Gaussian Mixture Model Fitting Research Articles

Computational analysis of GCaMP fluorescence data in neuronal activity

The background and motivation of our research is to explore how to use computational methods to analyze GCaMP fluorescence data. GCaMP is a genetically encoded calcium indicator that can be used to observe the activity of thousands of neurons simultaneously using modern fluorescence imaging techniques. Our research includes the application of principles such as basic signal processing, statistical inference, hypothesis testing, and graph theory to help understand raw GCaMP fluorescence data recorded from awake, behavioral mice. The data set includes GCaMP fluorescence trace and correlation coefficient matrix among neurons. Our methods include high-pass filtering, Gaussian mixture model fitting and online active set method peak inference (oasis). By analyzing the correlation between neurons, we can understand the connection and centrality between neurons.

The importance of context in extreme value analysis with application to extreme temperatures in the U.S. and Greenland

Abstract Statistical extreme value models allow estimation of the frequency, magnitude, and spatio-temporal extent of extreme temperature events in the presence of climate change. Unfortunately, the assumptions of many standard methods are not valid for complex environmental data sets, with a realistic statistical model requiring appropriate incorporation of scientific context. We examine two case studies in which the application of routine extreme value methods result in inappropriate models and inaccurate predictions. In the first scenario, incorporating random effects reflects shifts in unobserved climatic drivers that led to record-breaking US temperatures in 2021, permitting greater accuracy in return period prediction. In scenario two, a Gaussian mixture model fit to ice surface temperatures in Greenland improves fit and predictive abilities, especially in the poorly-defined upper tail around 0∘C.

Blanco DECam Bulge Survey (BDBS)

Aims. The Blanco DECam Bulge Survey (BDBS) has imaged more than 200 square degrees of the southern Galactic bulge, providing photometry in the ugrizy filters for ∼250 million unique stars. The presence of a strong foreground disk population, along with complex reddening and extreme image crowding, has made it difficult to constrain the presence of young and intermediate age stars in the bulge population. Methods. We employed an accurate cross-match of BDBS with the latest data release (EDR3) from the Gaia mission, matching more than 140 million sources with BDBS photometry and Gaia EDR3 photometry and astrometry. We relied on Gaia EDR3 astrometry, without any photometric selection, to produce clean BDBS bulge colour-magnitude diagrams (CMDs). Gaia parallaxes were used to filter out bright foreground sources, and a Gaussian mixture model fit to Galactic proper motions could identify stars kinematically consistent with bulge membership. We applied this method to 127 different bulge fields of 1 deg2 each, with |ℓ| ≤ 9.5° and −9.5° ≤b ≤ −2.5°. Results. The astrometric cleaning procedure removes the majority of blue stars in each field, especially near the Galactic plane, where the ratio of blue to red stars is ≲10%, increasing to values ∼20% at higher Galactic latitudes. We rule out the presence of a widespread population of stars younger than 2 Gyr. The vast majority of blue stars brighter than the turnoff belong to the foreground population, according to their measured astrometry. We introduce the distance between the observed red giant branch bump and the red clump as a simple age proxy for the dominant population in the field, and we confirm the picture of a predominantly old bulge. Further work is needed to apply the method to estimate ages to fields at higher latitudes, and to model the complex morphology of the Galactic bulge. We also produce transverse kinematic maps, recovering expected patterns related to the presence of the bar and of the X-shaped nature of the bulge.

Categorization model of moving small-scale intensity enhancements in solar active regions

