Does PCA with Only One Factor Represent a Single Dimension?
Yes, if principal component analysis (PCA) extracts only one principal component (or "factor"), it can be considered the main dimension in the data that captures the greatest variance. This means that this single principal component summarizes the primary pattern or trend of variation in the data.
Extracting a single principal component is meaningful in certain cases, especially when that component explains most of the variance in the data. However, the decision to extract only one principal component should be based on understanding the data, the proportion of variance explained, and the research objectives.
For example, if the first principal component explains over 90% of the variance in the data, it may effectively represent the data. But if it explains only 40% of the variance, additional principal components might be needed to more comprehensively describe the data.
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