Random Projection (RP) is a computationally efficient dimension-reduction technique that approximately preserves distances; whether this leads to better anomaly detection is rarely tested. We compare four RP variants (Gaussian, sparse, subsampled randomized Hadamard transform (SRHT) and Count Sketch) and PCA for window-based k-NN anomaly detection on a synthetic multivariate benchmark and on the Server Machine Dataset (SMD) and Mars Science Laboratory (MSL) datasets, using 20 random seeds. Geometry is measured by distance distortion and neighbourhood preservation, over all points and over anomalous points. At projected dimension p=100, RP distorts pairwise distances by only 4-6% but keeps just 44-72% of each point's nearest neighbours, and its detection AUC stays within 0.04 of the unreduced data. PCA preserves geometry best on the synthetic data but detects worst there. The association between geometry measures and detection quality is weak and varies between datasets. Our results indicate that preserving distances or nearest-neighbour structure is neither sufficient nor always necessary for better anomaly-detection performance.

random projection, time-series anomaly detection, dimension reduction, geometry preservation, neighbourhood preservation, k-NN