ydinPCA

ydinPCA is a dimensionality reduction technique designed to extract principal directions from data whose structure evolves over time. The name suggests a focus on dynamic or time-dependent patterns, distinguishing it from classical PCA by incorporating temporal variation into the analysis. It is used to uncover low-dimensional representations that remain informative as underlying relationships shift.

The core idea of ydinPCA is to form a covariance-like matrix that reflects the changing geometry of the data rather than a single, static snapshot. This is done by applying a sliding window to a time-ordered data set, computing a local covariance matrix for each window, and then aggregating these local covariances with time-sensitive weights. The weights emphasize periods where the data exhibits stable, coherent variance or, alternatively, periods of rapid change depending on the application. The resulting dynamic covariance matrix serves as the basis for standard eigen decomposition, with the top eigenvectors constituting the ydinPCA components. Data can then be projected onto these components to obtain a reduced representation.

Compared with traditional PCA, ydinPCA explicitly accounts for nonstationarity in the data and can adapt to gradual shifts in the underlying structure. It is particularly relevant for time-series analysis, sensor networks, finance, and video data where patterns evolve. Computationally, it is more demanding due to windows and weighting, and its performance depends on choices such as window size and the form of the temporal weights. Variants may employ incremental updates to improve efficiency.

See also PCA, dynamic PCA, and incremental PCA.