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$index)
##      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 7191 1462 4096 3121 2907 1516 1841 2792 7749  8251
## [2,]  438 5791  327 6616 2840 7244 4938 7626 1891  9606
## [3,] 6566  185 4028 5499 7924 4469 7770 1485  124  1483
## [4,] 7521 3625 1520 6983 3315 6498 4392 1281 3569   860
## [5,] 4648 3584 5404 8916  999 5006 3654 7227 9936  5280
## [6,] 4637 8330 1488 7770 7864 8986  185 5194 4892  8134
head(fout$distance)
##           [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
## [1,] 0.8708924 0.9201971 0.9778174 1.0183202 1.0234785 1.0301259 1.0595636
## [2,] 0.8885668 0.8919418 0.9135027 0.9238924 0.9469747 0.9561982 0.9860298
## [3,] 0.7205864 1.0103204 1.0300944 1.0570358 1.0636051 1.0699366 1.1028218
## [4,] 1.0429268 1.0746384 1.0890863 1.1089108 1.1372968 1.1413801 1.1541716
## [5,] 0.9937217 1.0027014 1.0347068 1.0525789 1.1410241 1.1661737 1.1766642
## [6,] 0.8931364 0.9494966 0.9624577 0.9634194 0.9882307 0.9974183 0.9984540
##           [,8]      [,9]    [,10]
## [1,] 1.0640060 1.0647048 1.069014
## [2,] 0.9873471 0.9949265 1.008371
## [3,] 1.1131444 1.1422718 1.145583
## [4,] 1.1713729 1.1752270 1.182554
## [5,] 1.1803154 1.1863912 1.210942
## [6,] 1.0074879 1.0219098 1.028828

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$index)
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 8431 2200 2114 4208 9732
## [2,] 9491 4517 6476 1727 6297
## [3,] 4697  166 3022 3391 1193
## [4,] 7114  206 4478 8399 1891
## [5,] 4439 3167 1112 7095 1774
## [6,] 9235 6646 1281 3133 3277
head(qout$distance)
##           [,1]      [,2]      [,3]      [,4]      [,5]
## [1,] 1.0445930 1.0707749 1.0805953 1.1079738 1.1312418
## [2,] 0.9895988 0.9994723 1.0012251 1.0509707 1.0870900
## [3,] 0.8710847 0.9248948 0.9709811 0.9844105 0.9930291
## [4,] 0.7749339 0.8814268 0.8843094 0.9072486 0.9114492
## [5,] 0.8673612 0.9486401 0.9687132 0.9850274 0.9986081
## [6,] 0.8231861 0.8742477 0.8788669 0.9018787 0.9058378

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] "F:\\biocbuild\\bbs-3.18-bioc\\tmpdir\\RtmpMHvReU\\file446040bf7356.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 4.3.2 (2023-10-31 ucrt)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows Server 2022 x64 (build 20348)
## 
## Matrix products: default
## 
## 
## locale:
## [1] LC_COLLATE=C                          
## [2] LC_CTYPE=English_United States.utf8   
## [3] LC_MONETARY=English_United States.utf8
## [4] LC_NUMERIC=C                          
## [5] LC_TIME=English_United States.utf8    
## 
## time zone: America/New_York
## tzcode source: internal
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] BiocNeighbors_1.20.2 knitr_1.45           BiocStyle_2.30.0    
## 
## loaded via a namespace (and not attached):
##  [1] cli_3.6.2           rlang_1.1.2         xfun_0.41          
##  [4] jsonlite_1.8.8      S4Vectors_0.40.2    htmltools_0.5.7    
##  [7] stats4_4.3.2        sass_0.4.8          rmarkdown_2.25     
## [10] grid_4.3.2          evaluate_0.23       jquerylib_0.1.4    
## [13] fastmap_1.1.1       yaml_2.3.8          lifecycle_1.0.4    
## [16] bookdown_0.37       BiocManager_1.30.22 compiler_4.3.2     
## [19] codetools_0.2-19    Rcpp_1.0.11         BiocParallel_1.36.0
## [22] lattice_0.22-5      digest_0.6.33       R6_2.5.1           
## [25] parallel_4.3.2      bslib_0.6.1         Matrix_1.6-4       
## [28] tools_4.3.2         BiocGenerics_0.48.1 cachem_1.0.8