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These studies suggest that principal component analysis (PCA) is a multivariate technique used for dimensionality reduction, data visualization, and outlier detection, while preserving as much relevant information as possible.
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Principal Component Analysis (PCA) is a statistical technique widely used for dimensionality reduction, data visualization, and simplifying complex datasets. It transforms correlated variables into a set of uncorrelated variables called principal components, which capture the maximum variance in the data.
Dimensionality Reduction and Data Simplification:
Mathematical Foundation:
Applications and Use Cases:
Generalizations and Adaptations:
Evaluation and Validation:
Principal Component Analysis (PCA) is a powerful tool for reducing the dimensionality of complex datasets while retaining essential information. It transforms correlated variables into uncorrelated principal components, facilitating data simplification and visualization. PCA's mathematical foundation involves eigen-decomposition and SVD, and it finds applications across diverse fields. Generalizations like CA and MFA, as well as adaptations like SPCA, enhance its versatility. Evaluating PCA models through cross-validation ensures their reliability and effectiveness in capturing data variability.
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