot of helpful CCA explainers like this one by @ttnphns. ...
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Statistical analysis on cortisol reactivity (longitudinal)

I collected stress data (cortisol reactivity) on 4 timepoints. I also collected psychological measures at 1 timepoint. I would like to know if the psychological measure (one measurement time point) is ...
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incongruences between F-stats in the R cancor package

I'm using the R package candisc to perform canonical correlations. Since my dataset has missing values (only 36 rows without any NAs out of 88 rows total), I have two options: I can use the raw ...
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Multiple group analysis in canonical correlation analysis

Canonical correlation analysis estimates the relationship between two canonical sets of variables. However, I am interested in using a technique to compare these CCA results across groups (something ...
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Canonical correlation analysis

I have data on variables such as age category, sex (3 categories), habits (each with a yes or no question), drug habits (each with a yes or no question), and osteoporosis index (oi) as continuous ...
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What is the difference in interpretation between adding ellipse.type = "confidence" in PCA biplots?

I am trying to identify if three groups of species (like here) overlap or seperate out. I tried a popular method to identify ellipses: ...
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Standardized and unstandardized canonical correlation coefficients

What exactly are the standardized and unstandardized canonical correlation coefficients and what is the difference between them?
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How to calculate Pearson correlation coefficient of two 3-dimensional features?

The book I read, Applied Predictive Modeling Textbook, mentions: Even though, single features do not correlate with each other, sets of features can correlate with other sets of features. I have an ...
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Interpreting results of the vegan anova.cca function

1st question here! I've scoured the internet, including the vegan documentation, but am still confused about the meaning of the F versus ChiSquare values in the results of the anova.cca() vegan ...
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What's the difference between a CCA analysis and PCA with ellipses?

I have a data set with abundace of 4 species (S. spp, in bright colours here) across 72 sites and corresponding temperature, pH, altitude, moisture. First, I performed a CCA where ...
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Post-hoc pairwise comparison in `anova.cca` (package `vegan`)

Is there a way to perform a post-hoc pairwise comparison following anova.cca, for categorical independent variables with >2 levels, in the same sense as ...
Michael Dorman's user avatar
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Applications of Canonical Correlation Analysis in real-life problems?

I have been exposed to Canonical Correlation Analysis (CCA) a few years ago and I still find it mathematically elegant and beautiful. On Cross Validated there are several interesting posts on CCA, ...
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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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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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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 ...
Johannes Wiesner's user avatar
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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 ...
Johannes Wiesner's user avatar
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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 ...
Charlie Parker's user avatar
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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 ...
chars fregtun's user avatar
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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 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 ...
Venk Murthy's user avatar
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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 ...
blueskyddd's user avatar
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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 $\sum_{12}=0$. ...
Chicago1988's user avatar
4 votes
2 answers
392 views

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 ...
Tomas's user avatar
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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 ...
Tomas's user avatar
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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 ...
Yaroslav Bulatov's user avatar
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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 ...
mark polo's user avatar
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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 ...
Ash's user avatar
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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 ...
kiddwill's user avatar
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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: ...
Ziqi's user avatar
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1 answer
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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 ...
eric_kernfeld's user avatar
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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: ...
user3406207's user avatar