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$index)
##      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 9914 4887 1905 5420  886 7911 9385 6633 4443  7307
## [2,]  472 7043 3864   22 4758 1742 7150 2154  648  9269
## [3,] 2983 4217 6705 3479 9993 9038 2177 6777 6126  8163
## [4,] 8717 9615 4092 4330 7798 1944 5011 1028 8256  5285
## [5,] 8544 3641  348 6107 9659 2349  914 8990 3003  9151
## [6,] 5487 5502  605 8506  110 3400 1709 9257 2876  7274
head(fout$distance)
##           [,1]      [,2]      [,3]      [,4]      [,5]      [,6]     [,7]
## [1,] 0.8746893 0.9142388 0.9416809 0.9836461 1.0059603 1.0093969 1.016923
## [2,] 0.9342504 0.9876963 1.0723996 1.0802686 1.0895022 1.1108315 1.123464
## [3,] 0.7903494 0.9019915 0.9205718 0.9427502 0.9465615 0.9586173 0.985653
## [4,] 0.8401635 0.8422725 0.9640290 1.0012240 1.0118080 1.0222057 1.028501
## [5,] 0.9436089 0.9973082 1.0294535 1.0579594 1.0846288 1.1207398 1.122880
## [6,] 0.8672464 0.9721619 0.9863429 0.9867064 1.0011046 1.0268304 1.042644
##          [,8]     [,9]    [,10]
## [1,] 1.018853 1.038106 1.039073
## [2,] 1.130734 1.143806 1.153106
## [3,] 1.018336 1.030459 1.037817
## [4,] 1.031136 1.040623 1.041168
## [5,] 1.139928 1.155217 1.159286
## [6,] 1.049732 1.050953 1.060267

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$index)
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 9828 5920 6255   17 4432
## [2,] 2569  135 3802 3705 3990
## [3,] 8150 6144 8632 4597 2945
## [4,] 1558 3188  712 1813 4915
## [5,]  464 4117 9385 9844 2955
## [6,] 4372 7359 6682 1870  418
head(qout$distance)
##           [,1]      [,2]      [,3]      [,4]      [,5]
## [1,] 0.9509446 0.9660091 0.9772828 0.9929542 0.9930505
## [2,] 1.0248313 1.0255874 1.0346212 1.0599446 1.0846179
## [3,] 1.1336325 1.1553030 1.1573037 1.1610074 1.1670579
## [4,] 0.8689280 0.9612259 0.9707019 0.9786192 1.0004725
## [5,] 0.8250182 0.8269905 0.8936530 0.9698160 0.9773988
## [6,] 0.9199631 0.9365416 1.0380791 1.0584692 1.0680044

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-3.16-bioc\\tmpdir\\RtmpoX64Pd\\file3c04bb5dfd.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 4.2.1 (2022-06-23 ucrt)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows Server 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    
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] BiocNeighbors_1.16.0 knitr_1.40           BiocStyle_2.26.0    
## 
## loaded via a namespace (and not attached):
##  [1] Rcpp_1.0.9          magrittr_2.0.3      BiocGenerics_0.44.0
##  [4] BiocParallel_1.32.0 lattice_0.20-45     R6_2.5.1           
##  [7] rlang_1.0.6         fastmap_1.1.0       stringr_1.4.1      
## [10] tools_4.2.1         parallel_4.2.1      grid_4.2.1         
## [13] xfun_0.34           cli_3.4.1           jquerylib_0.1.4    
## [16] htmltools_0.5.3     yaml_2.3.6          digest_0.6.30      
## [19] bookdown_0.29       Matrix_1.5-1        BiocManager_1.30.19
## [22] S4Vectors_0.36.0    sass_0.4.2          codetools_0.2-18   
## [25] cachem_1.0.6        evaluate_0.17       rmarkdown_2.17     
## [28] stringi_1.7.8       compiler_4.2.1      bslib_0.4.0        
## [31] stats4_4.2.1        jsonlite_1.8.3