What Canonical root is
In statistics, canonical root is a method used to reduce the dimensionality of a dataset. It works by transforming a set of variables into a new set of variables that are uncorrelated and have maximum variance. The new set of variables is called the canonical variables.
The steps for canonical root are as follows:
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Calculate the correlation matrix of the original dataset.
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Determine the eigenvalues and eigenvectors of the correlation matrix.
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Select the eigenvectors with the highest eigenvalues as the canonical variables.
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Calculate the canonical correlations between the original variables and the canonical variables.
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Choose the canonical variables that are most strongly correlated with the original variables.
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Transform the original dataset into the new set of canonical variables.
Examples
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Canonical root analysis is used to identify the underlying structure of a set of variables. It can be used to identify latent factors that can explain the relationship between observed variables.
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Canonical root analysis is used to identify patterns among a set of variables that can explain the variability of a response variable.
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Canonical root analysis can be used to identify relationships between variables in a multivariate data set and to reduce a high dimensional data set to a smaller set of variables that capture the same information.