Dekompositionsmodeller

Dekompositionsmodeller refer to a class of statistical and data-analytic models whose primary purpose is to decompose a complex data set into interpretable constituent components. The term, derived from the concept of decomposition in statistics, covers a range of modeling approaches across disciplines such as time series analysis, signal processing, chemometrics and image analysis. In general, these models seek to represent data as a sum or product of simpler factors that capture underlying structures such as trend, periodic variation, and residual noise, or as low-rank factors that explain shared variation across variables.

Two common forms are additive and multiplicative decompositions. Additive models express the observation as a sum of components (for example X = T + S + E), while multiplicative models use a product (X = T · S · E) when scale effects are important. In multivariate contexts, dekompositionsmodeller often rely on matrix or tensor factorization to extract latent components, such as principal components, independent components, or nonnegative factors.

Typical methods include singular value decomposition, principal component analysis, independent component analysis, nonnegative matrix/tensor factorization, and model-based approaches using Bayesian inference or EM algorithms. Preprocessing, component selection, and validation are important steps to ensure identifiability and interpretability.

Applications span finance, climatology, energy forecasting, biomedical signal processing, and image or audio analysis. Ongoing developments address nonstationarity, missing data, noise robustness, and computational scalability, aiming to provide stable, interpretable decompositions in high-dimensional settings.

See also: time series decomposition, matrix factorization, tensor decomposition, and related factor-analysis methods.