How to Convert Categorical Variables into Numerical Representations in Principal Component Analysis?
In Principal Component Analysis (PCA), the input data must be numerical, as the method relies on computations involving the covariance matrix and subsequent eigenvalue or singular value decomposition. If your dataset contains categorical variables (such as character strings), these must be transformed into numerical form before applying PCA. Below are several commonly used techniques for performing this transformation:
One-Hot Encoding
For categorical variables with a finite number of distinct values, one-hot encoding can be applied to transform each category into a separate binary feature. Each resulting feature indicates the presence or absence of a specific category. While this method effectively retains categorical information, it can significantly increase the dimensionality of the dataset.
Label Encoding
For categorical variables with an inherent order or ranking, label encoding assigns a unique integer to each category. However, this approach may lead to unintended consequences, as the model might incorrectly interpret the assigned integers as representing ordinal relationships.
Target Encoding
Target encoding involves mapping each category to a statistical measure (such as the mean) of the target variable for that category. This method can capture informative patterns in certain scenarios, particularly in supervised learning contexts.
Binary Encoding
Binary encoding first converts each category into a unique integer, which is then represented in binary form. Each bit of the binary representation becomes a separate feature. This approach helps reduce dimensionality compared to one-hot encoding and mitigates the ordinal implication issues found in label encoding.
Frequency Encoding
In frequency encoding, each category is replaced by its frequency of occurrence in the dataset. This method is simple to implement and can capture the relative prevalence of categories, although it may not always retain meaningful distinctions among them.
Ordinal Encoding
When categorical variables have a clear and meaningful order, ordinal encoding can be used to assign an integer to each category that reflects its relative rank. This technique preserves the natural order of the categories in the numerical representation.
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