Is Data Standardization Necessary in Principal Component Analysis and Why?
Data standardization is a critical preprocessing step in principal component analysis (PCA), as it ensures that differences in the scales of variables do not distort the resulting components.
Purpose of Data Standardization
1. To bring variables onto a common scale, thereby eliminating potential bias in the results caused by differing units or magnitudes.
2. To make the variances of different variables comparable, minimizing the risk that the PCA outcome is disproportionately influenced by variables with larger numerical ranges.
Necessity of Data Standardization
1. PCA relies on either the covariance matrix or the correlation matrix, both of which are sensitive to the scale of the variables involved.
2. Without standardization, variables with larger scales may dominate the extracted principal components, while those with smaller scales may have a diminished influence.
3. Standardization helps ensure that all variables contribute more equally to the principal components, preventing the analysis from being skewed toward variables with inherently larger scales.
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