Agent skill
pca-decomposition
Reduce dimensionality of multivariate data using PCA with varimax rotation. Use when you have many correlated variables and need to identify underlying factors or reduce collinearity.
Install this agent skill to your Project
npx add-skill https://github.com/benchflow-ai/skillsbench/tree/main/tasks/lake-warming-attribution/environment/skills/pca-decomposition
SKILL.md
PCA Decomposition Guide
Overview
Principal Component Analysis (PCA) reduces many correlated variables into fewer uncorrelated components. Varimax rotation makes components more interpretable by maximizing variance.
When to Use PCA
- Many correlated predictor variables
- Need to identify underlying factor groups
- Reduce multicollinearity before regression
- Exploratory data analysis
Basic PCA with Varimax Rotation
from sklearn.preprocessing import StandardScaler
from factor_analyzer import FactorAnalyzer
# Standardize data first
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)
# PCA with varimax rotation
fa = FactorAnalyzer(n_factors=4, rotation='varimax')
fa.fit(X_scaled)
# Get factor loadings
loadings = fa.loadings_
# Get component scores for each observation
scores = fa.transform(X_scaled)
Workflow for Attribution Analysis
When using PCA for contribution analysis with predefined categories:
- Combine ALL variables first, then do PCA together:
# Include all variables from all categories in one matrix
all_vars = ['AirTemp', 'NetRadiation', 'Precip', 'Inflow', 'Outflow',
'WindSpeed', 'DevelopedArea', 'AgricultureArea']
X = df[all_vars].values
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)
# PCA on ALL variables together
fa = FactorAnalyzer(n_factors=4, rotation='varimax')
fa.fit(X_scaled)
scores = fa.transform(X_scaled)
-
Interpret loadings to map factors to categories (optional for understanding)
-
Use factor scores directly for R² decomposition
Important: Do NOT run separate PCA for each category. Run one global PCA on all variables, then use the resulting factor scores for contribution analysis.
Interpreting Factor Loadings
Loadings show correlation between original variables and components:
| Loading | Interpretation |
|---|---|
| > 0.7 | Strong association |
| 0.4 - 0.7 | Moderate association |
| < 0.4 | Weak association |
Example: Economic Indicators
import pandas as pd
from sklearn.preprocessing import StandardScaler
from factor_analyzer import FactorAnalyzer
# Variables: gdp, unemployment, inflation, interest_rate, exports, imports
df = pd.read_csv('economic_data.csv')
variables = ['gdp', 'unemployment', 'inflation',
'interest_rate', 'exports', 'imports']
X = df[variables].values
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)
fa = FactorAnalyzer(n_factors=3, rotation='varimax')
fa.fit(X_scaled)
# View loadings
loadings_df = pd.DataFrame(
fa.loadings_,
index=variables,
columns=['RC1', 'RC2', 'RC3']
)
print(loadings_df.round(2))
Choosing Number of Factors
Option 1: Kaiser Criterion
# Check eigenvalues
eigenvalues, _ = fa.get_eigenvalues()
# Keep factors with eigenvalue > 1
n_factors = sum(eigenvalues > 1)
Option 2: Domain Knowledge
If you know how many categories your variables should group into, specify directly:
# Example: health data with 3 expected categories (lifestyle, genetics, environment)
fa = FactorAnalyzer(n_factors=3, rotation='varimax')
Common Issues
| Issue | Cause | Solution |
|---|---|---|
| Loadings all similar | Too few factors | Increase n_factors |
| Negative loadings | Inverse relationship | Normal, interpret direction |
| Low variance explained | Data not suitable for PCA | Check correlations first |
Best Practices
- Always standardize data before PCA
- Use varimax rotation for interpretability
- Check factor loadings to name components
- Use Kaiser criterion or domain knowledge for n_factors
- For attribution analysis, run ONE global PCA on all variables
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