A clustering procedure for three-way RNA sequencing data using data transformations and matrix-variate Gaussian mixture models

RNA sequencing of time-course experiments results in three-way count data where the dimensions are the genes, the time points and the biological units. Clustering RNA-seq data allows to extract groups of co-expressed genes over time. After standardisation, the normalised counts of individual genes across time points and biological units have similar properties as compositional data. We propose the following procedure to suitably cluster three-way RNA-seq data: (1) pre-process the RNA-seq data by calculating the normalised expression profiles, (2) transform the data using the additive log ratio transform to map the composition in the D-part Aitchison simplex to a D - 1 -dimensional Euclidean vector, (3) cluster the transformed RNA-seq data using matrix-variate Gaussian mixture models and (4) assess the quality of the overall cluster solution and of individual clusters based on cluster separation in the transformed space using density-based silhouette information and on compactness of the cluster in the original space using cluster maps as a suitable visualisation. The proposed procedure is illustrated on RNA-seq data from fission yeast and results are also compared to an analogous two-way approach after flattening out the biological units.

BRAQUE: Bayesian Reduction for Amplified Quantization in UMAP Embedding

Single-cell biology has revolutionized the way we understand biological processes. In this paper, we provide a more tailored approach to clustering and analyzing spatial single-cell data coming from immunofluorescence imaging techniques. We propose Bayesian Reduction for Amplified Quantization in UMAP Embedding (BRAQUE) as an integrative novel approach, from data preprocessing to phenotype classification. BRAQUE starts with an innovative preprocessing, named Lognormal Shrinkage, which is able to enhance input fragmentation by fitting a lognormal mixture model and shrink each component towards its median, in order to help further the clustering step in finding more separated and clear clusters. Then, BRAQUE's pipeline consists of a dimensionality reduction step performed using UMAP, and a clustering performed using HDBSCAN on UMAP embedding. In the end, clusters are assigned to a cell type by experts, using effects size measures to rank markers and identify characterizing markers (Tier 1), and possibly characterize markers (Tier 2). The number of total cell types in one lymph node detectable with these technologies is unknown and difficult to predict or estimate. Therefore, with BRAQUE, we achieved a higher granularity than other similar algorithms such as PhenoGraph, following the idea that merging similar clusters is easier than splitting unclear ones into clear subclusters.

A Labeled GM-PHD Filter for Explicitly Tracking Multiple Targets

In this study, an explicit track continuity algorithm is proposed for multitarget tracking (MTT) based on the Gaussian mixture (GM) implementation of the probability hypothesis density (PHD) filter. Trajectory maintenance and multitarget state extraction in the GM-PHD filter have not been effectively integrated to date. To address this problem, we propose an improved GM-PHD filter. In this approach, the Gaussian components are classified and labeled, and multitarget state extraction is converted into multiple single-state extractions. This provides the identity label of the individual target and can shield against the negative effects of clutter in the prior density region on the estimates, thus realizing the integration of trajectory maintenance with state extraction in the GM-PHD filter. As no additional associated procedures are required, the overall real-time performance of the proposed filter is similar to or slightly lower than that of the basic GM-PHD filter. The results of numerical experiments demonstrate that the proposed approach can achieve explicit track continuity.

Multiplicative Decomposition of Heterogeneity in Mixtures of Continuous Distributions

A system's heterogeneity (diversity) is the effective size of its event space, and can be quantified using the Rényi family of indices (also known as Hill numbers in ecology or Hannah-Kay indices in economics), which are indexed by an elasticity parameter q≥0. Under these indices, the heterogeneity of a composite system (the γ-heterogeneity) is decomposable into heterogeneity arising from variation within and between component subsystems (the α- and β-heterogeneity, respectively). Since the average heterogeneity of a component subsystem should not be greater than that of the pooled system, we require that γ≥α. There exists a multiplicative decomposition for Rényi heterogeneity of composite systems with discrete event spaces, but less attention has been paid to decomposition in the continuous setting. We therefore describe multiplicative decomposition of the Rényi heterogeneity for continuous mixture distributions under parametric and non-parametric pooling assumptions. Under non-parametric pooling, the γ-heterogeneity must often be estimated numerically, but the multiplicative decomposition holds such that γ≥α for q>0. Conversely, under parametric pooling, γ-heterogeneity can be computed efficiently in closed-form, but the γ≥α condition holds reliably only at q=1. Our findings will further contribute to heterogeneity measurement in continuous systems.

