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$index)
##      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 9029 8027 2917 3095 1741  993   46 9150 6089  9519
## [2,] 1547 4800 6860 2301 5008 6184 3439  506 7117  5209
## [3,] 9602 6522 6694 2036 4976 6993  660  467 3733  1447
## [4,] 7477 4276 1108 9859 5371 9573 6651  768  152  8384
## [5,] 6578 2381 3130  969 8100 9944 8742 2739 7167  2018
## [6,] 9823 4219 8196 1573 2633 9070 6223 1259 2742   317
head(fout$distance)
##           [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
## [1,] 0.9087563 0.9343576 0.9347140 1.0349810 1.0577810 1.0673149 1.1129901
## [2,] 0.8973757 0.9503361 0.9542246 0.9850744 1.0054473 1.0234799 1.0377213
## [3,] 0.9285746 0.9432272 0.9434503 0.9592357 0.9711123 0.9745569 0.9797416
## [4,] 0.7483439 0.9228959 0.9531658 0.9778813 1.0250983 1.0392928 1.0474914
## [5,] 0.9112917 0.9257460 0.9629084 0.9707109 0.9809361 1.0048245 1.0293660
## [6,] 0.9647995 0.9920351 1.0091248 1.0317351 1.0323133 1.0497558 1.0500126
##           [,8]      [,9]     [,10]
## [1,] 1.1133852 1.1186256 1.1307123
## [2,] 1.0397594 1.0435059 1.0454148
## [3,] 0.9853271 0.9886528 0.9957427
## [4,] 1.0547801 1.0624410 1.0645828
## [5,] 1.0814184 1.0824766 1.0932744
## [6,] 1.0612317 1.0615163 1.0632228

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$index)
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 3663 6964 7208 8609 2757
## [2,] 5938 4834 5184 4502 1547
## [3,] 7779 2441 8523 5783 1266
## [4,] 1266  650 6017 5571 3787
## [5,]  663 3275 2695 3148 2146
## [6,] 4350 7500  102 6155 1944
head(qout$distance)
##           [,1]      [,2]      [,3]      [,4]      [,5]
## [1,] 0.8507525 0.8554255 0.9079689 0.9630135 0.9758449
## [2,] 0.7649354 0.9067363 0.9191303 0.9256787 0.9549022
## [3,] 0.8744318 0.8982485 0.9080981 0.9415722 0.9811068
## [4,] 0.9711310 0.9856623 1.0184327 1.0205659 1.0536278
## [5,] 0.8746908 0.8758898 1.0192007 1.0312262 1.0363630
## [6,] 1.0116752 1.0203203 1.0655837 1.0705638 1.0816413

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/Rtmp0PrimQ/fileee1c1cf2cbe2.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 Patched (2024-04-24 r86482)
## Platform: aarch64-apple-darwin20
## Running under: macOS Ventura 13.6.6
## 
## 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] C/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_1.23.0 knitr_1.46           BiocStyle_2.33.0    
## 
## 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_0.43.0    htmltools_0.5.8.1  
##  [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_0.39       BiocManager_1.30.22 compiler_4.4.0     
## [19] codetools_0.2-20    Rcpp_1.0.12         BiocParallel_1.39.0
## [22] lattice_0.22-6      digest_0.6.35       R6_2.5.1           
## [25] parallel_4.4.0      bslib_0.7.0         Matrix_1.7-0       
## [28] tools_4.4.0         BiocGenerics_0.51.0 cachem_1.0.8