Dimensionality Reduction: Linear Transformations and Autoencoders

About

**The Need for Dimensionality Reduction** High-dimensional datasets often contain redundancy, noise, and complex internal structures, making direct interpretation and processing challenging. Dimensionality reduction methods offer effective solutions providing a compressed representation by projecting data into lower-dimensions while preserving their underlying structures. A set of powerful techniques are available: **. SVD-based Linear Transformations**: Methods like Principal Component Analysis (PCA) learn projection vectors based on data variance. These linear models perform well in near-linear subspaces but struggle with complex, nonlinear data manifolds. **. Deep Learning Approaches**: In contrast, deep learning methods such as AutoEncoders (AEs) excel at learning nonlinear mappings and extracting complex latent-space representations from data. The compressed representation is an essential component of modern AI-driven analysis and feature abstraction.

**Lecture Overview** This lecture introduces and motivates the need for dimensionality reduction, reviews key methods, and addresses their importance in data-intensive workflows. Through conceptual learning and practical examples, participants will gain the knowledge and motivation to apply these methods in their own research problems. A practical aspect of the lecture will also cover applying these methods in post-processing and downstream tasks such as clustering, classification, and noise removal through data reconstruction.

**Lecture Outline:** 1- Introduction to Dimension Reduction . Basic ideas . How Dimension Reduction works 2- Concepts and Examples . Principal Component Analysis . AutoEncoders: Fully-connected AE, Convolutional AE 3- Applications . Compression and Denoising . Classification and Clustering . Tips: How to best select the appropriate models for specific problems

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