NNS SD-based Clustering

Clusters a set of variables by iteratively extracting Stochastic Dominance (SD)-efficient sets, subject to a minimum cluster size.

Usage

NNS.SD.cluster(
  data,
  degree = 1,
  type = "discrete",
  min_cluster = 1,
  dendrogram = FALSE
)

Arguments

data

A numeric matrix or data frame of variables to be clustered.

degree

Numeric options: (1, 2, 3). Degree of stochastic dominance test.

type

Character, either "discrete" (default) or "continuous"; specifies the type of CDF.

min_cluster

Integer. The minimum number of elements required for a valid cluster.

dendrogram

Logical; FALSE (default). If TRUE, a dendrogram is produced based on a simple "distance" measure between clusters.

Value

A list with the following components:

• Clusters: A named list of cluster memberships where each element is the set of variable names belonging to that cluster.

• Dendrogram (optional): If dendrogram = TRUE, an hclust object is also returned.

Details

The function applies NNS.SD.efficient.set iteratively, peeling off the SD-efficient set at each step if it meets or exceeds min_cluster in size, until no more subsets can be extracted or all variables are exhausted. Variables in each SD-efficient set form a cluster, with any remaining variables aggregated into the final cluster if it meets the min_cluster threshold.

References

Viole, F. and Nawrocki, D. (2016) "LPM Density Functions for the Computation of the SD Efficient Set." Journal of Mathematical Finance, 6, 105-126. doi:10.4236/jmf.2016.61012 .

Viole, F. (2017) "A Note on Stochastic Dominance." doi:10.2139/ssrn.3002675

Author

Fred Viole, OVVO Financial Systems

Examples

if (FALSE) { # \dontrun{
set.seed(123)
x <- rnorm(100)
y <- rnorm(100)
z <- rnorm(100)
A <- cbind(x, y, z)

# Perform SD-based clustering (degree 1), requiring at least 2 elements per cluster
results <- NNS.SD.cluster(data = A, degree = 1, min_cluster = 2)
print(results$Clusters)

# Produce a dendrogram as well
results_with_dendro <- NNS.SD.cluster(data = A, degree = 1, min_cluster = 2, dendrogram = TRUE)
} # }