Lecture

Principal Component Analysis: Dimensionality Reduction

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In course

MICRO-455: Machine learning I

Real-world engineering applications must cope with a large dataset of dynamic variables, which cannot be well approximated by classical or deterministic models. This course gives an overview of methods from Machine Learning for the analysis of non-linear, highly noisy and multi dimensional data

Description

This lecture covers the application of Principal Component Analysis (PCA) for dimensionality reduction in machine learning. The instructor demonstrates how PCA can reduce redundant information in joint angle trajectories, project high-dimensional state spaces onto lower dimensions, and preprocess data for classification and compression. PCA is shown to extract features and reduce computational costs, making it a valuable tool for data storage, retrieval, and classification tasks.

Instructor

Aude Billard

Expertise RoboticsMachine LearningArtificial IntelligenceHuman-Robot InteractionMechatronicsDynamical Systems ControlComputational Neuroscience Aude Billard is full professor and head of the LASA laboratory at the School of Engineering at the Swiss Institute of Technology Lausanne (EPFL), and the Director of the Swiss Innovation Booster on Robotics. Dr. Billard acts as the President of the IEEE Robotics and Automation Society (RAS), after serving in several roles in the administrative and executive committe

Official source

Related concepts (20)

Nonlinear dimensionality reduction

Nonlinear dimensionality reduction, also known as manifold learning, refers to various related techniques that aim to project high-dimensional data onto lower-dimensional latent manifolds, with the goal of either visualizing the data in the low-dimensional space, or learning the mapping (either from the high-dimensional space to the low-dimensional embedding or vice versa) itself. The techniques described below can be understood as generalizations of linear decomposition methods used for dimensionality reduction, such as singular value decomposition and principal component analysis.

Curse of dimensionality

The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The expression was coined by Richard E. Bellman when considering problems in dynamic programming. Dimensionally cursed phenomena occur in domains such as numerical analysis, sampling, combinatorics, machine learning, data mining and databases.

Independent component analysis

In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and that the subcomponents are statistically independent from each other. ICA is a special case of blind source separation. A common example application is the "cocktail party problem" of listening in on one person's speech in a noisy room.

Feature engineering

Feature engineering or feature extraction or feature discovery is the process of extracting features (characteristics, properties, attributes) from raw data. Due to deep learning networks, such as convolutional neural networks, that are able to learn it by itself, domain-specific- based feature engineering has become obsolete for vision and speech processing.

Feature (machine learning)

In machine learning and pattern recognition, a feature is an individual measurable property or characteristic of a phenomenon. Choosing informative, discriminating and independent features is a crucial element of effective algorithms in pattern recognition, classification and regression. Features are usually numeric, but structural features such as strings and graphs are used in syntactic pattern recognition. The concept of "feature" is related to that of explanatory variable used in statistical techniques such as linear regression.

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Kernel PCA: Nonlinear Dimensionality Reduction

Explores Kernel Principal Component Analysis, a nonlinear method using kernels for linear problem solving and dimensionality reduction.

Principal Component Analysis: Dimensionality Reduction

Covers Principal Component Analysis for dimensionality reduction, exploring its applications, limitations, and importance of choosing the right components.

Clustering & Density Estimation

Covers clustering, PCA, LDA, K-means, GMM, KDE, and Mean Shift algorithms for density estimation and clustering.

Principal Component Analysis: Dimensionality Reduction

Explores Principal Component Analysis for dimensionality reduction and unsupervised feature selection.

Linear Dimensionality Reduction

Explores linear dimensionality reduction through PCA, variance maximization, and real-world applications like medical data analysis.

Related concepts (20)

Nonlinear dimensionality reduction

Curse of dimensionality

Independent component analysis

Feature engineering

Feature (machine learning)