BiocNeighbors 1.14.0

The *BiocNeighbors* package implements a few algorithms for exact nearest neighbor searching:

- The k-means for k-nearest neighbors (KMKNN) algorithm (Wang 2012) uses k-means clustering to create an index. Within each cluster, the distance of each of that cluster’s points to the cluster center are computed and used to sort all points. Given a query point, the distance to each cluster center is determined and the triangle inequality is applied to determine which points in each cluster warrant a full distance calculation.
- The vantage point (VP) tree algorithm (Yianilos 1993) involves constructing a tree where each node is located at a data point and is associated with a subset of neighboring points. Each node progressively partitions points into two subsets that are either closer or further to the node than a given threshold. Given a query point, the triangle inequality is applied at each node in the tree to determine if the child nodes warrant searching.
- The exhaustive search is a simple brute-force algorithm that computes distances to between all data and query points. This has the worst computational complexity but can actually be faster than the other exact algorithms in situations where indexing provides little benefit, e.g., data sets with few points and/or a very large number of dimensions.

Both KMKNN and VP-trees involve a component of randomness during index construction, though the k-nearest neighbors result is fully deterministic1 Except in the presence of ties, see `?"BiocNeighbors-ties"`

for details..

The most obvious application is to perform a k-nearest neighbors search. We’ll mock up an example here with a hypercube of points, for which we want to identify the 10 nearest neighbors for each point.

```
nobs <- 10000
ndim <- 20
data <- matrix(runif(nobs*ndim), ncol=ndim)
```

The `findKNN()`

method expects a numeric matrix as input with data points as the rows and variables/dimensions as the columns.
We indicate that we want to use the KMKNN algorithm by setting `BNPARAM=KmknnParam()`

(which is also the default, so this is not strictly necessary here).
We could use a VP tree instead by setting `BNPARAM=VptreeParam()`

.

```
fout <- findKNN(data, k=10, BNPARAM=KmknnParam())
head(fout$index)
```

```
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 6824 785 310 5417 6452 1299 8029 6280 1327 5011
## [2,] 6336 1355 8299 3386 7678 6633 3882 8351 7917 8375
## [3,] 976 2926 525 916 3486 8238 3259 2300 8044 6738
## [4,] 4318 9353 7170 4508 5422 9890 7656 2897 738 5625
## [5,] 7260 7473 225 9144 4646 969 4769 2857 6447 6142
## [6,] 8296 2670 3217 4491 585 3904 7244 8106 6281 2688
```

`head(fout$distance)`

```
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.9316278 0.9544263 0.9659454 0.9951629 1.0046510 1.0096569 1.0630784
## [2,] 0.8712304 0.8949821 0.9091715 0.9106557 0.9226406 0.9372379 0.9593607
## [3,] 0.9552110 0.9793939 1.0738635 1.1039845 1.1140267 1.1243279 1.1258000
## [4,] 1.1038792 1.1303407 1.1389502 1.1482181 1.1605684 1.1700002 1.1705975
## [5,] 0.8386672 0.8653343 0.8764472 0.8801504 0.9953194 1.0272324 1.0273986
## [6,] 0.8538452 0.9031763 0.9551028 0.9694123 0.9696303 0.9706063 1.0033187
## [,8] [,9] [,10]
## [1,] 1.0705245 1.0764675 1.0765348
## [2,] 0.9619467 0.9665224 0.9813825
## [3,] 1.1488759 1.1774701 1.1835828
## [4,] 1.1717133 1.1803322 1.1806312
## [5,] 1.0314364 1.0380102 1.0628315
## [6,] 1.0189871 1.0257382 1.0332624
```

Each row of the `index`

matrix corresponds to a point in `data`

and contains the row indices in `data`

that are its nearest neighbors.
For example, the 3rd point in `data`

has the following nearest neighbors:

`fout$index[3,]`

`## [1] 976 2926 525 916 3486 8238 3259 2300 8044 6738`

… with the following distances to those neighbors:

`fout$distance[3,]`

```
## [1] 0.9552110 0.9793939 1.0738635 1.1039845 1.1140267 1.1243279 1.1258000
## [8] 1.1488759 1.1774701 1.1835828
```

Note that the reported neighbors are sorted by distance.

