A Julia implementation of Nearest Neighbor Descent.
Dong, Wei et al. Efficient K-Nearest Neighbor Graph Construction for Generic Similarity Measures. WWW (2011).
Nearest Neighbor Descent (NNDescent) is an approximate K-nearest neighbor graph construction algorithm that has several useful properties:
- general: works with arbitrary dissimilarity functions
- scalable: has an empirical complexity of O(n^1.14) pairwise comparisons for a dataset of size n
- space efficient: the only data structure required is an approximate KNN graph which is operated on in-place and is also the final output
- accurate: converges to above 90% recall while only comparing each data point to a small percentage of the whole dataset on average
NNDescent is based on the heuristic argument that a neighbor of a neighbor is also likely to be a neighbor. That is, given a list of approximate nearest neighbors to a point, we can improve that list by exploring the neighbors of each point in the list. The algorithm is in essence the repeated application of this principle.
Approximate kNN graph construction on a dataset:
using NearestNeighborDescent using Distances data = [rand(20) for _ in 1:1000] n_neighbors = 10 metric = Euclidean() graph = nndescent(data, n_neighbors, metric)
The approximate KNNs of the original dataset can be retrieved from the resulting graph with
# return the approximate knns as KxN matrices of indexes and distances, where # indices[j, i] and distances[j, i] are the index of and distance to node i's jth # nearest neighbor, respectively. indices, distances = knn_matrices(graph)
To find the approximate neighbors for new points with respect to an already constructed graph:
queries = [rand(20) for _ in 1:20] n_neighbors = 5 indices, distances = search(graph, queries, n_neighbors)