Uncategorized . April 1, 2025
Understanding PCA from Scratch
When working with high-dimensional datasets, visualization and computation become complex. This is where Principal Component Analysis (PCA) comes in—a powerful dimensionality reduction technique. In this post, I’ll break PCA down step by step and show you how I built it from scratch.
What is PCA?
PCA transforms a dataset into a new coordinate system where the greatest variance lies along the first axis (the first principal component), the second greatest along the second axis, and so on.
In simpler terms: PCA helps us compress data while preserving as much useful information as possible.
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Steps to Implement PCA from Scratch
Standardize the Data – Subtract the mean and scale to unit variance.
Compute Covariance Matrix – Capture relationships between features.
Find Eigenvalues & Eigenvectors – These tell us the directions of maximum variance.
Sort & Select Principal Components – Keep the top k components that explain most of the variance.
Transform Data – Project original data onto these new axes.
Example Application
I tested PCA on the Iris dataset. With just two principal components, we can plot the dataset in 2D while still capturing over 95% of the variance. This makes classification tasks easier and visualization more intuitive.
Why PCA Matters
- Efficiency: Reduces dataset size without losing much information.
- Noise Reduction: Eliminates less significant features.
- Visualization: Turns complex, high-dimensional data into understandable visuals.
Key Takeaway
PCA isn’t just math—it’s a way to see patterns that were hidden in noise. Learning to implement it from scratch gave me a deep appreciation for its role in modern machine learning.
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Kia Hoffman
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