fdars (version 0.3.3)

cluster.optim: Optimal Number of Clusters for Functional K-Means

Description

Determines the optimal number of clusters for functional k-means clustering using various criteria: elbow method, silhouette score, or Calinski-Harabasz index.

Usage

cluster.optim(
  fdataobj,
  ncl.range = 2:10,
  criterion = c("silhouette", "CH", "elbow"),
  metric = "L2",
  max.iter = 100,
  nstart = 10,
  seed = NULL,
  ...
)

Value

A list of class 'cluster.optim' with components:

optimal.k

Optimal number of clusters based on criterion

criterion

Name of criterion used

scores

Vector of criterion values for each k

ncl.range

Range of k values tested

models

List of cluster.kmeans objects for each k

best.model

The cluster.kmeans object for optimal k

Arguments

fdataobj

An object of class 'fdata'.

ncl.range

Range of number of clusters to evaluate. Default is 2:10.

criterion

Criterion to use for selecting optimal k:

"silhouette"

Mean silhouette coefficient (default). Higher is better.

"CH"

Calinski-Harabasz index. Higher is better.

"elbow"

Within-cluster sum of squares. Look for elbow in plot.

metric

Either a string ("L2", "L1", "Linf") or a metric function.

max.iter

Maximum iterations for k-means (default 100).

nstart

Number of random starts (default 10).

seed

Random seed for reproducibility.

...

Additional arguments passed to cluster.kmeans.

Details

Silhouette score: Measures how similar each curve is to its own cluster compared to other clusters. Values range from -1 to 1, with higher being better. Optimal k maximizes the mean silhouette.

Calinski-Harabasz index: Ratio of between-cluster to within-cluster dispersion. Higher values indicate better defined clusters. Optimal k maximizes CH.

Elbow method: Plots total within-cluster sum of squares vs k. The optimal k is at the "elbow" where adding more clusters doesn't significantly reduce WSS. This is subjective and best assessed visually using plot().

Examples

# Create functional data with 3 groups
set.seed(42)
t <- seq(0, 1, length.out = 50)
n <- 60
X <- matrix(0, n, 50)
true_k <- rep(1:3, each = 20)
for (i in 1:n) {
  if (true_k[i] == 1) {
    X[i, ] <- sin(2*pi*t) + rnorm(50, sd = 0.1)
  } else if (true_k[i] == 2) {
    X[i, ] <- cos(2*pi*t) + rnorm(50, sd = 0.1)
  } else {
    X[i, ] <- sin(4*pi*t) + rnorm(50, sd = 0.1)
  }
}
fd <- fdata(X, argvals = t)

# Find optimal k using silhouette
opt <- cluster.optim(fd, ncl.range = 2:6, criterion = "silhouette")
print(opt)
plot(opt)