SVD Image Compression & PCA Deep Dive

Explore the mechanics of Singular Value Decomposition (SVD) and its application in Principal Component Analysis (PCA).

Explore the mechanics of Singular Value Decomposition (SVD) and its application in Principal Component Analysis (PCA). Features interactive image compression simulations and a comparison of PCA methods like Incremental, Randomized, and Kernel PCA.

Singular Value Decomposition (SVD)Principal Component Analysis (PCA)Dimensionality ReductionImage CompressionEigenvaluesMatrix FactorizationKernel PCAScikit-LearnNumPy

Feature Lists

Interactive SVD Rank Adjustment
Step-by-step Mathematical Derivation of PCA
Comparison of 5 PCA methods (Incremental, Kernel, etc.)
Real-world Telecom Churn Data Simulation
Low-Rank Approximation Visualizations

Enter an image URL, then adjust the Rank (number of singular values) to see how image quality changes. Lower ranks mean more compression but less detail.

Original Image (0x0)

Original Pixels: 0
Input Vector X before SVD

Reconstructed (Rank: 1)

Approx. SVD Data Points: 0
U S V^T components
Data Retained: 0%
% of Compression of the SVD components to the full vector
Mean Abs. Diff: 0
Reconstruction Error - how well SVD components approximate original

Architected by Kuriko Iwai

Continue Your Learning

If you enjoyed this blog, these related entries will complete the picture:

Dimensionality Reduction Unveiled: LLM Fine-tuning and Mechanics of SVD and PCA
A deep dive into SVD and PCA for dimensionality reduction. Learn LLM Fine-tuning behind matrix factorization, SVD-based PCA, and compare Incremental, Randomized, and Kernel PCA.

Related Books for Further Understanding

These books cover the wide range of theories and practices; from fundamentals to PhD level.

Linear Algebra Done Right

Foundations of Machine Learning, second edition (Adaptive Computation and Machine Learning series)

Designing Machine Learning Systems: An Iterative Process for Production-Ready Applications

Machine Learning Design Patterns: Solutions to Common Challenges in Data Preparation, Model Building, and MLOps

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Kuriko IWAI, "SVD Image Compression & PCA Deep Dive" in ML Labs

https://kuriko-iwai.com/labs/svd-image-compression-and-pca

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Written by Kuriko IWAI. All images, unless otherwise noted, are by the author. All experimentations on this blog utilize synthetic or licensed data.