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$index)
##      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 7585 6096 5103 3529 9976 3415 1910 2404 9571  1648
## [2,] 8835 7063 2014 1742 8736 7701 6900 5101 4778  8465
## [3,] 3076 2390 3752 8468 5212 5401 2678 6416 4012  2065
## [4,] 3572  109 7240 9176 6278 2866 6706 2588 8903  2663
## [5,] 6228  287 9535  836 1177 3209 7709 9800 7773  4041
## [6,] 7591 9579 1050 3651 7984 6208 6250 6345 3925  8118
head(fout$distance)
##           [,1]      [,2]      [,3]      [,4]      [,5]      [,6]     [,7]
## [1,] 0.8562882 0.9785632 0.9955938 1.0029528 1.0154270 1.0189490 1.036193
## [2,] 0.8980052 0.9264596 0.9304165 0.9488965 0.9520898 0.9711837 0.988787
## [3,] 0.8909540 0.9162792 0.9691771 1.0108618 1.0434083 1.0516258 1.078825
## [4,] 0.8938934 1.0189710 1.0424507 1.0498170 1.0501077 1.0742526 1.085795
## [5,] 0.9439647 1.0002828 1.0523891 1.0920228 1.0920416 1.0932543 1.098912
## [6,] 1.1933516 1.2220123 1.2371436 1.2576003 1.2633315 1.2724845 1.278140
##           [,8]      [,9]    [,10]
## [1,] 1.0381757 1.0398611 1.056635
## [2,] 0.9930208 0.9975103 1.002489
## [3,] 1.0908662 1.0932020 1.093322
## [4,] 1.0986246 1.1096017 1.110590
## [5,] 1.1026709 1.1068655 1.109273
## [6,] 1.2812349 1.2950578 1.306112

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$index)
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 9291 8417 4496  944 1505
## [2,] 8223 6341 6101 3826 8639
## [3,] 6639 2815  622 7802 5025
## [4,] 4314 3986 2075 1006 9606
## [5,]  729 5634 6383 8336 6407
## [6,] 6261 6205 8184 9407 8448
head(qout$distance)
##           [,1]      [,2]      [,3]      [,4]      [,5]
## [1,] 1.0299851 1.0347896 1.0756702 1.0787002 1.0796717
## [2,] 0.9112312 1.0651323 1.0655141 1.1191463 1.1643677
## [3,] 0.8830458 0.9194919 0.9801800 1.0236783 1.0753007
## [4,] 0.7582997 0.8892292 0.9390271 0.9575239 0.9592733
## [5,] 0.8588887 0.9869007 1.0197400 1.0462971 1.0939988
## [6,] 0.7314596 0.8228635 0.8780414 0.9247340 0.9578670

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] "/tmp/RtmpVyyuJN/fileb8bb514afcb5.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 4.1.1 Patched (2021-08-22 r80813)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Mojave 10.14.6
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] BiocNeighbors_1.12.0 knitr_1.36           BiocStyle_2.22.0    
## 
## loaded via a namespace (and not attached):
##  [1] Rcpp_1.0.7          magrittr_2.0.1      BiocGenerics_0.40.0
##  [4] BiocParallel_1.28.0 lattice_0.20-45     R6_2.5.1           
##  [7] rlang_0.4.12        fastmap_1.1.0       stringr_1.4.0      
## [10] tools_4.1.1         parallel_4.1.1      grid_4.1.1         
## [13] xfun_0.27           jquerylib_0.1.4     htmltools_0.5.2    
## [16] yaml_2.2.1          digest_0.6.28       bookdown_0.24      
## [19] Matrix_1.3-4        BiocManager_1.30.16 S4Vectors_0.32.0   
## [22] sass_0.4.0          evaluate_0.14       rmarkdown_2.11     
## [25] stringi_1.7.5       compiler_4.1.1      bslib_0.3.1        
## [28] stats4_4.1.1        jsonlite_1.7.2