DIBcont.Rd

\name{DIBcont}
\alias{DIBcont}
\title{Cluster Continuous Data Using the Deterministic Information Bottleneck Algorithm}
\description{
The \code{DIBcont} function implements the Deterministic Information Bottleneck (DIB) algorithm
for clustering continuous data. This method optimizes an information-theoretic objective to
preserve relevant information while forming concise and interpretable cluster representations
(Costa, Papatsouma & Markos, 2024).
}
\usage{
DIBcont(X, ncl, randinit = NULL, s = -1, scale = TRUE,
        maxiter = 100, nstart = 100, select_features = FALSE)
}
\arguments{
  \item{X}{
    A numeric matrix or data frame containing the continuous data to be clustered. All variables should be of type \code{numeric}.
  }
  \item{ncl}{
    An integer specifying the number of clusters to form.
  }
  \item{randinit}{
    Optional. A vector specifying initial cluster assignments. If \code{NULL}, cluster assignments are initialized randomly.
  }
\item{s}{
A numeric value or vector specifying the bandwidth parameter(s) for continuous variables. The values must be greater than \eqn{0}. The default value is \eqn{-1}, which enables the automatic selection of optimal bandwidth(s).
}
  \item{scale}{
    A logical value indicating whether the continuous variables should be scaled to have unit variance before clustering. Defaults to \code{TRUE}.
  }
  \item{maxiter}{
    The maximum number of iterations allowed for the clustering algorithm. Defaults to \eqn{100}.
  }
  \item{nstart}{
    The number of random initializations to run. The best clustering result (based on the information-theoretic criterion) is returned. Defaults to \code{100}.
  }
  \item{select_features}{
    Logical. If \code{TRUE}, uses an eigengap heuristic for feature selection, potentially improving clustering quality by reducing dimensionality. Defaults to \code{FALSE}.
  }
}

\value{
A list containing the following elements:
  \itemize{
    \item{\code{Cluster}: An integer vector indicating the cluster assignment for each observation.}
    \item{\code{Entropy}: A numeric value representing the entropy of the cluster assignments at convergence.}
    \item{\code{MutualInfo}: A numeric value representing the mutual information, \eqn{I(Y;T)}, between the underlying data distribution and the cluster assignments.}
    \item{\code{beta}: A numeric vector of the final beta values used during the iterative optimization.}
    \item{\code{s}: A numeric value or vector of bandwidth parameters used for the continuous variables. Typically, this will be a single value if all continuous variables share the same bandwidth.}
    \item{\code{ents}: A numeric vector tracking the entropy values over the iterations, providing insight into the convergence process.}
    \item{\code{mis}: A numeric vector tracking the mutual information values over the iterations.}
  }
}

\details{
The \code{DIBcont} function applies the Deterministic Information Bottleneck algorithm to cluster datasets comprising only continuous variables. This method leverages an information-theoretic objective to optimize the trade-off between data compression and the preservation of relevant information about the underlying data distribution.

The function utilizes the Gaussian kernel (Silverman, 1998) for estimating probability densities of continuous features. The kernel is defined as:

\deqn{K_c\left(\frac{x - x'}{s}\right) = \frac{1}{\sqrt{2\pi}} \exp\left\{-\frac{\left(x - x'\right)^2}{2s^2}\right\}, \quad s > 0.}

The bandwidth parameter \eqn{s}, which controls the smoothness of the density estimate, is automatically determined by the algorithm if not provided by the user.
}


\examples{
# Generate simulated continuous data
set.seed(123)
X <- matrix(rnorm(1000), ncol = 5)  # 200 observations, 5 features

# Run DIBcont with automatic bandwidth selection and multiple initializations
result <- DIBcont(X = X, ncl = 3, s = -1, nstart = 50)

# Print clustering results
print(result$Cluster)       # Cluster assignments
print(result$Entropy)       # Final entropy
print(result$MutualInfo)    # Mutual information
}
\seealso{
\code{\link{DIBmix}}, \code{\link{DIBcat}}
}
\author{
Efthymios Costa, Ioanna Papatsouma, Angelos Markos
}
\references{
Costa, E., Papatsouma, I., & Markos, A. (2024). A Deterministic Information Bottleneck Method for Clustering Mixed-Type Data. \emph{arXiv:2407.03389 [stat.ME]}. Retrieved from https://arxiv.org/abs/2407.03389

Silverman, B. W. (1998). Density estimation for statistics and data analysis (1st ed.). Routledge.
}
\keyword{clustering}