Context. The small-scale moving intensity enhancements remotely observed in the extreme ultraviolet images of the solar active regions, which we refer to as active region moving campfires (ARMCs), are related to local plasma temperature and/or density enhancements. Their dynamics is driven by the physical processes in the entire coronal plasma. Our previous study of ARMCs indicates that they have characteristic velocities at around the background sound speed. In the present paper, we further investigate the dynamical and statistical properties of ARMCs. Aims. The main goal of our work is to carry out a simultaneous analysis of EUV images from two observational missions, SDO/AIA and Hi-C 2.1. The aims of the performed cross-validating analysis of both SDO/AIA and Hi-C 2.1 data were to reveal how the observed moving features are distributed over the studied active region, AR12712, and to perform a statistical hypothesis test of the existence of different groups of ARMCs with distinct physical characteristics. Methods. We use the statistical model of intensity centroid convergence and tracking that was developed in our previous paper. Furthermore, a Gaussian mixture model fit of the observed complex of moving ARMCs is elaborated to reveal the existence of distinct ARMC groups and to study the physical characteristics of these different groups. Results. In data from the 171 Å, 193 Å and 211 Å channels of SDO/AIA, we identified several groups of ARMCs with respect to both blob intensity and velocity profiles. The existence of such groups is confirmed by the cross-validation of the 172 Å data sets from Hi-C 2.1. Conclusions. The ARMCs studied in this paper have characteristic velocities in the range of the typical sound speeds in coronal loops. Hence, these moving objects differ from the well-known rapid Alfvénic velocity jets from magnetic reconnection sites. This is also proven by the fact that ARMCs propagate along the active region magnetic structure (strands). The nature of the discovered statistical grouping of the ARMC events is not known. Further theoretical studies and modeling is required to reveal this nature.

Transdiagnostic and sex differences in cognitive profiles of autism spectrum disorder and attention-deficit/hyperactivity disorder.

An increasing number of studies have shown that autism spectrum disorder (ASD) and attention-deficit/hyperactivity disorder (ADHD) share symptoms and aetiologies. However, transdiagnostic comparisons between ASD and ADHD is complicated due to the sex differences within each condition. To clarify the similarities and differences in the cognitive functioning between ASD and ADHD, while considering potential sex differences, this study compared cognitive profiles assessed by the WAIS-III between the four groups created by orthogonally combining diagnosis and sex based on the data from 277 ASD males, 86 ASD females, 99 ADHD males and 64 ADHD females. The analysis revealed three major findings. First, performance IQ and perceptual organization index were higher in ADHD males than in ASD males and ADHD females. Second, Gaussian mixture model fitting revealed two clusters underlying the distribution of subindex scores. The percentage of being classified into the cluster that scored lower in all the subindices was higher in females than in males irrespective of diagnosis. Third, feature importance for classification of ASD and ADHD yielded by random forest classifier, a supervised machine learning algorithm, revealed that autism quotient was most informative feature in classifying ASD and ADHD in males, while the discrepancy between verbal and performance intelligence quotient was in females, indicating that the set of behavioral features contributing to classification differs between males and females. Thus, these findings indicate that sex as well as diagnosis is critical in determining the cognitive profiles of people with ASD and ADHD. LAY SUMMARY: The present study compared profiles of cognitive functions measured by Wechsler Adult Intelligence Scale between males and females with ASD and ADHD. The analyses revealed clear sex differences in cognitive functions in both ASD and ADHD and that the set of cognitive functions useful in classifying ASD and ADHD differed between males and females. Thus, biological sex seems to be a critical factor in determining the cognitive profiles of people with ASD and ADHD.

Strategies to Enhance the Performance of Gaussian Mixture Model Fitting for Uncertainty Quantification

Summary When formulating history matching within the Bayesian framework, we may quantify the uncertainty of model parameters and production forecasts using conditional realizations sampled from the posterior probability density function (PDF). It is quite challenging to sample such a posterior PDF. Some methods [e.g., Markov chain Monte Carlo (MCMC)] are very expensive, whereas other methods are cheaper but may generate biased samples. In this paper, we propose an unconstrained Gaussian mixture model (GMM) fitting method to approximate the posterior PDF and investigate new strategies to further enhance its performance. To reduce the central processing unit (CPU) time of handling bound constraints, we reformulate the GMM fitting formulation such that an unconstrained optimization algorithm can be applied to find the optimal solution of unknown GMM parameters. To obtain a sufficiently accurate GMM approximation with the lowest number of Gaussian components, we generate random initial guesses, remove components with very small or very large mixture weights after each GMM fitting iteration, and prevent their reappearance using a dedicated filter. To prevent overfitting, we add a new Gaussian component only if the quality of the GMM approximation on a (large) set of blind-test data sufficiently improves. The unconstrained GMM fitting method with the new strategies proposed in this paper is validated using nonlinear toy problems and then applied to a synthetic history-matching example. It can construct a GMM approximation of the posterior PDF that is comparable to the MCMC method, and it is significantly more efficient than the constrained GMM fitting formulation (e.g., reducing the CPU time by a factor of 800 to 7,300 for problems we tested), which makes it quite attractive for large-scale history-matching problems. NOTE: This paper is also published as part of the 2021 SPE Reservoir Simulation Conference Special Issue.

