Density and prototype clustering: DENCLUE, FLAME, PFCM, growing neural gas

Denclue: Gaussian-kernel hill climbing to density attractors, noise below xi. FlameClustering: fuzzy clustering by local approximation of memberships, as the reference C code. PossibilisticFcm: possibilistic fuzzy c-means started from fuzzy c-means. GrowingNeuralGas: Fritzke's growing neural gas, clusters are graph components. Identical to the Python arm morie.fn.clusterdensity.

Usage

Denclue(X, h, xi, eps = NULL, tol = 1e-10, maxit = 1000L)

FlameClustering(
  X,
  knn = 10L,
  outlier_threshold = -2,
  steps = 500L,
  epsilon = 1e-06
)

PossibilisticFcm(
  X,
  centers,
  a = 1,
  b = 1,
  m = 2,
  eta = 2,
  K = 1,
  tol = 1e-09,
  maxit = 1000L
)

GrowingNeuralGas(
  X,
  n_signals = 5000L,
  max_nodes = 30L,
  eps_b = 0.2,
  eps_n = 0.006,
  lam = 100L,
  alpha = 0.5,
  a_max = 50L,
  d = 0.995,
  seed = 1
)

Arguments

X: Data matrix (rows are points).
h: Kernel bandwidth.
xi: Density threshold for noise.
eps: Attractor merge distance (default h / 2).
tol: Convergence tolerance.
maxit: Maximum iterations.
knn: Number of neighbours.
outlier_threshold: Outlier density threshold in standard deviations.
steps, epsilon: FLAME iteration budget and tolerance.
centers: Initial centres (matrix).
a, b: Weights of memberships and typicalities.
m, eta: Fuzzifier and typicality exponent.
K: Scale of the typicality penalties.
n_signals, max_nodes: Signals presented and node cap.
eps_b, eps_n: Winner and neighbour learning rates.
lam: Insertion interval.
alpha: Error reduction on insertion.
a_max: Maximum edge age.
d: Error decay.
seed: Philox seed.

Value

List with cluster (0 = noise or outlier where applicable).

References

Hinneburg, A. and Gabriel, H.-H. (2007). DENCLUE 2.0: fast clustering based on kernel density estimation. Proceedings of IDA, 70-80.

Fu, L. and Medico, E. (2007). FLAME, a novel fuzzy clustering method for the analysis of DNA microarray data. BMC Bioinformatics 8, 3.

Pal, N. R., Pal, K., Keller, J. M. and Bezdek, J. C. (2005). A possibilistic fuzzy c-means clustering algorithm. IEEE Transactions on Fuzzy Systems 13, 517-530.

Fritzke, B. (1995). A growing neural gas network learns topologies. Advances in Neural Information Processing Systems 7, 625-632.

Examples

Denclue(matrix(c(0, 0.3, 0.1, 9, 9.2, 30)), 0.5, 0.2)$cluster
#> [1] 1 1 1 2 2 0
PossibilisticFcm(matrix(c(0, 1, 9, 10, 4)), matrix(c(0, 10)))$cluster
#> [1] 1 1 2 2 1