Preliminary results of computer-aided diagnosis for magnetic resonance imaging of solid breast lesions

PURPOSE

The present study aimed to determine suitable optimal classifiers and investigate the general applicability of computer-aided diagnosis (CAD) to compare magnetic resonance (MR)-CAD with MR imaging (MRI) in distinguishing benign from malignant solid breast masses.

METHODS

We analyzed a total of 251 patients (mean age: 44.8 ± 12.3 years; range: 21-81 years) with 274 breast masses (154 benign masses, 120 malignant masses) using a Gaussian mixture model and a random forest machine model for segmentation and classification.

RESULTS

The diagnostic performance of MRI alone and MRI plus CAD were compared with respect to sensitivity, specificity, and area under the curve (AUC), using receiver operating characteristic curve analysis. The discriminating power to detect malignancy using MR-CAD with an AUC of 0.955 (sensitivity was 95.8% and the specificity was 92.9%) was significantly higher than that of MRI alone with an AUC of 0.785 (sensitivity was 71.7% and the specificity was 85.7%).

CONCLUSION

CAD is feasible to differentiate breast lesions, and it can complement MRI, thereby making it easier to diagnose breast lesions and obviating the need for unnecessary biopsies.

A study of the properties of Gaussian mixture model for stable isotope standard quantification in MALDI-TOF MS

The quantification of peptides in Matrix assisted laser desorption/ionization time-of-flight mass spectrum analysis coupled with stable isotope standards has been used to quantify native peptides under many experimental conditions. This approach has difficulties quantifying samples containing peptides with ion currents in overlapping (convolved) spectra. In a previous article we proposed a reparametrized Gaussian mixture model based on the known characteristics of the peptides that could also accommodate overlapping spectra. We demonstrated the application of our model in a series of single and overlapping peptides quantification experiments. Here, we focus solely on studying the properties of our approach and examine the characteristics of the GMM approach in convolved peptides using simulated spectra and provide a method for simulating these spectra.

Quantitative reproducibility analysis for identifying reproducible targets from high-throughput experiments

BACKGROUND

High-throughput assays are widely used in biological research to select potential targets. One single high-throughput experiment can efficiently study a large number of candidates simultaneously, but is subject to substantial variability. Therefore it is scientifically important to performance quantitative reproducibility analysis to identify reproducible targets with consistent and significant signals across replicate experiments. A few methods exist, but all have limitations.

METHODS

In this paper, we propose a new method for identifying reproducible targets. Considering a Bayesian hierarchical model, we show that the test statistics from replicate experiments follow a mixture of multivariate Gaussian distributions, with the one component with zero-mean representing the irreproducible targets.

RESULTS

A target is thus classified as reproducible or irreproducible based on its posterior probability belonging to the reproducible components. We study the performance of our proposed method using simulations and a real data example.

CONCLUSION

The proposed method is shown to have favorable performance in identifying reproducible targets compared to other methods.

Iterative Diffusion-Based Distributed Cubature Gaussian Mixture Filter for Multisensor Estimation

In this paper, a distributed cubature Gaussian mixture filter (DCGMF) based on an iterative diffusion strategy (DCGMF-ID) is proposed for multisensor estimation and information fusion. The uncertainties are represented as Gaussian mixtures at each sensor node. A high-degree cubature Kalman filter provides accurate estimation of each Gaussian mixture component. An iterative diffusion scheme is utilized to fuse the mean and covariance of each Gaussian component obtained from each sensor node. The DCGMF-ID extends the conventional diffusion-based fusion strategy by using multiple iterative information exchanges among neighboring sensor nodes. The convergence property of the iterative diffusion is analyzed. In addition, it is shown that the convergence of the iterative diffusion can be interpreted from the information-theoretic perspective as minimization of the Kullback-Leibler divergence. The performance of the DCGMF-ID is compared with the DCGMF based on the average consensus (DCGMF-AC) and the DCGMF based on the iterative covariance intersection (DCGMF-ICI) via a maneuvering target-tracking problem using multiple sensors. The simulation results show that the DCGMF-ID has better performance than the DCGMF based on noniterative diffusion, which validates the benefit of iterative information exchanges. In addition, the DCGMF-ID outperforms the DCGMF-ICI and DCGMF-AC when the number of iterations is limited.

