Principal Component Analysis (PCA)
Last Updated: July 29, 2026 | By Mihail Sebastian | AI Dictionary
Rotates data onto new axes ranked by how much variance each captures, so the first few components hold most of the signal and the rest can be dropped.
What is Principal Component Analysis (PCA)?
Principal component analysis is a dimensionality reduction method that rotates a dataset onto new axes ordered by how much variance each one explains. Keep the first few of these principal components and you keep most of the spread in the data with a fraction of the columns.
Each component is a weighted combination of every original feature, not a selection from among them. PCA is linear, deterministic, and reversible: the same data always yields the same components, and you can project back to approximate the original values. That last property separates it from t-SNE, which is nonlinear, stochastic, and produces a picture rather than reusable features.
How PCA Works
- Standardize. Center each feature at zero and scale it to unit variance. Skip this and whichever feature has the largest units dominates the result.
- Measure covariance. Build the covariance matrix, which records how strongly each pair of features moves together.
- Decompose. Extract eigenvectors and eigenvalues. The eigenvectors give the directions of the new axes; the eigenvalues say how much variance each direction holds.
- Project. Multiply the data by the top components. A cumulative variance plot shows where the returns flatten out and how many components to keep.
Applications of PCA
- Preprocessing correlated features: Twenty sensors reading the same physical quantity produce unstable regression coefficients. A handful of components fixes that.
- Anomaly detection: Reconstruct each record from its components and measure the error. Records the components cannot rebuild are the unusual ones.
- Compression: Storing coefficients for a few components instead of full feature vectors shrinks datasets and image archives with limited visible loss.
Example of PCA
A factory logs 60 sensor readings per finished unit: thermocouples, pressure gauges, motor currents. Most move together, since eight probes near the same oven report nearly the same temperature.
PCA standardizes the readings, then finds that the first component is essentially “how hot the oven ran” and the second is “how fast the line moved”. Together they account for the bulk of the variation across units.
Plotting every unit on those two axes reveals two separated clouds. They turn out to be the day and night shifts, running the same equipment at different set points, a pattern invisible in 60 columns of raw numbers.
Related AI terms: Dimensionality Reduction · t-SNE · UMAP · Matrix Factorization · Feature Selection
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Mihail Sebastian — Writes about AI governance, regulation, and the technology behind them. Placeholder bio — replace with a real credential line. About