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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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: ...
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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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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/...
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380 views

Canonical correlation using spss

I wanted to prove the correlation between 8 variables. I used spss MANOVA MANOVA S K A E WITH D AC C AS / discrim all alpha(1) / print=sig(eigen dim). But I don't get the canonical correlation ...
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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 ...
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987 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 ...
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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 ...
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86 views

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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81 views

CCA dimension reduction generate complex matrix, what does that mean?

I use CCA to get the redundant information from two matrix $A$ and $B$. The goal is to reduce the Data matrix into $K$. I got $W_1$ for $A$, $W_2$ for $B$, these two matrix is used for dimension ...
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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 ...
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is there a geometric interpretation of canoncial correlation analysis? [duplicate]

I am looking for a geometric interpretation of CCA. Especially one that relies on the fact we are doing singular value decomposition, which has the geometric interpretation of a rotation, scaling and ...
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Doing CCA vs. building a dependent variable with PCA and then doing regression

Given two multidimensional datasets, $X$ and $Y$, some people perform multivariable analysis by building a surrogate dependent variable using principal component analysis (PCA). That is, run PCA on $Y$...
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Differences between linear and canonical discriminant analyses (LDA and CDA)

I'm using R to try and compare the results of variable chemical compositions, following on from an article I've read. In it, the authors used CDA to do something very similar to what I want to do, ...
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223 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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Interpreting Canonical Correspondence Analysis (CCA) Inertia - in Vegan

I am wanting to know if I can use the ratio of Constrained/Total Inertia in my CCA to describe 'The variability explained by my constraining variables'. I am asking because I've seen different ...
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604 views

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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Probabilistic models for partial least squares, reduced rank regression, and canonical correlation analysis?

This question results from the discussion following a previous question: What is the connection between partial least squares, reduced rank regression, and principal component regression? For ...
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Objective function of canonical correlation analysis (CCA)

Given two vectors of random variables $X$ and $Y$, Canonical Correlation Analysis (CCA) finds the transformation matrices $A$ and $B$ so that $\operatorname{corr}(A_{1*} X, B_{1*} Y)$ is first maximal,...
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correlation using a single transformation

I was presently working on Canonical Correlation Analysis which maximizes the correlation between two variables $X$ and $Y$ of two modalities in some transformed domain using transformations $T_1$ and ...
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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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453 views

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 ...
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How LDA, a classification technique, also serves as dimensionality reduction technique like PCA

In this article , the author links linear discriminant analysis (LDA) to principal component analysis (PCA). With my limited knowledge, I am not able to follow how LDA can be somewhat similar to PCA. ...
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Correlation between principal components

I have two matrices a, b of dimensions (100x500), (100x15000) and I am trying to find associations between sets of variables in both matrices. When I perform principal component analysis on matrix a,...
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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 ...
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What is canonical r squared?

I know r-squared is the the percent of variance explained by a model. I am currently reading materials about canonical correlation and found a new concept "canonical r squared". The material does not ...
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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 ...
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565 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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637 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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What models allow the study of the relation between two sets of variables? [closed]

Usually when you think of a model you have a single target variable which you associate to explanatory variables to try and find a pattern. In contrast with the idea of having a single target (...
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Using canonical correlation analysis (CCA) to find matches

I have a training dataset of images: X (Visual) and Y (Infrared). Each set has $300$ training examples. I extract feature ...
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How does CCA find a low-dimensional common subspace?

According to Wikipedia, canonical correlation analysis (CCA) finds pairs of canonical variables. CCA has also been used in many cases as dimensionality reduction tool to find low-dimensional subspaces....
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996 views

Dimensionality reduction technique similar to LDA when class labels are probabilistic

Given discrete class labels, say True and False, LDA (linear discriminant analysis) can be used to perform discriminant dimensionality reduction and attempt to find a subspace that best separates the ...
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Vectorise Within-Groups Sum of Squares in R

I've got a multivariate dataset (p=2) that I'm trying to calculate the W matrix for use in canonical variates analysis If each $x_{kj}$ is the jth observational unit from the kth group, and $\bar{x}...
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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 discriminant analysis - lack of equality of covariance matrices [duplicate]

I have a dataset with 92 observations and two groups that corresponde to two analytical fractions of soil samples (i.e., light fraction or LF, and mineral-associated fraction or MoM). Each group has ...
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Do I always need to log transform my data to do a canonical correspondence analysis?

I have species relative abundance data (as percentages) and several environmental parameters- and I have done normality tests on my data and it all seems to be normally distributed, but do I need to ...
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Transforming data for canonical correlation analysis

Okay, I'm a stats newbie so I'll try to be as specific and clear as possible. I have a set of predictor variables (2 predictor variables) and a set of response variables (7 response variables). I am ...
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1answer
233 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 ...
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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 ...
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2answers
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Find matching samples via Canonical Correlation Analysis (CCA) [duplicate]

I want to use Canonical Correlation Analysis (CCA) to identify relationships between two sets of variables X and Y. The CCA should give a score (highest correlation) between two samples of X and Y. I ...
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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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Recovering true data from many noisy samples with varying unknown amounts of noise

Input: $k$ vectors $x^1,\ldots,x^k \in \mathbb{R}^n$, where $x^i \sim \mathcal{N}(x,\mathbb{1} \cdot \sigma_i^2)$. Goal: approximate the vector $x$ as well as possible. The quality of approximation ...
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300 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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169 views

Principal Components, Canonical Correlation and Eigenvalue problems [duplicate]

It is well known that the solution to the optimization problems proposed in Principal Components and Canonical Correlation Analysis are given by the solution to eigenvalue problems and generalized ...
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1answer
650 views

Statistical modeling of land use - 3 types of variables

I am struggling at the moment with how to determine links between different sets of variables. I have data on land use/cover changes in a number of regions in a period of 20 years. They are all ...
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1answer
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Use variables selected from DISTLM multivariate regressions in CAP

I would like to know if the following analysis strategy is correct conceptually, if it makes sense. I found difference in fish assemblage structure between two estuarine sectors, through PERMANOVA. I ...
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Canonical Correlation Analysis for different data types

I have to do canonical correlation analysis between two multivariate datasets X and Y. One dataset contain numerical data and the other binary data. I would like to know what features are highly ...