Cubature Information SMC-PHD for Multi-Target Tracking

In multi-target tracking, the key problem lies in estimating the number and states of individual targets, in which the challenge is the time-varying multi-target numbers and states. Recently, several multi-target tracking approaches, based on the sequential Monte Carlo probability hypothesis density (SMC-PHD) filter, have been presented to solve such a problem. However, most of these approaches select the transition density as the importance sampling (IS) function, which is inefficient in a nonlinear scenario. To enhance the performance of the conventional SMC-PHD filter, we propose in this paper two approaches using the cubature information filter (CIF) for multi-target tracking. More specifically, we first apply the posterior intensity as the IS function. Then, we propose to utilize the CIF algorithm with a gating method to calculate the IS function, namely CISMC-PHD approach. Meanwhile, a fast implementation of the CISMC-PHD approach is proposed, which clusters the particles into several groups according to the Gaussian mixture components. With the constructed components, the IS function is approximated instead of particles. As a result, the computational complexity of the CISMC-PHD approach can be significantly reduced. The simulation results demonstrate the effectiveness of our approaches.

Detection and tracking of overlapping cell nuclei for large scale mitosis analyses

Background

Cell culture on printed micropatterns slides combined with automated fluorescent microscopy allows for extraction of tens of thousands of videos of small isolated growing cell clusters. The analysis of such large dataset in space and time is of great interest to the community in order to identify factors involved in cell growth, cell division or tissue formation by testing multiples conditions. However, cells growing on a micropattern tend to be tightly packed and to overlap with each other. Consequently, image analysis of those large dynamic datasets with no possible human intervention has proven impossible using state of the art automated cell detection methods.

Results

Here, we propose a fully automated image analysis approach to estimate the number, the location and the shape of each cell nucleus, in clusters at high throughput. The method is based on a robust fit of Gaussian mixture models with two and three components on each frame followed by an analysis over time of the fitting residual and two other relevant features. We use it to identify with high precision the very first frame containing three cells. This allows in our case to measure a cell division angle on each video and to construct division angle distributions for each tested condition. We demonstrate the accuracy of our method by validating it against manual annotation on about 4000 videos of cell clusters.

Conclusions

The proposed approach enables the high throughput analysis of video sequences of isolated cell clusters obtained using micropatterns. It relies only on two parameters that can be set robustly as they reduce to the average cell size and intensity.

How many segments are necessary to characterize delayed colonic transit time?

BACKGROUND AND AIMS

Measuring colonic transit time with radiopaque markers is simple, inexpensive, and very useful in constipated patients. Yet, the algorithm used to identify colonic segments is subjective, rather than founded on prior experimentation. The aim of the present study is to describe a rational way to determine the colonic partition in the measurement of colonic transit time.

METHODS

Colonic transit time was measured in seven segments: ascending colon, hepatic flexure, right and left transverse colon, splenic flexure, descending colon, and rectosigmoid in 852 patients with functional bowel and anorectal disorders. An unsupervised algorithm for modeling Gaussian mixtures served to estimate the number of subgroups from this oversegmented colonic transit time. After that, we performed a k-means clustering that separated the observations into homogenous groups of patients according to their oversegmented colonic transit time.

RESULTS

The Gaussian mixture followed by the k-means clustering defined 4 populations of patients: "normal and fast transit" (n = 548) and three groups of patients with delayed colonic transit time "right delay" (n = 82) in which transit is delayed in the right part of the colon, "left delay" (n = 87) with transit delayed in the left part of colon and "outlet constipation" (n = 135) for patients with transit delayed in the terminal intestine. Only 3.7 % of patients were "erroneously" classified in the 4 groups recognized by clustering.

