CLIQUE is a clustering algorithm that falls under the category of density-based methods, specifically designed for identifying clusters in high-dimensional datasets. Unlike traditional density-based algorithms like DBSCAN, which focus on identifying dense regions in the data space, CLIQUE operates on a different principle called “density-connected subspaces.” Let’s explore CLIQUE and then discuss model-based methods with a statistical approach:
CLIQUE (CLustering In QUEst)
CLIQUE is a density-based algorithm designed to identify clusters in high-dimensional datasets by discovering dense regions in subspaces of the feature space. It operates on the following principles:
- Grid-Based Partitioning:
- CLIQUE partitions the feature space into a grid of cells, with each cell representing a subspace of the data.
- The size of the grid cells is determined based on a user-defined parameter or by adaptive methods.
- Density Analysis:
- For each grid cell, CLIQUE calculates the density of data points within that cell.
- It identifies dense regions within grid cells by comparing their density to a user-defined threshold.
- Clustering Subspaces:
- CLIQUE identifies dense subspaces, known as density-connected subspaces, by considering neighboring grid cells with densities above the threshold.
- It connects these dense subspaces to form clusters in the high-dimensional space.
- Incremental Refinement:
- CLIQUE iteratively refines the clustering by merging overlapping density-connected subspaces and eliminating noise points.
Model-Based Methods – Statistical Approach
Model-based clustering algorithms use statistical models to represent the underlying structure of the data and identify clusters based on the fit of the data to these models. One common statistical approach is Gaussian mixture models (GMMs), which assume that the data is generated from a mixture of Gaussian distributions. The key steps involved in model-based clustering with a statistical approach include:
- Model Specification:
- Choose an appropriate probability distribution to represent the data, such as Gaussian distributions for continuous data or multinomial distributions for categorical data.
- Parameter Estimation:
- Estimate the parameters of the probability distribution, such as the mean, variance, and mixing coefficients, using maximum likelihood estimation (MLE) or expectation-maximization (EM) algorithms.
- Model Selection:
- Select the number of clusters or components in the mixture model using criteria such as Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC).
- Cluster Assignment:
- Assign data points to clusters based on the posterior probabilities or likelihoods computed from the fitted mixture model.
- Model Evaluation:
- Assess the quality of the clustering model using validation metrics such as silhouette score, Davies-Bouldin index, or log-likelihood.
CLIQUE is a density-based algorithm that identifies clusters in high-dimensional datasets by discovering dense regions in subspaces of the feature space. Model-based clustering algorithms with a statistical approach, such as Gaussian mixture models, use probabilistic models to represent the underlying structure of the data and identify clusters based on the fit of the data to these models. Both approaches offer different advantages and are suitable for different types of data and clustering tasks.