Detecting nearest neighbors using the kmknn package

In kmknn: k-Means for k-Nearest Neighbors

require(knitr)
opts_chunk$set(error=FALSE, message=FALSE, warning=FALSE)
library(kmknn)

Introduction

The r Biocpkg("kmknn") package provides an implementation of the k-means for k-nearest neighbors algorithm, as described by @wang2012fast. For a dataset with $N$ points, the pre-training is done as follows:

1. Apply k-means clustering to all points, partitioning the data into $\sqrt{N}$ clusters.
2. Compute the distance from each data point to its cluster center.
3. Store the cluster identities and distances.

For each query point, identification of the nearest neighbors is done as follows:

1. Start with a threshold distance $d$ to the current kth-nearest neighbor (this can be set with arbitrary points).
2. Compute the distance from the query to each cluster center.
3. For any given cluster center, apply the triangle inequality on the query-center distance, the center-point distances and $d$. Only compute query-point distances for points where the triangle inequality holds.
4. Update $d$ with the new closest kth-nearest neighbor and repeat for the next cluster.

The pre-clustering arranges the points in a manner that effectively reduces the search space, even in high-dimensional data. Note that, while kmeans itself is random, the k-nearest neighbors result is fully deterministic^[Except in the presence of ties, see ?findKNN for details.].

The algorithm is implemented in a combination of R and C++, derived from code in r Biocpkg("cydar") [@lun2017testing]. We observe 2-5-fold speed-ups in 20- to 50-dimensional data, compared to KD-trees in r CRANpkg("FNN") and r CRANpkg("RANN") (see https://github.com/LTLA/OkNN2018 for timings). This is consistent with results from @wang2012fast.

Identifying k-nearest neighbors

The most obvious application is to perform a k-nearest neighbors search. The findKNN() function expects a numeric matrix as input with data points as the rows and variables/dimensions as the columns. 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)

fout <- findKNN(data, k=10)
head(fout$index)
head(fout$distance)

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,]

... with the following distances to those neighbors:

fout$distance[3,]

Note that the reported neighbors are sorted by distance.

Querying k-nearest neighbors

Another application is to identify the k-nearest neighbors in one dataset based on query points in another dataset. This is achieved using the queryKNN() function:

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

qout <- queryKNN(data, query, k=5)
head(qout$index)
head(qout$distance)

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,]

... with the following distances to those neighbors:

qout$distance[3,]

Again, the reported neighbors are sorted by distance.

Identifying all neighbors within range

Another application is to identify all neighboring points within a certain (Euclidean) distance of the current point. This is done using the findNeighbors() function:

fout <- findNeighbors(data, threshold=1)
head(fout$index)
head(fout$distance)

Each entry of the index list corresponds to a point in data and contains the row indices in data that are within threshold. For example, the 3rd point in data has the following neighbors:

fout$index[[3]]

... with the following distances to those neighbors:

fout$distance[[3]]

Note that, for this function, the reported neighbors are not sorted by distance. The order of the output is completely arbitrary and will vary depending on the random seed. However, the identity of the neighbors is fully deterministic.

The queryNeighbors() function is also provided for identifying all points within a certain distance of a query point. This is analogous to queryKNN() for identifying the nearest neighbors of a query.

Further options

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)

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))

For multiple queries to a constant data, the pre-clustering can be performed in a separate step with precluster(). The result can then be passed to multiple calls, avoiding the overhead of repeated clustering.

pre <- precluster(data)
out1 <- findKNN(precomputed=pre, k=5)
out2 <- queryKNN(precomputed=pre, query=query, k=2)
out3 <- findNeighbors(precomputed=pre, threshold=2)

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 during package development where it is more convenient to work on the common precomputed object.

Use case with single-cell RNA-seq data

To demonstrate a practical use of this package, let's have a look at a small single-cell RNA seq dataset from the r Biocexptpkg("scRNAseq") package. The allen dataset contains a subset of cells from a study of the mouse visual cortex [@tasic2016adult].

library(scRNAseq)
data(allen)

We use the r Biocpkg("scater") package [@mccarthy2017scater] to obtain the first 20 principal components of the log-normalized expression matrix.

library(scater)
sce <- as(allen, "SingleCellExperiment")
sce <- normalize(sce, exprs_values="tophat_counts")
sce <- runPCA(sce, ncomponents=50)
dim(reducedDim(sce, "PCA"))

We can then identify cels that are nearest neighbors of each other using findKNN(). This is the basis of a number of procedures such as shared nearest-neighbors clustering [@xu2015identification] and mutual nearest neighbors batch correction [@haghverdi2018batch].

nns <- findKNN(reducedDim(sce, "PCA"), k=10)
head(nns$index)
head(nns$distance)

Session information

sessionInfo()

References

kmknn documentation built on Nov. 1, 2018, 4:21 a.m.