Traditional statistical methods break down partly because of the increase in the number of observations, but mostly because of the high-dimensionality of measurements. This is the well known curse of dimensionality effect, which usually requires a large number of samples to build good models. In this situation, dimensionality reduction techniques are often necessary. The problem of dimensionality reduction arises in many scientific disciplines such as machine learning, data compression, scientific visualization, signal processing, pattern recognition, and neural computation. This project explores the use of component analysis (CA) techniques for embedding high-dimensional signals in low dimensional spaces. The aim of CA techniques (e.g. KPCA, Spectral Clustering, Linear Discriminant analysis) is to decompose a signal into relevant components optimal for a given task (e.g. classification, visualization); these components explicitly or implicitly (e.g. kernel methods) define the representation of the signal and uncover an optimal low-dimensional embedding.