Constructing a High-Dimensional k NN-Graph Using a Z-Order Curve

Abstract

Although many fast methods exist for constructing a k NN-graph for low-dimensional data, it is still an open question how to do it efficiently for high-dimensional data. We present a new method to construct an approximate k NN-graph for medium- to high-dimensional data. Our method uses one-dimensional mapping with a Z-order curve to construct an initial graph and then continues to improve this using neighborhood propagation. Experiments show that the method is faster than the compared methods with five different benchmark datasets, the dimensionality of which ranges from 14 to 784. Compared to a brute-force approach, the method provides a speedup between 12.7:1 and 414.2:1 depending on the dataset. We also show that errors in the approximate k NN-graph originate more likely from outlier points; and, it can be detected during runtime, which points are likely to have errors in their neighbors.