Dimensionality Reduction as Flow Allocation: The Engineering Essence of Point Set Flattening

Within the framework of Multiple Origin Curvature (MOC), the continuous transition from three dimensions to two dimensions is essentially both a progressive flattening process of the point set and a typical process of flow redistribution.

This process does not simply eliminate nodes or reduce branches; on the contrary, the number of network nodes may even increase to adapt the structure to a planar form. Its essence lies in that the flow along the high-dimensional depth direction is gradually constrained and converged, and the components flowing into each branch are correspondingly reduced. The overall structure achieves controllable dimensional collapse while preserving topological connectivity.

From an information-theoretic perspective, dimensionality reduction is reflected in the orderly reduction of information volume—not crude information loss, but the constraint of the distribution originally diffused in three-dimensional space onto a two-dimensional plane through flow redirection. The main structure and key features are fully preserved while reducing system redundancy and complexity.

This is the engineering essence of dimensionality reduction: the redistribution of flow, not the deletion of nodes; the convergence of information, not the annihilation of information.