Dimension Reduction - Interactive Lesson

What is Dimension Reduction?

Dimension reduction is the process of reducing the number of features (dimensions) in your data while preserving as much information as possible. It's essential for visualizing high-dimensional data, improving model performance, and reducing computational costs. Common techniques include PCA (Principal Component Analysis), t-SNE, and autoencoders.

Controls

PCA

Linear dimensionality reduction

Random Projection

Fast approximation method

Original Dimensions:3

Reduced Dimensions:2

Variance Retained:0%

Data Points:100

Key Concepts:

Principal Components: Directions of maximum variance
Eigenvalues: Amount of variance in each component
Variance Explained: Information preserved after reduction
Feature Space: Original high-dimensional space

Why Reduce Dimensions?

Visualize high-dimensional data
Remove noise and redundancy
Speed up algorithms
Avoid curse of dimensionality

Original 3D Data

PCA Reduced to 2D

How PCA Works:

Standardize the data: Center data around origin
Compute covariance matrix: Measure how variables relate
Find eigenvectors & eigenvalues: Directions of max variance
Project data: Transform to new coordinate system
Keep top components: Retain most important dimensions

🖼️ Image Compression

Reduce image data while keeping quality

🔍 Data Visualization

Plot high-D data in 2D/3D

🚀 ML Preprocessing

Improve model training speed