Lecture

Principal Component Analysis: Dimensionality Reduction

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture introduces Principal Component Analysis (PCA) as a method for dimensionality reduction. It covers the concepts of projecting high-dimensional data onto lower-dimensional subspaces to find patterns and clusters. The limitations of PCA, applications in data compression, denoising, and regression are discussed. The lecture also explores the Wine Dataset and demonstrates how PCA can be used for visualization and linear subspaces. The importance of choosing the right number of principal components in PCA and Principal Component Regression is highlighted.

Official source

Ontological neighbourhood

Information engineering

Data science: Dimensionality reduction

Mathematics

Algebra: Linear algebra

Related concepts (32)

Feature learning

In machine learning, feature learning or representation learning is a set of techniques that allows a system to automatically discover the representations needed for feature detection or classification from raw data. This replaces manual feature engineering and allows a machine to both learn the features and use them to perform a specific task. Feature learning is motivated by the fact that machine learning tasks such as classification often require input that is mathematically and computationally convenient to process.

Linear subspace

In mathematics, and more specifically in linear algebra, a linear subspace or vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces. If V is a vector space over a field K and if W is a subset of V, then W is a linear subspace of V if under the operations of V, W is a vector space over K.

Machine learning

Machine learning (ML) is an umbrella term for solving problems for which development of algorithms by human programmers would be cost-prohibitive, and instead the problems are solved by helping machines 'discover' their 'own' algorithms, without needing to be explicitly told what to do by any human-developed algorithms. Recently, generative artificial neural networks have been able to surpass results of many previous approaches.

Cluster analysis

Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters). It is a main task of exploratory data analysis, and a common technique for statistical data analysis, used in many fields, including pattern recognition, , information retrieval, bioinformatics, data compression, computer graphics and machine learning.

Hierarchical clustering

In data mining and statistics, hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis that seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two categories: Agglomerative: This is a "bottom-up" approach: Each observation starts in its own cluster, and pairs of clusters are merged as one moves up the hierarchy. Divisive: This is a "top-down" approach: All observations start in one cluster, and splits are performed recursively as one moves down the hierarchy.

Related lectures (64)

Clustering & Density Estimation

Covers dimensionality reduction, PCA, clustering techniques, and density estimation methods.

Unsupervised Learning: Clustering & Dimensionality Reduction

Introduces unsupervised learning through clustering with K-means and dimensionality reduction using PCA, along with practical examples.

Machine Learning: Supervised and Unsupervised Learning Techniques

Covers supervised and unsupervised learning techniques in machine learning, highlighting their applications in finance and environmental analysis.

Unsupervised Learning: Dimensionality Reduction and Clustering

Covers unsupervised learning, focusing on dimensionality reduction and clustering, explaining how it helps find patterns in data without labels.