aroundPCA
aroundPCA is a statistical technique that extends classical principal component analysis (PCA) by incorporating local neighborhood structures in high‑dimensional data sets. While traditional PCA seeks linear combinations of original variables that capture the greatest variance, aroundPCA introduces a weighting scheme based on proximity in the embedding space. This approach allows the method to preserve local geometry more effectively, especially in datasets where global variance explanations are insufficient.
The algorithm begins by computing a pairwise distance matrix for the data points. A neighborhood graph is
Applications of aroundPCA include manifold learning, where it serves as a linear approximation to nonlinear structures,