Basisnoden

Basisnoden is a concept in distributed computing and graph-based data processing describing a node that maintains a local basis for a vector space of signals defined over a network. It stores a set of basis vectors that span a local feature space, enabling efficient representation, projection of data, and linear transformations within a decentralized setting.

Operation and data: Each basisnoden holds a basis matrix B_i with columns as basis vectors. Nodes exchange compact summaries of their bases with neighbors and use coordination protocols, such as consensus, to align a coherent global basis. Updates may be prompted by new measurements or topology changes and aim to preserve the spanning property while limiting communication.

Architecture and operations: The node stores vectors with indices and may perform projections x_i → c_i = B_i^T x_i and reconstructions x_hat_i = B_i c_i. Incremental updates, re-orthogonalization, or learning-based refinement can adjust B_i. Local data and neighboring information drive the basis adjustments to reflect network structure.

Applications: Basisnoden concepts appear in distributed principal component analysis, graph signal processing, sensor networks, and model reduction for large-scale simulations, supporting scalable learning and inference by reducing dimensionality and enabling local computations that reflect global structure.

Notes: The term basisnoden appears in some Nordic and academic contexts to denote the basis-providing node; terminology varies by domain. The concept relates to broader ideas of basis functions and distributed linear algebra.