Principal Component Analysis (PCA)

Principal component analysis (PCA) is a dimensionality reduction method that transforms correlated variables into a smaller set of uncorrelated components that capture the maximum variance in the data.

주성분분석(PCA)은 서로 상관된 변수들을 자료의 분산을 최대한 보존하는 더 적은 수의 서로 상관없는 성분으로 변환하는 차원축소 방법이다.

How do I reduce many correlated variables to a few summary dimensions?

서로 상관된 많은 변수를 몇 개의 요약 차원으로 어떻게 줄이나요?

Principal component analysis creates linear combinations of the original variables, ordered by how much of the total variance each explains. It fits compressing many correlated numeric features into a few components for visualization, indexing or use as predictors in later models.

When to use Principal Component Analysis (PCA)

• Many correlated numeric variables that need to be summarized
• Creating composite indices or reducing predictors before regression or clustering
• Visualizing high-dimensional data in two or three dimensions

When to use something else

• You want to model latent constructs that cause item responses: use exploratory factor analysis
• Nonlinear structure matters for visualization: use t-SNE or UMAP

Assumptions and requirements

• Numeric variables
• Variables standardized when measured on different scales
• Linear relationships among variables
• Adequate sample size relative to the number of variables

What the analysis reports

• Eigenvalues and proportion of variance explained
• Scree plot
• Component loadings
• Component scores
• Biplot

How to report it

The first [k] principal components had eigenvalues greater than 1 and together explained [value]% of the total variance.

Related methods

• Exploratory Factor Analysis (EFA)
• Non Negative Matrix Factorization (NMF)
• t-SNE

Run Principal Component Analysis (PCA) on Quorant