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Modes of variation
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<p>In statistics, modes of variation are a continuously indexed set of vectors or functions that are centered at a mean and are used to depict the variation in a population or sample. Typically, variation patterns in the data can be decomposed in descending order of <a href="/facts/Eigenvalues_and_eigenvectors/8TjEoT8u">eigenvalues</a> with the directions represented by the corresponding <a href="/facts/Eigenbasis/8TjEoT8u">eigenvectors</a> or <a href="/facts/Eigenfunction/62EJS0XB">eigenfunctions</a>. Modes of variation provide a visualization of this decomposition and an efficient description of variation around the mean. Both in <a href="/facts/Principal_component_analysis/pCbVTqdR">principal component analysis</a> (PCA) and in <a href="/facts/Functional_principal_component_analysis/LN8Vsqmg">functional principal component analysis</a> (FPCA), modes of variation play an important role in visualizing and describing the variation in the data contributed by each eigencomponent. In real-world applications, the eigencomponents and associated modes of variation aid to interpret complex data, especially in <a href="/facts/Exploratory_data_analysis/8hvnf7JS">exploratory data analysis</a> (EDA). </p>