List the extraction techniques used for dimensionality reduction

In the context of dimensionality reduction, several extraction techniques are commonly employed to reduce the number of features or variables while preserving relevant information in the dataset. Here’s a list of some widely used techniques:

1. Principal Component Analysis (PCA): PCA is a linear technique that transforms the original features into a new set of orthogonal components, known as principal components, which capture the maximum variance in the data. These components are ordered by the amount of variance they explain.
2. Linear Discriminant Analysis (LDA): LDA is a supervised dimensionality reduction technique that aims to find a linear combination of features that characterizes or separates two or more classes in the data while preserving as much information as possible about the class labels.
3. Kernel PCA: Kernel PCA is an extension of PCA that employs nonlinear mappings through the use of kernel functions. It allows for the capture of nonlinear relationships between variables in high-dimensional space.
4. Autoencoders: Autoencoders are neural network-based techniques that learn to encode the input data into a lower-dimensional representation and then decode it back to the original space. By training to minimize the reconstruction error, autoencoders can capture meaningful features in the data.
5. Independent Component Analysis (ICA): ICA is a technique that aims to separate a multivariate signal into additive, independent components. It assumes that the observed data is a linear mixture of independent sources and seeks to recover the original sources from the observed data.
6. Non-Negative Matrix Factorization (NMF): NMF is a matrix factorization technique that decomposes the data matrix into two low-rank matrices, where all elements are constrained to be non-negative. It is particularly useful for data that is inherently non-negative, such as text or images.
7. Factor Analysis: Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. It aims to identify the underlying structure in the data.
8. Random Projection: Random projection techniques aim to reduce dimensionality by projecting the data onto a lower-dimensional subspace using random matrices. Despite its simplicity, random projection can preserve the pairwise distances between data points reasonably well in high-dimensional spaces.

Each of these techniques has its advantages and is suitable for different types of data and problem domains. The choice of technique often depends on factors such as the nature of the data, computational efficiency requirements, interpretability of the reduced features, and the specific goals of the analysis.