DIBmix {IBclust} | R Documentation |
Deterministic Information Bottleneck Clustering for Mixed-Type Data
Description
The DIBmix
function implements the Deterministic Information Bottleneck (DIB) algorithm
for clustering datasets containing mixed-type variables, including categorical (nominal and ordinal)
and continuous variables. This method optimizes an information-theoretic objective to preserve
relevant information in the cluster assignments while achieving effective data compression
(Costa et al. 2025).
Usage
DIBmix(X, ncl, catcols, contcols, randinit = NULL,
lambda = -1, s = -1, scale = TRUE,
maxiter = 100, nstart = 100,
verbose = FALSE)
Arguments
X |
A data frame containing the input data to be clustered. It should include categorical variables
( |
ncl |
An integer specifying the number of clusters. |
catcols |
A vector indicating the indices of the categorical variables in |
contcols |
A vector indicating the indices of the continuous variables in |
randinit |
An optional vector specifying the initial cluster assignments. If |
lambda |
A numeric value or vector specifying the bandwidth parameter for categorical variables. The default value is |
s |
A numeric value or vector specifying the bandwidth parameter(s) for continuous variables. The values must be greater than |
scale |
A logical value indicating whether the continuous variables should be scaled to have unit variance before clustering. Defaults to |
maxiter |
The maximum number of iterations allowed for the clustering algorithm. Defaults to |
nstart |
The number of random initializations to run. The best clustering solution is returned. Defaults to |
verbose |
Logical. Default to |
Details
The DIBmix
function clusters data while retaining maximal information about the original variable
distributions. The Deterministic Information Bottleneck algorithm optimizes an information-theoretic
objective that balances information preservation and compression. Bandwidth parameters for categorical
(nominal, ordinal) and continuous variables are adaptively determined if not provided. This iterative
process identifies stable and interpretable cluster assignments by maximizing mutual information while
controlling complexity. The method is well-suited for datasets with mixed-type variables and integrates
information from all variable types effectively.
The following kernel functions are used to estimate densities for the clustering procedure:
-
Continuous variables: Gaussian kernel
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.
-
Nominal categorical variables: Aitchison & Aitken kernel
K_u\left(x = x' ; \lambda\right) = \begin{cases} 1-\lambda & \text{if } x = x' \\ \frac{\lambda}{\ell-1} & \text{otherwise} \end{cases}, \quad 0 \leq \lambda \leq \frac{\ell-1}{\ell}.
-
Ordinal categorical variables: Li & Racine kernel
K_o\left(x = x' ; \nu\right) = \begin{cases} 1 & \text{if } x = x' \\ \nu^{|x - x'|} & \text{otherwise} \end{cases}, \quad 0 \leq \nu \leq 1.
Here, s
, \lambda
, and \nu
are bandwidth or smoothing parameters, while \ell
is the number of levels of the categorical variable. s
and \lambda
are automatically determined by the algorithm if not provided by the user. For ordinal variables, the lambda parameter of the function is used to define \nu
.
Value
A list containing the following elements:
Cluster |
An integer vector giving the cluster assignments for each data point. |
Entropy |
A numeric value representing the entropy of the cluster assignments at convergence. |
MutualInfo |
A numeric value representing the mutual information, |
beta |
A numeric vector of the final beta values used in the iterative procedure. |
s |
A numeric vector of bandwidth parameters used for the continuous variables. |
lambda |
A numeric vector of bandwidth parameters used for the categorical variables. |
ents |
A numeric vector tracking the entropy values across iterations. |
mis |
A numeric vector tracking the mutual information values across iterations. |
Author(s)
Efthymios Costa, Ioanna Papatsouma, Angelos Markos
References
Costa E, Papatsouma I, Markos A (2025). “A Deterministic Information Bottleneck Method for Clustering Mixed-Type Data.” doi:10.48550/arXiv.2407.03389, arXiv:2407.03389, https://arxiv.org/abs/2407.03389.
Aitchison J, Aitken CG (1976). “Multivariate binary discrimination by the kernel method.” Biometrika, 63(3), 413–420.
Li Q, Racine J (2003). “Nonparametric estimation of distributions with categorical and continuous data.” Journal of Multivariate Analysis, 86(2), 266–292.
Silverman BW (1998). Density Estimation for Statistics and Data Analysis (1st Ed.). Routledge.
See Also
Examples
# Example dataset with categorical, ordinal, and continuous variables
set.seed(123)
data <- data.frame(
cat_var = factor(sample(letters[1:3], 100, replace = TRUE)), # Nominal categorical variable
ord_var = factor(sample(c("low", "medium", "high"), 100, replace = TRUE),
levels = c("low", "medium", "high"),
ordered = TRUE), # Ordinal variable
cont_var1 = rnorm(100), # Continuous variable 1
cont_var2 = runif(100) # Continuous variable 2
)
# Perform Mixed-Type Clustering
result <- DIBmix(X = data, ncl = 3, catcols = 1:2, contcols = 3:4)
# Print clustering results
print(result$Cluster) # Cluster assignments
print(result$Entropy) # Final entropy
print(result$MutualInfo) # Mutual information