Lecture Notes: Factor Analysis and Dimension Reduction

Introduction

• Lecturer: Farooq Hashmi from thinkingneuron.com
• Topic: Understanding factor analysis, a dimension reduction technique.

Dimension Reduction Overview

• Definition: An unsupervised machine learning technique used to reduce a large number of columns into a smaller number of columns.
• Purpose: To simplify data, making it manageable for machine learning models.

Application in Data Sets

• Problem: Large data sets (e.g., 500 predictors) slow down model training.
• Solution: Shrink predictors to a manageable number (e.g., use principal components).

Importance of Dimension Reduction

• Performance: Enhances model training speed by reducing computation.
• Complexity: Reduces model complexity, affecting prediction time.
• Applications: Used in supervised and unsupervised learning, and data visualization.

Use Cases

1. Supervised Learning: After preprocessing, use dimension reduction to simplify predictors.
2. Unsupervised Learning: Simplify data before applying algorithms like clustering.
3. Data Visualization: Reduces dimensions to create simpler visual representations (e.g., 2D plots).

Popular Algorithms for Dimension Reduction

• Factor Analysis
• Principal Component Analysis (PCA)
• Independent Component Analysis (ICA)
• T-SNE (T-Distributed Stochastic Neighbor Embedding)
• UMAP (Uniform Manifold Approximation and Projection)

Factor Analysis Explained

• Objective: Identifying hidden factors driving observed data columns.
• Example: Employee satisfaction survey ratings might be driven by factors like work culture and promotions.
• Equation Formulation:
  • Factor analysis equations: Column value = (Factor weight) * (Factor) + Constant.
  • Identifies alpha, beta, and constants to define factors.*

Comparison: Factor Analysis vs. Principal Component Analysis (PCA)

• Factor Analysis: Seeks hidden factors affecting data columns.
• PCA: Focuses on explaining data variance through principal components.
• Equation Differences:
  • Factor Analysis: Column = Factor Influence.
  • PCA: Principal Component = Weighted Sum of Columns.
• Commonality: Both aim to reduce data dimensions.

Conclusion

• Factor analysis helps uncover underlying factors affecting data.
• Distinguishing factor analysis from PCA is key but both aim to simplify data.
• Understanding these techniques enhances data handling and model training efficiency.