BiocNeighbors 1.3.2

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.

Both methods involve a component of randomness during index construction, though the k-nearest neighbors result is fully deterministic1 Except in the presence of ties, see `?findKNN`

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,] 8689 9674 1715 5268 4825 2953 2014 8495 6700 515
## [2,] 8143 3454 3678 2145 5704 7971 6335 3176 9265 8057
## [3,] 4085 100 7520 1328 99 3880 4237 6908 9623 2985
## [4,] 6690 2876 5359 7754 3015 9976 8018 9550 8479 1056
## [5,] 1427 8448 3824 3956 7901 7724 4494 6241 7797 3792
## [6,] 6898 702 6276 1713 1105 5904 8814 3967 7011 7320
```

`head(fout$distance)`

```
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.8959479 0.9201659 0.9779226 0.9790988 0.9855343 1.0032347 1.0035816
## [2,] 0.8560283 0.8889203 0.9085646 0.9368956 0.9434487 0.9462028 0.9579706
## [3,] 1.0082185 1.0320893 1.0358297 1.0723616 1.0759531 1.0763841 1.0776739
## [4,] 0.8793344 0.9825183 0.9874073 0.9999368 1.0109222 1.0184248 1.0370691
## [5,] 0.9546003 0.9844909 1.0127349 1.0525597 1.0642416 1.0690185 1.0731933
## [6,] 0.9988366 1.0190078 1.0199900 1.0313229 1.0501413 1.0602339 1.0619406
## [,8] [,9] [,10]
## [1,] 1.0097023 1.0158156 1.0189978
## [2,] 0.9587032 0.9589145 0.9620609
## [3,] 1.0873479 1.0910444 1.0922318
## [4,] 1.0619503 1.0677022 1.0833311
## [5,] 1.0744999 1.0772461 1.0793413
## [6,] 1.0876117 1.1194489 1.1296613
```

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] 4085 100 7520 1328 99 3880 4237 6908 9623 2985`

… with the following distances to those neighbors:

`fout$distance[3,]`

```
## [1] 1.008219 1.032089 1.035830 1.072362 1.075953 1.076384 1.077674 1.087348
## [9] 1.091044 1.092232
```

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,] 7557 5152 5390 1500 9906
## [2,] 6337 8172 1490 406 3071
## [3,] 3788 9556 3963 6570 5689
## [4,] 9050 338 5483 8974 3349
## [5,] 4123 2894 9297 9248 2616
## [6,] 8033 4703 9546 9229 4156
```

`head(qout$distance)`

```
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.7788202 0.8314470 0.8689862 0.8705281 0.8711024
## [2,] 0.8718284 0.9362180 0.9401400 1.0109214 1.0289175
## [3,] 0.8978702 0.9228632 0.9406342 0.9612989 0.9649704
## [4,] 0.9315198 0.9778405 1.0046366 1.0085137 1.0338306
## [5,] 0.7850513 0.9218201 0.9928727 1.0072714 1.0170828
## [6,] 0.7952307 0.9643012 0.9764935 0.9955798 1.0104670
```

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] 3788 9556 3963 6570 5689`

… with the following distances to those neighbors:

`qout$distance[3,]`

`## [1] 0.8978702 0.9228632 0.9406342 0.9612989 0.9649704`

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,] 4085 100 7520 1328 99
## [2,] 6690 2876 5359 7754 3015
## [3,] 1427 8448 3824 3956 7901
##
## $distance
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1.0082185 1.0320893 1.0358297 1.0723616 1.075953
## [2,] 0.8793344 0.9825183 0.9874073 0.9999368 1.010922
## [3,] 0.9546003 0.9844909 1.0127349 1.0525597 1.064242
```

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 3.6.0 (2019-04-26)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.2 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] BiocParallel_1.19.0 BiocNeighbors_1.3.2 knitr_1.23
## [4] BiocStyle_2.13.1
##
## loaded via a namespace (and not attached):
## [1] Rcpp_1.0.1 bookdown_0.11 lattice_0.20-38
## [4] digest_0.6.19 grid_3.6.0 stats4_3.6.0
## [7] magrittr_1.5 evaluate_0.14 stringi_1.4.3
## [10] S4Vectors_0.23.10 Matrix_1.2-17 rmarkdown_1.13
## [13] tools_3.6.0 stringr_1.4.0 parallel_3.6.0
## [16] xfun_0.7 yaml_2.2.0 compiler_3.6.0
## [19] BiocGenerics_0.31.3 BiocManager_1.30.4 htmltools_0.3.6
```

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.