Another application is to identify the k-nearest neighbors in one dataset based on query points in another dataset. Again, we mock up a small data set:

```
nquery <- 1000
ndim <- 20
query <- matrix(runif(nquery*ndim), ncol=ndim)
```

We then use the `queryKNN()`

function to identify the 5 nearest neighbors in `data`

for each point in `query`

.

```
qout <- queryKNN(data, query, k=5, BNPARAM=KmknnParam())
head(qout$index)
```

```
## [,1] [,2] [,3] [,4] [,5]
## [1,] 9806 3674 692 1647 9390
## [2,] 7799 2670 6302 1370 3062
## [3,] 7076 4098 3130 2343 6550
## [4,] 3463 4173 3170 4518 4232
## [5,] 8056 9714 8225 5218 5504
## [6,] 2278 3417 4590 6595 389
```

`head(qout$distance)`

```
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.9318871 0.9622434 0.9720072 1.0064636 1.0287397
## [2,] 0.9722240 0.9929964 1.0331243 1.0450943 1.0853969
## [3,] 0.9231742 0.9409917 0.9531869 0.9558733 0.9635372
## [4,] 1.0453552 1.0651827 1.1110755 1.1545569 1.1551394
## [5,] 0.8763046 0.9339019 0.9738064 0.9838785 0.9854353
## [6,] 0.9005429 0.9581917 0.9611703 0.9799628 1.0038721
```

Each row of the `index`

matrix contains the row indices in `data`

that are the nearest neighbors of a point in `query`

.
For example, the 3rd point in `query`

has the following nearest neighbors in `data`

:

`qout$index[3,]`

`## [1] 7076 4098 3130 2343 6550`

… with the following distances to those neighbors:

`qout$distance[3,]`

`## [1] 0.9231742 0.9409917 0.9531869 0.9558733 0.9635372`

Again, the reported neighbors are sorted by distance.

Users can perform the search for a subset of query points using the `subset=`

argument.
This yields the same result as but is more efficient than performing the search for all points and subsetting the output.

`findKNN(data, k=5, subset=3:5)`

```
## $index
## [,1] [,2] [,3] [,4] [,5]
## [1,] 976 2926 525 916 3486
## [2,] 4318 9353 7170 4508 5422
## [3,] 7260 7473 225 9144 4646
##
## $distance
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.9552110 0.9793939 1.0738635 1.1039845 1.1140267
## [2,] 1.1038792 1.1303407 1.1389502 1.1482181 1.1605684
## [3,] 0.8386672 0.8653343 0.8764472 0.8801504 0.9953194
```

If only the indices are of interest, users can set `get.distance=FALSE`

to avoid returning the matrix of distances.
This will save some time and memory.

`names(findKNN(data, k=2, get.distance=FALSE))`

`## [1] "index"`

It is also simple to speed up functions by parallelizing the calculations with the *BiocParallel* framework.

```
library(BiocParallel)
out <- findKNN(data, k=10, BPPARAM=MulticoreParam(3))
```

For multiple queries to a constant `data`

, the pre-clustering can be performed in a separate step with `buildIndex()`

.
The result can then be passed to multiple calls, avoiding the overhead of repeated clustering2 The algorithm type is automatically determined when `BNINDEX`

is specified, so there is no need to also specify `BNPARAM`

in the later functions..

```
pre <- buildIndex(data, BNPARAM=KmknnParam())
out1 <- findKNN(BNINDEX=pre, k=5)
out2 <- queryKNN(BNINDEX=pre, query=query, k=2)
```

The default setting is to search on the Euclidean distance.
Alternatively, we can use the Manhattan distance by setting `distance="Manhattan"`

in the `BiocNeighborParam`

object.

`out.m <- findKNN(data, k=5, BNPARAM=KmknnParam(distance="Manhattan"))`

Advanced users may also be interested in the `raw.index=`

argument, which returns indices directly to the precomputed object rather than to `data`

.
This may be useful inside package functions where it may be more convenient to work on a common precomputed object.

`sessionInfo()`

```
## R version 4.2.0 RC (2022-04-19 r82224)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 20.04.4 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.15-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.15-bioc/R/lib/libRlapack.so
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_GB 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] BiocParallel_1.30.0 BiocNeighbors_1.14.0 knitr_1.38
## [4] BiocStyle_2.24.0
##
## loaded via a namespace (and not attached):
## [1] Rcpp_1.0.8.3 magrittr_2.0.3 BiocGenerics_0.42.0
## [4] lattice_0.20-45 R6_2.5.1 rlang_1.0.2
## [7] fastmap_1.1.0 stringr_1.4.0 tools_4.2.0
## [10] parallel_4.2.0 grid_4.2.0 xfun_0.30
## [13] cli_3.3.0 jquerylib_0.1.4 htmltools_0.5.2
## [16] yaml_2.3.5 digest_0.6.29 bookdown_0.26
## [19] Matrix_1.4-1 BiocManager_1.30.17 S4Vectors_0.34.0
## [22] sass_0.4.1 evaluate_0.15 rmarkdown_2.14
## [25] stringi_1.7.6 compiler_4.2.0 bslib_0.3.1
## [28] stats4_4.2.0 jsonlite_1.8.0
```

Wang, X. 2012. “A Fast Exact k-Nearest Neighbors Algorithm for High Dimensional Search Using k-Means Clustering and Triangle Inequality.” *Proc Int Jt Conf Neural Netw* 43 (6): 2351–8.

Yianilos, P. N. 1993. “Data Structures and Algorithms for Nearest Neighbor Search in General Metric Spaces.” In *SODA*, 93:311–21. 194.