Density-Adaptive Rank Space Neighbor Extraction from Multidimensional Data Using Boundary-Corrected Hyper Windows

k-nearest-neighbor (k-NN) methods remain fundamental to pattern recognition, classification, and image analysis because they are simple, non-parametric, and effective for nonlinear decision structures. However, k-NN methods are constrained by two related limitations: explicit pairwise distance computation and reliance on fixed neighborhood parameters, most notably the parameter k in k-NN and the fixed window-size parameter Diff in Fast Geometrical Extraction of Nearest Neighbors (FGENN). FGENN introduced a distance-free method by transforming data into rank space and extracting nearest neighbors through a geometric hyper-window rather than metric-distance ordering, but its fixed window size does not adapt to local density variation, causing over-selection in dense regions and under-selection in sparse or boundary regions. In this paper, we propose Density-Adaptive Rank-Space Neighbor Extraction using Boundary-Corrected Hyper-windows (DARNE), an adaptive rank-space neighbor-extraction and geometric neighborhood-filtering mechanism that generalizes FGENN, where its fixed window and exhaustive sweep are replaced using an adaptive window size governed by a two-stage local-to-global occupancy-density control law. DARNE outputs ordinal rank neighborhoods in two steps: Stage 1 checks the local rank-lattice occupancy of the query neighborhood by using boundary-corrected hyper-window volumes; Stage 2 analytically scales the window, based on the local-to-global density ratio, without calculating pairwise Euclidean distances. DARNE also outperforms fixed-window FGENN in query latency for all benchmarks and brute-force k-NN variants on the IRIS, SONAR and Covertype datasets, achieving speedups of 2.78×, 11.55× and 21.14×. DARNE achieved accuracies of 97.78%, 94.09%, and 69.12% on the IRIS, SONAR and Covertype datasets, respectively, at a lower computational cost for queries relative to existing methods. Together, these results demonstrate that two-stage density-adaptive windowing in rank space is a reproducible and computationally scalable neighborhood-filtering framework for a wide range of multi-dimensional classification and hashing benchmarks.