Topology

Study of geometric properties preserved under continuous deformations.

What is Topology?Open and Closed SetsContinuous Functions
Topological InvariantsCompactness and ConnectednessManifolds and Higher Dimensions
Computer Graphics and AnimationRobotics and Path PlanningData Analysis and Machine Learning
Visualize and DrawUse Analogies and Stories
What is Topology?Open and Closed SetsContinuous FunctionsTopological Invarian...Compactness and Conn...Manifolds and Higher...Computer Graphics an...Robotics and Path Pl...Data Analysis and Ma...Visualize and DrawUse Analogies and St...
Practical Applications

Data Analysis and Machine Learning

Finding Patterns: Topology in Data Science

Topological Data Analysis (TDA) is a field that uses ideas from topology to find hidden shapes and patterns in complex data. TDA helps researchers uncover relationships that traditional analysis might miss.

Key Uses

  • Reveals clusters, loops, and holes in data.
  • Helps classify shapes, images, and even medical data.

Examples

  • Detecting unusual heartbeats in ECG data by finding loops in signal space.

  • Analyzing social networks using topological features of connections.

Next
Visualize and Draw