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Principal components analysis (PCA) is a linear technique used to reduce a high-dimensional dataset to a lower dimensional representations for analysis and indexing. For a dataset P in D-dimensional space with its principal component set Φ, given a point p∈P, its projection on the lower d-dimensional subspace can be defined as: p. Φd, where Φd represents the matrix containing 1st to dth largest principal components in Φ and d < D.
Key Points
PCA finds a low-dimensional embedding of the data points that best preserves their variance as measured in the high-dimensional input space [1]. It identifies the directions that best preserve the associated variances of the data points while minimize “least-squares” (Euclidean) error measured by analyzing data covariance matrix. The first principal component is the eigenvector corresponding to the largest eigenvalue of the dataset’s co-variance matrix, the second component corresponds to the eigenvector with the second...
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Recommended Reading
Jolliffe I.T. Principlal Componet Analysis. 2nd edn. Springer, New-York, 2002.
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© 2009 Springer Science+Business Media, LLC
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Shen, H. (2009). Principal Component Analysis. In: LIU, L., ÖZSU, M.T. (eds) Encyclopedia of Database Systems. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-39940-9_540
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DOI: https://doi.org/10.1007/978-0-387-39940-9_540
Publisher Name: Springer, Boston, MA
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