A Penalized Matrix Normal Mixture Model for Clustering Matrix Data

Along with advances in technology, matrix data, such as medical/industrial images, have emerged in many practical fields. These data usually have high dimensions and are not easy to cluster due to their intrinsic correlated structure among rows and columns. Most approaches convert matrix data to multi dimensional vectors and apply conventional clustering methods to them, and thus, suffer from an extreme high-dimensionality problem as well as a lack of interpretability of the correlated structure among row/column variables. Recently, a regularized model was proposed for clustering matrix-valued data by imposing a sparsity structure for the mean signal of each cluster. We extend their approach by regularizing further on the covariance to cope better with the curse of dimensionality for large size images. A penalized matrix normal mixture model with lasso-type penalty terms in both mean and covariance matrices is proposed, and then an expectation maximization algorithm is developed to estimate the parameters. The proposed method has the competence of both parsimonious modeling and reflecting the proper conditional correlation structure. The estimators are consistent, and their limiting distributions are derived. We applied the proposed method to simulated data as well as real datasets and measured its clustering performance with the clustering accuracy (ACC) and the adjusted rand index (ARI). The experiment results show that the proposed method performed better with higher ACC and ARI than those of conventional methods.

A Bayesian Neo-Normal Mixture Model (Nenomimo) for MRI-Based Brain Tumor Segmentation

The detection of a brain tumor through magnetic resonance imaging (MRI) is still challenging when the image is in low quality. Image segmentation could be done to provide a clear brain tumor area as the region of interest. In this study, we propose an improved model-based clustering approach for MRI-based image segmentation. The main contribution is the use of the adaptive neo-normal distributions in the form of a finite mixture model that could handle both symmetrical and asymmetrical patterns in an MRI image. The neo-normal mixture model (Nenomimo) also resolves the limitation of the Gaussian mixture model (GMM) and the generalized GMM (GGMM), which are limited by the short-tailed form of their distributions and their sensitivity against noise. Model estimation is done through an optimization process using the Bayesian method coupled with a Markov chain Monte Carlo (MCMC) approach, and it employs a silhouette coefficient to find the optimum number of clusters. The performance of the Nenomimo was evaluated against the GMM and the GGMM using the misclassification ratio (MCR). Finally, this study discovered that the Nenomimo provides better segmentation results for both simulated and real data sets, with an average MCR for MRI brain tumor image segmentation of less than 3%.