Factor Analysis of Mixed Data (FAMD) is a specialized statistical technique used to reduce dimensions and visualize datasets containing both numerical (quantitative) and categorical (qualitative) variables simultaneously. It works by combining the mechanisms of Principal Component Analysis (PCA) for continuous fields and Multiple Correspondence Analysis (MCA) for categorical groups. This ensures that both variable types are balanced equally and can be analyzed on a single, shared coordinate system. Step 1: Prepare and Standardize the Data
Before running the algorithm, the dataset must be preprocessed so that large numerical fields or highly frequent categories do not skew the results.
Standardize Continuous Fields: Convert continuous features into z-scores by centering them around zero and scaling them to a unit variance.
Disjunctive Coding: One-hot encode the categorical variables into discrete binary columns.
Balance Variances: Divide each binary column by the square root of its modality probability ( μmthe square root of mu sub m end-root ) to balance its variance against the continuous columns. Step 2: Extract Principal Components
Once the data matrix is unified into a purely numerical format, standard singular value decomposition (equivalent to PCA) is applied. Factor analysis of mixed-type data (FAMD) – RPubs
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