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Temporal Matrix Factorization (TMF)
Extension of classical matrix factorization that incorporates temporal constraints to capture the dynamics and evolution of latent factors over time in data.
Temporal Singular Value Decomposition (SVD)
Application of SVD on temporally structured data matrices, where left and right singular vectors can represent temporal profiles and spatial or thematic entities.
Dynamic Principal Component Analysis (DPCA)
Dimensionality reduction technique that extends PCA to time series by considering temporal lags of variables to capture dynamic relationships.
Temporal Latent Factor Model
Statistical framework assuming that observed time series are generated by a smaller number of unobserved latent processes evolving according to their own temporal dynamics.
PARAFAC/CANDECOMP Decomposition
Tensor factorization method (generalization of matrices to higher dimensions) adapted to multivariate time series, decomposing a tensor into a sum of rank-one tensors.
Kalman Filter for Decomposition
Recursive state estimation algorithm in a linear dynamic system, used to decompose a time series into components (trend, cycle, seasonality) modeled as hidden states.
Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN)
Improved variant of empirical mode decomposition (EMD) that adds adaptive noise to solve mode mixing problems and provide a more stable and complete decomposition.
Wavelet Decomposition
Technique transforming a time series into the time-frequency domain, allowing isolation of components at different time scales, useful for analyzing non-stationary phenomena.
Hankel Structured Matrix
Construction of a matrix from a time series where each anti-parallel diagonal has a constant value, a frequent preliminary step for rank-based decomposition methods (SSA).
Singular Spectrum Analysis (SSA)
Non-parametric method for time series decomposition that projects the series onto a basis of eigenvectors derived from the trajectory matrix (Hankel matrix), separating signal and noise.
Empirical Mode Decomposition (EMD)
Adaptive, data-driven decomposition algorithm that extracts intrinsic oscillatory components (IMF) from a nonlinear and non-stationary time series through a sifting process.
Temporal Non-Negative Matrix Factorization (NMF)
Application of NMF to sequential data with temporal regularization constraints (e.g., smoothing) to ensure that basis factors and activation coefficients evolve consistently.
Stochastic Variance Decomposition (Stochastic SVD)
Variant of SVD computed iteratively on mini-batches of data, suitable for high-dimensional time series streams where exact decomposition is computationally too expensive.
Temporal PLS Regression (Partial Least Squares)
Modeling method that constructs latent variables by maximizing covariance with the target, while incorporating information from time lags for prediction in time series.