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Nonlinear Dimensionality Reduction: t-SNE, UMAP & Python
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Nonlinear Dimensionality Reduction: t-SNE, UMAP & Python

Master nonlinear dimensionality reduction with t-SNE, UMAP and Kernel PCA to visualize high-dimensional data via Python.
Created byACHRAF ER-RAYA
Last updated 10/2026
English

What you'll learn

  • Identify non-linear manifold structures where standard linear PCA fails and select optimal non-linear dimensionality reduction algorithms for high-D data.
  • Implement t-SNE and UMAP, tune hyperparameters like perplexity and n_neighbors, and eliminate common visual cluster misinterpretations.
  • Quantify embedding distortion using trustworthiness and continuity metrics to debug and validate complex tabular and text embeddings.
  • Build Kernel PCA pre-image reconstructions and interactive TDA Mapper topological graph networks in Python for real-world production pipelines.

Course content

6 sections • 10 lectures • 2h 21m total length

  • Uncovering Non-Linear Manifolds: When Linear Methods Fail11:00
  • Uncovering Non-Linear Manifolds: When Linear Methods Fail (PART2)10:45

Requirements

  • Intermediate Python skills (NumPy, Pandas, Matplotlib) and basic familiarity with machine learning and linear algebra concepts.

Description

This course contains the use of artificial intelligence.

Unlock the power of complex, high-dimensional datasets by mastering modern non-linear dimensionality reduction and topological visualization techniques. High-dimensional data often hides non-linear structures that standard linear tools miss. This comprehensive, practical guide equips you with the exact tools and statistical intuition required to analyze, embed, project, and visualize complex manifolds effectively.

Who this course is for:

  • Data scientists looking to go beyond standard linear PCA algorithms

  • Machine learning engineers building high-dimensional feature embeddings

  • Bioinformaticians and researchers analyzing high-dimensional single-cell data

  • Quantitative analysts seeking topological insights in noisy financial data

What you will learn:

  • Uncover complex manifold structures where standard linear PCA fails completely

  • Master t-SNE hyperparameter tuning and avoid critical visual interpretation errors

  • Leverage UMAP to preserve global topology and project unseen test data

  • Measure embedding quality using mathematical trustworthiness metrics

  • Implement Kernel PCA and construct pre-image spatial reconstructions

  • Build topological graphs using Topological Data Analysis (TDA) Mapper

  • Debug embedding distortion artifacts in complex tabular and text data

  • Develop end-to-end Python pipelines using scikit-learn, UMAP, and TDA tools

Requirements:

  • Intermediate Python programming skills (NumPy, Pandas, Matplotlib)

  • Basic understanding of linear algebra and machine learning concepts

Final Project: You will build an end-to-end embedding evaluation pipeline on high-dimensional data. You will benchmark Kernel PCA, t-SNE, UMAP, and TDA Mapper, calculate quantitative trustworthiness scores, perform out-of-sample projections, and generate interactive, publication-ready manifold visualizations.

Who this course is for:

  • Data scientists, ML engineers, bioinformaticians, and quantitative analysts who want to move beyond linear PCA and master advanced non-linear manifold visual embeddings.

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