Principal Component
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A Principal Component is a linear function that minimizes the square of the distance from each data point to the line, and is Orthogonal to all other principal components.
- Context:
- It can range from being a (typically) Linear Principal Component to being a Non-linear Principal Compoent.
- It can range from being a First Principal Component (the linear combination with the largest variance), to being a Second Principal Component, to being ...
- It can be produced by a Principal Components Analysis System (that implements a principal components analysis algorithm).
- See: Eigenvector, Principal Curve.
References
2009
- http://www.statistics.com/resources/glossary/p/pca.php
- … Principal components are linear combinations of variables that retain maximal amount of information about the variables. The term "maximal amount of information" here means the best least-square fit, or, in other words, maximal ability to explain variance of the original data.
In technical terms, a principal component for a given set of N-dimensional data, is a linear combination of the original variables with coefficients equal to the components of an eigenvector of the correlation or covariance matrix. Principal components are usually sorted by descending order of the eigenvalues - i.e. the first principal component corresponds to the eigenvector with the maximal eigenvalue.
- … Principal components are linear combinations of variables that retain maximal amount of information about the variables. The term "maximal amount of information" here means the best least-square fit, or, in other words, maximal ability to explain variance of the original data.