How Should Data Be Processed After Principal Component Analysis?
After Principal Component Analysis (PCA), the data is projected onto a new coordinate system defined by the principal components. The following steps can be undertaken to process the PCA-transformed data:
Selecting The Number of Principal Components
Based on the cumulative proportion of variance explained or specific analytical objectives, determine the number of principal components to retain. Typically, components that account for the majority of the variance are preferred.
Constructing The Score Matrix
Compute the score matrix by multiplying the original dataset by the selected principal components (i.e., eigenvectors). The resulting matrix indicates the position of each observation in the principal component space.
Interpreting The Principal Components
Analyze the loading values of each principal component on the original features to infer their meaning. Larger loading values suggest a greater contribution of the corresponding feature to that component.
Visualization
If two or three principal components are retained, the transformed data can be visualized in two-dimensional or three-dimensional space to reveal underlying structures or patterns.
Further Analysis
The output of PCA can serve as input for subsequent analytical tasks. For example:
1. Clustering
Perform clustering on the PCA-transformed data to identify groupings or latent structures.
2. Regression or Classification
Use the principal component scores as predictors in regression or classification models.
Inverse Transformation (If Necessary)
To reconstruct data or patterns in the original feature space, an inverse transformation can be applied. However, if certain components were discarded during PCA, this reconstruction will only approximate the original data.
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