Synonyms
PCA
Definition
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 [16411,16412,3]. 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...
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Jolliffe IT. Principal component analysis. 2nd ed. New-York: Springer; 2002.
Huang Z, Shen HT, Shao J, Rüger SM, Zhou X. Locality condensation: a new dimensionality reduction method for image retrieval. In: Proceedings of the 16th ACM International Conference on Multimedia; 2008. p. 219–28.
Shen HT, Zhou X, Zhou A. An adaptive and dynamic dimensionality reduction method for high-dimensional indexing. VLDB J. 2007;16(2):219–34.
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Shen, H.T. (2018). Principal Component Analysis. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_540
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DOI: https://doi.org/10.1007/978-1-4614-8265-9_540
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