1 Introduction

The BiocNeighbors package provides several algorithms for approximate neighbor searches:

  • The Annoy (Approximate Nearest Neighbors Oh Yeah) method uses C++ code from the RcppAnnoy package. It works by building a tree where a random hyperplane partitions a group of points into two child groups at each internal node. This is repeated to construct a forest of trees where the number of trees determines the accuracy of the search. Given a query data point, we identify all points in the same leaf node for each tree. We then take the union of leaf node sets across trees and search them exactly for the nearest neighbors.
  • The HNSW (Hierarchical Navigable Small Worlds) method uses C++ code from the RcppHNSW package. It works by building a series of nagivable small world graphs containing links between points across the entire data set. The algorithm walks through the graphs where each step is chosen to move closer to a given query point. Different graphs contain links of different lengths, yielding a hierarchy where earlier steps are large and later steps are small. The accuracy of the search is determined by the connectivity of the graphs and the size of the intermediate list of potential neighbors.

These methods complement the exact algorithms described previously. Again, it is straightforward to switch from one algorithm to another by simply changing the BNPARAM argument in findKNN and queryKNN.

2 Identifying nearest neighbors

We perform the k-nearest neighbors search with the Annoy algorithm by specifying BNPARAM=AnnoyParam().

nobs <- 10000
ndim <- 20
data <- matrix(runif(nobs*ndim), ncol=ndim)

fout <- findKNN(data, k=10, BNPARAM=AnnoyParam())
head(fout$index)
##      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 7185 6235 9282 2873 5047 8585 6871 4713 2789  3316
## [2,] 6741 9689 7636 6359 2993 4731 1581 4386 9981  1681
## [3,] 5412 2374 3733  302 2129 6824 7520 9180 5357  3684
## [4,] 6571 8002 3109 2092 2286  363 9654 8747 3922  6185
## [5,] 3456 8448 7858 5895 7870  860  507 2462  118  7448
## [6,] 6534 4985  200 7427 9027 4778 7579 2558 6726  4197
head(fout$distance)
##           [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
## [1,] 0.8076415 0.9000395 0.9005997 0.9801784 1.0043234 1.0091287 1.0101857
## [2,] 0.8706856 0.9875263 1.0073107 1.0092914 1.0869757 1.0896205 1.1030468
## [3,] 0.8577539 0.9109335 0.9523353 0.9560369 0.9569755 0.9608607 0.9939891
## [4,] 0.7341259 0.8933441 0.9612451 1.0078721 1.0298184 1.0537697 1.0744098
## [5,] 0.8997407 0.9145612 0.9612712 0.9838849 0.9842784 0.9926714 0.9929001
## [6,] 0.9207253 0.9832393 0.9843387 1.0050380 1.0198334 1.0308520 1.0423095
##          [,8]     [,9]    [,10]
## [1,] 1.037611 1.050631 1.052028
## [2,] 1.109873 1.113673 1.127582
## [3,] 1.007553 1.008265 1.010376
## [4,] 1.075423 1.080180 1.097522
## [5,] 1.022584 1.027323 1.029023
## [6,] 1.045436 1.051560 1.058640

We can also identify the k-nearest neighbors in one dataset based on query points in another dataset.

nquery <- 1000
ndim <- 20
query <- matrix(runif(nquery*ndim), ncol=ndim)

qout <- queryKNN(data, query, k=5, BNPARAM=AnnoyParam())
head(qout$index)
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 2029 9727 7104 4337 7649
## [2,] 5758 3584 8983 3863  884
## [3,] 2435  925 5892 1385 3492
## [4,] 6615 6693 9567 9469  134
## [5,] 5201 8773 3078 3615  790
## [6,] 1152  501 9812 9760 8282
head(qout$distance)
##           [,1]      [,2]      [,3]      [,4]      [,5]
## [1,] 0.9775436 0.9846010 0.9996586 1.0210204 1.0483401
## [2,] 1.0020682 1.0271850 1.0344262 1.0970036 1.1021838
## [3,] 0.8052995 0.9297472 0.9565524 1.0217369 1.0438033
## [4,] 0.9118630 0.9746927 1.0185562 1.0784415 1.0974541
## [5,] 0.9531181 0.9647527 0.9669973 0.9699942 0.9768789
## [6,] 0.8380350 0.8832462 0.9639988 0.9690495 0.9718001

It is similarly easy to use the HNSW algorithm by setting BNPARAM=HnswParam().

3 Further options

Most of the options described for the exact methods are also applicable here. For example:

  • subset to identify neighbors for a subset of points.
  • get.distance to avoid retrieving distances when unnecessary.
  • BPPARAM to parallelize the calculations across multiple workers.
  • BNINDEX to build the forest once for a given data set and re-use it across calls.

The use of a pre-built BNINDEX is illustrated below:

pre <- buildIndex(data, BNPARAM=AnnoyParam())
out1 <- findKNN(BNINDEX=pre, k=5)
out2 <- queryKNN(BNINDEX=pre, query=query, k=2)

Both Annoy and HNSW perform searches based on the Euclidean distance by default. Searching by Manhattan distance is done by simply setting distance="Manhattan" in AnnoyParam() or HnswParam().

Users are referred to the documentation of each function for specific details on the available arguments.

4 Saving the index files

Both Annoy and HNSW generate indexing structures - a forest of trees and series of graphs, respectively - that are saved to file when calling buildIndex(). By default, this file is located in tempdir()1 On HPC file systems, you can change TEMPDIR to a location that is more amenable to concurrent access. and will be removed when the session finishes.

AnnoyIndex_path(pre)
## [1] "/var/folders/r0/l4fjk6cj5xj0j3brt4bplpl40000gt/T//RtmpkDuFzV/file60522d7e9fe.idx"

If the index is to persist across sessions, the path of the index file can be directly specified in buildIndex. This can be used to construct an index object directly using the relevant constructors, e.g., AnnoyIndex(), HnswIndex(). However, it becomes the responsibility of the user to clean up any temporary indexing files after calculations are complete.

5 Session information

sessionInfo()
## R version 4.4.0 alpha (2024-03-27 r86216)
## Platform: aarch64-apple-darwin20
## Running under: macOS Ventura 13.6.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRblas.0.dylib 
## LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## time zone: America/New_York
## tzcode source: internal
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] BiocNeighbors_1.22.0 knitr_1.45           BiocStyle_2.32.0    
## 
## loaded via a namespace (and not attached):
##  [1] cli_3.6.2           rlang_1.1.3         xfun_0.43          
##  [4] jsonlite_1.8.8      S4Vectors_0.42.0    htmltools_0.5.8    
##  [7] stats4_4.4.0        sass_0.4.9          rmarkdown_2.26     
## [10] grid_4.4.0          evaluate_0.23       jquerylib_0.1.4    
## [13] fastmap_1.1.1       yaml_2.3.8          lifecycle_1.0.4    
## [16] bookdown_0.38       BiocManager_1.30.22 compiler_4.4.0     
## [19] codetools_0.2-19    Rcpp_1.0.12         BiocParallel_1.38.0
## [22] lattice_0.22-6      digest_0.6.35       R6_2.5.1           
## [25] parallel_4.4.0      bslib_0.6.2         Matrix_1.7-0       
## [28] tools_4.4.0         BiocGenerics_0.50.0 cachem_1.0.8