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Principal Component Analysis
Linear dimensionality reduction statistical method that transforms correlated variables into new uncorrelated variables called principal components, maximizing the explained variance.
t-SNE
Non-linear dimensionality reduction algorithm particularly effective for visualizing high-dimensional data by preserving local structures and similarities between neighboring points.
UMAP
Non-linear dimensionality reduction technique based on algebraic topology that preserves both local and global data structure while being faster than t-SNE.
Independent Component Analysis
Blind source separation statistical method that transforms data into statistically independent components, assuming that source signals are non-Gaussian.
Non-Negative Matrix Factorization
Dimensionality reduction algorithm that decomposes a non-negative matrix into two lower-rank matrices that are also non-negative, facilitating component interpretability.
Linear Discriminant Analysis
Supervised dimensionality reduction method that maximizes separation between classes while minimizing within-class variance, primarily used for classification.
Variational Autoencoders
Deep learning generative model that learns a probabilistic latent representation of data using encoder-decoder neural networks with variational regularization.
Isomap
Non-linear dimensionality reduction algorithm that preserves geodesic distances on the data manifold using shortest paths in the nearest neighbor graph.
Locally Linear Embedding
Nonlinear technique that preserves local linear relationships between points by reconstructing each point as a linear combination of its nearest neighbors in the low-dimensional space.
Factor Analysis
Exploratory statistical method that identifies unobserved latent variables (factors) that explain the correlations between observed variables in a multivariate dataset.
Covariance Matrix
Symmetric square matrix quantifying the covariances between pairs of variables, fundamental for understanding linear relationships in data and calculating principal components.
Eigenvalues
Scalars associated with the eigenvectors of a linear transformation, representing the relative importance of each principal component in principal component analysis.
Eigenvectors
Directions in which a linear transformation acts by simple scaling, corresponding to the principal axes of maximum variation in the original data space.
Gram Matrix
Symmetric positive definite matrix containing the dot products between all pairs of vectors, essential for kernel methods and singular value decomposition.
Kernel PCA
Nonlinear extension of PCA that uses kernel functions to implicitly map data into a higher-dimensional space before applying linear PCA.
Diffusion Maps
Dimensionality reduction method based on diffusion processes that captures the intrinsic geometry of data by constructing a Markov transition graph.
Truncated SVD
Variant of singular value decomposition that retains only the k largest singular values and corresponding vectors, optimized for sparse and large matrices.
Manifold Learning
Set of nonlinear techniques assuming that high-dimensional data resides on a lower-dimensional manifold, seeking to discover this underlying structure.