Dimensionality reduction

Dimensionality reduction is the process of reducing the number of variables under consideration in a dataset. It is useful for compression and identifying underlying structure. Key techniques:

Principal component analysis (PCA) - Orthogonal transformation to principal components.
Singular value decomposition (SVD) - Factorizes into singular vectors/values.
Autoencoders' - Neural networks encode and reconstruct data.
t-SNE - Nonlinear embedding that clusters similar points.

Purposes include:

Simplifying datasets.
Noise filtering.
Identifying correlations.
Compression.

Challenges involve preserving essential information when projecting to lower dimensions. Many linear and nonlinear techniques provide alternative approaches to dimensionality reduction.

The process is critical for machine learning pipelines to avoid overfitting and the curse of dimensionality. It enables deriving insights from complex high-dimensional data.