Factor Analysis and Its Role in Dimensionality Reduction
Factor Analysis (FA) is a statistical technique used for dimensionality reduction by identifying latent (hidden) variables that explain the observed correlations between features. It assumes that multiple observed variables are influenced by a smaller number of unobserved factors.
How Factor Analysis Works:
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Identify Correlated Variables: FA examines the relationships between variables and groups them based on shared variance.
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Extract Common Factors: Instead of working with all features, FA represents them using fewer latent factors.
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Factor Loadings: These indicate how strongly each variable is associated with a factor.
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Dimensionality Reduction: By retaining only the most significant factors, FA reduces the number of features while preserving important information.
Types of Factor Analysis:
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Exploratory Factor Analysis (EFA): Used when the structure of the data is unknown.
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Confirmatory Factor Analysis (CFA): Tests predefined hypotheses about the relationships between variables.
Use in Dimensionality Reduction:
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Eliminates Redundancy: Removes correlated variables, reducing model complexity.
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Enhances Interpretability: Latent factors provide meaningful insights into data structure.
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Improves Model Performance: Reducing the number of features speeds up machine learning algorithms and prevents overfitting.
Applications of Factor Analysis:
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Psychometrics: Identifying personality traits from survey responses.
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Finance: Extracting economic indicators from stock market data.
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Healthcare: Finding underlying causes of diseases from patient symptoms.
Conclusion:
Factor Analysis is a powerful method for reducing dimensionality while retaining essential data structure, making it valuable for data preprocessing in machine learning.
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