Standard Finite Normal Mixture Research Articles

A ground truth based comparative study on clustering of gene expression data

Given the variety of available clustering methods for gene expression data analysis, it is important to develop an appropriate and rigorous validation scheme to assess the performance and limitations of the most widely used clustering algorithms. In this paper, we present a ground truth based comparative study on the functionality, accuracy, and stability of five data clustering methods, namely hierarchical clustering, K-means clustering, self-organizing maps, standard finite normal mixture fitting, and a caBIG toolkit (VIsual Statistical Data Analyzer--VISDA), tested on sample clustering of seven published microarray gene expression datasets and one synthetic dataset. We examined the performance of these algorithms in both data-sufficient and data-insufficient cases using quantitative performance measures, including cluster number detection accuracy and mean and standard deviation of partition accuracy. The experimental results showed that VISDA, an interactive coarse-to-fine maximum likelihood fitting algorithm, is a solid performer on most of the datasets, while K-means clustering and self-organizing maps optimized by the mean squared compactness criterion generally produce more stable solutions than the other methods.

Magnetic resonance image analysis by information theoretic criteria and stochastic site models.

Quantitative analysis of magnetic resonance (MR) images is a powerful tool for image-guided diagnosis, monitoring, and intervention. The major tasks involve tissue quantification and image segmentation where both the pixel and context images are considered. To extract clinically useful information from images that might be lacking in prior knowledge, we introduce an unsupervised tissue characterization algorithm that is both statistically principled and patient specific. The method uses adaptive standard finite normal mixture and inhomogeneous Markov random field models, whose parameters are estimated using expectation-maximization and relaxation labeling algorithms under information theoretic criteria. We demonstrate the successful applications of the approach with synthetic data sets and then with real MR brain images.

Quantitative Analysis of MR Brain Image Sequences by Adaptive Self-Organizing Finite Mixtures

This paper presents an adaptive structure self-organizing finite mixture network for quantification of magnetic resonance (MR) brain image sequences. We present justification for the use of standard finite normal mixture model for MR images and formulate image quantification as a distribution learning problem. The finite mixture network parameters are updated such that the relative entropy between the true and estimated distributions is minimized. The new learning scheme achieves flexible classifier boundaries by forming winner-takes-in probability splits of the data allowing the data to contribute simultaneously to multiple regions. Hence, the result is unbiased and satisfies the asymptotic optimality properties of maximum likelihood. To achieve a fully automatic quantification procedure that can adapt to different slices in the MR image sequence, we utilize an information theoretic criterion that we have introduced recently, the minimum conditional bias/variance (MCBV) criterion. MCBV allows us to determine the suitable number of mixture components to represent the characteristics of each image in the sequence. We present examples to show that the new method yields very efficient and accurate performance compared to expectation-maximization, K-means, and competitive learning procedures.