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$index)
##      [,1] [,2] [,3] [,4]  [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 6517 5034 6083 6280  3946 1321 2573 3903 8792  1391
## [2,]   15 3647 4237 4479  8097 4620  839 8823 2664  9162
## [3,] 8729  962 7956 5344 10000 1102 4762 8057 2112  2868
## [4,] 5049 4376 6067 3980  9598 3815 3879 3650 1812  6682
## [5,] 2691 8359  416  388  2793 9033 3814  233 7444  2077
## [6,] 9726 6706 1705 1265  6953 9735 1765 3452 6240  4581
head(fout$distance)
##           [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
## [1,] 0.8605417 0.9011844 0.9598055 0.9906568 1.0115165 1.0232428 1.0299177
## [2,] 0.8203998 0.8889937 0.9243639 0.9317232 0.9691805 0.9804098 1.0009714
## [3,] 0.7097339 0.8187694 0.8552614 0.9166747 0.9915828 0.9933022 0.9963664
## [4,] 0.8513043 0.9897790 0.9964214 1.0439152 1.0475429 1.0496386 1.0623977
## [5,] 0.9504657 0.9642309 0.9957683 0.9980729 1.0243515 1.0412277 1.0679247
## [6,] 0.9641368 0.9917504 0.9967526 1.0047925 1.0260675 1.0399781 1.0428491
##          [,8]     [,9]    [,10]
## [1,] 1.035740 1.042568 1.069985
## [2,] 1.010033 1.013638 1.021102
## [3,] 1.009564 1.026669 1.034802
## [4,] 1.068869 1.070686 1.088625
## [5,] 1.069522 1.075323 1.076468
## [6,] 1.056430 1.060908 1.063288

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$index)
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 3748 1319 2076 7046 8557
## [2,] 4620  750 6533 5689 1725
## [3,] 4609 8092 3628 5591 3505
## [4,] 4938 1787 7226 4689 5716
## [5,] 5349 2805 1739 3241 6318
## [6,] 3703 1693 8180 4667 3696
head(qout$distance)
##           [,1]      [,2]      [,3]      [,4]      [,5]
## [1,] 0.7973912 0.8206508 0.8604583 0.8850521 0.9127023
## [2,] 0.9411416 0.9566611 0.9824429 0.9873756 1.0442573
## [3,] 0.8824219 0.9730743 1.1062536 1.1107501 1.1252599
## [4,] 0.7889428 0.8185468 0.9280216 0.9744157 0.9912663
## [5,] 1.0451206 1.0672330 1.0854192 1.1135842 1.1168857
## [6,] 0.8135959 0.9004993 0.9239533 0.9281310 0.9418005

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/Rtmp1dmTIx/filedc223a75b28.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 3.6.1 (2019-07-05)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.3 LTS
## 
## Matrix products: default
## BLAS:   /home/biocbuild/bbs-3.10-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.10-bioc/R/lib/libRlapack.so
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=C              
##  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
##  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] BiocNeighbors_1.4.1 knitr_1.25          BiocStyle_2.14.0   
## 
## loaded via a namespace (and not attached):
##  [1] Rcpp_1.0.2          bookdown_0.14       lattice_0.20-38    
##  [4] digest_0.6.22       grid_3.6.1          stats4_3.6.1       
##  [7] magrittr_1.5        evaluate_0.14       rlang_0.4.1        
## [10] stringi_1.4.3       S4Vectors_0.24.0    Matrix_1.2-17      
## [13] rmarkdown_1.16      BiocParallel_1.20.0 tools_3.6.1        
## [16] stringr_1.4.0       parallel_3.6.1      xfun_0.10          
## [19] yaml_2.2.0          compiler_3.6.1      BiocGenerics_0.32.0
## [22] BiocManager_1.30.9  htmltools_0.4.0