CONCLUSIONS

This unsupervised analysis of segmental colonic transit time shows that the classical division of the colon and the rectum into three segments is sufficient to characterize delayed segmental colonic transit time.

Quasi-supervised scoring of human sleep in polysomnograms using augmented input variables

The limitations of manual sleep scoring make computerized methods highly desirable. Scoring errors can arise from human rater uncertainty or inter-rater variability. Sleep scoring algorithms either come as supervised classifiers that need scored samples of each state to be trained, or as unsupervised classifiers that use heuristics or structural clues in unscored data to define states. We propose a quasi-supervised classifier that models observations in an unsupervised manner but mimics a human rater wherever training scores are available. EEG, EMG, and EOG features were extracted in 30s epochs from human-scored polysomnograms recorded from 42 healthy human subjects (18-79 years) and archived in an anonymized, publicly accessible database. Hypnograms were modified so that: 1. Some states are scored but not others; 2. Samples of all states are scored but not for transitional epochs; and 3. Two raters with 67% agreement are simulated. A framework for quasi-supervised classification was devised in which unsupervised statistical models-specifically Gaussian mixtures and hidden Markov models--are estimated from unlabeled training data, but the training samples are augmented with variables whose values depend on available scores. Classifiers were fitted to signal features incorporating partial scores, and used to predict scores for complete recordings. Performance was assessed using Cohen's Κ statistic. The quasi-supervised classifier performed significantly better than an unsupervised model and sometimes as well as a completely supervised model despite receiving only partial scores. The quasi-supervised algorithm addresses the need for classifiers that mimic scoring patterns of human raters while compensating for their limitations.

Estimating the composition of species in metagenomes by clustering of next-generation read sequences

Faster and cheaper sequencing technologies together with the ability to sequence uncultured microbes collected from any environment present us an opportunity to distill meaningful information from the millions of new genomic sequences from environmental samples, called metagenome. Contrary to conventional cultured microbes, however, the metagenomic data is extremely heterogeneous and noisy. Therefore the separation of the sets of sequenced genomic fragments that belong to different microbes is essential for successful assembly of microbial genomes. In this paper, we present a novel clustering method for a given metagenomic dataset. The metagenomic dataset has some distinguished features because (i) it is possible that similar sequence patterns may exist in different species and (ii) each species has different number of individuals in the given metagenomic dataset. Our method overcomes these obstacles by using the Gaussian mixture model and analysis of mixture profiles, and taking advantage of genomic signatures extracted from the metagenomic dataset. Unlike conventional clustering methods where clusters are discovered through global similarities of data instances, our method builds clusters by combining the data instances sharing local similarities captured by mixture analysis. By considering shared mixture components, our method is able to create clusters of genomic sequences although they are globally distinct each other. We applied our method to an artificial metagenomic dataset comprised of simulated 47 million reads from 25 real microbial genomes, and analyzed the resulting clusters in terms of the number of clusters, the number of participating species and dominant species in each cluster. Even though our approach cannot address all challenges in the field of metagenome sequence clustering, we believe that out method can contribute to take a step forward to achieve the goals.

FISST based method for multi-target tracking in the image plane of optical sensors

A finite set statistics (FISST)-based method is proposed for multi-target tracking in the image plane of optical sensors. The method involves using signal amplitude information in probability hypothesis density (PHD) filter which is derived from FISST to improve multi-target tracking performance. The amplitude of signals generated by the optical sensor is modeled first, from which the amplitude likelihood ratio between target and clutter is derived. An alternative approach is adopted for the situations where the signal noise ratio (SNR) of target is unknown. Then the PHD recursion equations incorporated with signal information are derived and the Gaussian mixture (GM) implementation of this filter is given. Simulation results demonstrate that the proposed method achieves significantly better performance than the generic PHD filter. Moreover, our method has much lower computational complexity in the scenario with high SNR and dense clutter.