sNN: Find Shared Nearest Neighbors

In dbscan: Density-Based Spatial Clustering of Applications with Noise (DBSCAN) and Related Algorithms

Find Shared Nearest Neighbors

Description

Calculates the number of shared nearest neighbors and creates a shared nearest neighbors graph.

Usage

sNN(
  x,
  k,
  kt = NULL,
  jp = FALSE,
  sort = TRUE,
  search = "kdtree",
  bucketSize = 10,
  splitRule = "suggest",
  approx = 0
)

## S3 method for class 'sNN'
sort(x, decreasing = TRUE, ...)

## S3 method for class 'sNN'
print(x, ...)

Arguments

x	a data matrix, a dist object or a kNN object.
k	number of neighbors to consider to calculate the shared nearest neighbors.
kt	minimum threshold on the number of shared nearest neighbors to build the shared nearest neighbor graph. Edges are only preserved if kt or more neighbors are shared.
jp	In regular sNN graphs, two points that are not neighbors can have shared neighbors. Javis and Patrick (1973) requires the two points to be neighbors, otherwise the count is zeroed out. TRUE uses this behavior.
sort	sort by the number of shared nearest neighbors? Note that this is expensive and sort = FALSE is much faster. sNN objects can be sorted using sort().
search	nearest neighbor search strategy (one of "kdtree", "linear" or "dist").
bucketSize	max size of the kd-tree leafs.
splitRule	rule to split the kd-tree. One of "STD", "MIDPT", "FAIR", "SL_MIDPT", "SL_FAIR" or "SUGGEST" (SL stands for sliding). "SUGGEST" uses ANNs best guess.
approx	use approximate nearest neighbors. All NN up to a distance of a factor of ⁠(1 + approx) eps⁠ may be used. Some actual NN may be omitted leading to spurious clusters and noise points. However, the algorithm will enjoy a significant speedup.
decreasing	logical; sort in decreasing order?
...	additional parameters are passed on.

Details

The number of shared nearest neighbors of two points p and q is the intersection of the kNN neighborhood of two points. Note: that each point is considered to be part of its own kNN neighborhood. The range for the shared nearest neighbors is [0, k]. The result is a n-by-k matrix called shared. Each row is a point and the columns are the point's k nearest neighbors. The value is the count of the shared neighbors.

The shared nearest neighbor graph connects a point with all its nearest neighbors if they have at least one shared neighbor. The number of shared neighbors can be used as an edge weight. Javis and Patrick (1973) use a slightly modified (see parameter jp) shared nearest neighbor graph for clustering.

Value

An object of class sNN (subclass of kNN and NN) containing a list with the following components:

id	a matrix with ids.
dist	a matrix with the distances.
shared	a matrix with the number of shared nearest neighbors.
k	number of k used.
metric	the used distance metric.

Author(s)

Michael Hahsler

References

R. A. Jarvis and E. A. Patrick. 1973. Clustering Using a Similarity Measure Based on Shared Near Neighbors. IEEE Trans. Comput. 22, 11 (November 1973), 1025-1034. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1109/T-C.1973.223640")}

See Also

Other NN functions: NN, comps(), frNN(), kNN(), kNNdist()

Examples

data(iris)
x <- iris[, -5]

# finding kNN and add the number of shared nearest neighbors.
k <- 5
nn <- sNN(x, k = k)
nn

# shared nearest neighbor distribution
table(as.vector(nn$shared))

# explore number of shared points for the k-neighborhood of point 10
i <- 10
nn$shared[i,]

plot(nn, x)

# apply a threshold to create a sNN graph with edges
# if more than 3 neighbors are shared.
nn_3 <- sNN(nn, kt = 3)
plot(nn_3, x)

# get an adjacency list for the shared nearest neighbor graph
adjacencylist(nn_3)

dbscan documentation built on June 29, 2024, 1:07 a.m.