Chemometric approach to characterization of the selected grape seed oils based on their fatty acids composition and FTIR spectroscopy

Addressing the issues arising from the production and trade of low-quality foods necessitates developing new quality control methods. Cooking oils, especially those produced from the grape seeds, are an example of food products that often suffer from questionable quality due to various adulterations and low-quality fruits used for their production. Among many methods allowing for fast and efficient food quality control, the combination of experimental and advanced mathematical approaches seems most reliable. In this work a method for grape seed oils compositional characterization based on the infrared (FTIR) spectroscopy and fatty acids profile is reported. Also, the relevant parameters of oils are characterized using a combination of standard techniques such as the Principal Component Analysis, k-Means, and Gaussian Mixture Model (GMM) fitting parameters. Two different approaches to perform unsupervised clustering using GMM were investigated. The first approach relies on the profile of fatty acids, while the second is FT-IR spectroscopy-based. The GMM fitting parameters in both approaches were compared. The results obtained from both approaches are consistent and complementary and provide the tools to address the characterization and clustering issues in grape seed oils.

Multiple Radio Transmitter Localization via UAV-Based Mapping

The widespread use of unmanned aerial vehicles (UAVs) has opened a novel perspective on spectrum awareness and localization because of their ability to overcome spatial limits and the burden of dedicated infrastructure. In such scenarios, an underinvestigated problem is the simultaneous localization of multiple non-collaborative primary users (PUs) of the spectrum, whose number, transmit power, activity pattern, and signal structure are unknown. This work proposes a framework for multiple PU localization based on the received power measured by an antenna array mounted on a UAV. A score map is firstly constructed based on the measured power. Then two algorithms, k-means clustering and weighted centroid (KCWC), and Gaussian mixture model fitting (GMMF) are applied to the score map to estimate the number and the positions of the PUs. The performance is evaluated in terms of optimal subpattern assignment (OSPA) distance, compared with a genie-aided (GA) localization algorithm capable of separating the signals emitted by the PUs. Despite the blind nature of the method proposed, numerical results exhibit very good localization accuracy, with an OSPA distance below <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$6\,$</tex-math></inline-formula> m in large, line-of-sight (LOS)-dominated, outdoor scenarios with five PUs, even in the presence of channel impairments and UAV position and heading uncertainties.

Optimal pooling of data for the reliable estimation of trait probability distributions

AbstractAimFunctional diversity indices that summarize trait variation between organisms within communities are widely used tools in community ecology. Although intraspecific trait variation is often an important component of the total variation, traditional functional diversity indices neglect this component. Recently, Carmona et al. proposed a framework to overcome this limitation based on fitting trait probability distributions (TPDs). Unfortunately, this article does not contain any guidance on pooling data before fitting TPDs.InnovationReliable fitting of TPDs needs larger sample size than usually used. This larger sample size can be reached pooling of data comes from different localities. If the TPD is the same in these localities, pooling results in a more reliable estimation. Moreover, if pooled data represent different TPDs, the fitted distribution is an artefact. In this paper, we suggest an algorithm for the automated selection of optimal pooling. It is based on fitting Gaussian mixture models and model selection using Bayes information criterion (BIC).Main conclusionsThe new algorithm was able to select the optimal pooling of data, which is illustrated using artificial data. Analysis of field data examples showed that optimal pooling is often not obvious: both merging all data and analysing measurements from each locality separately might result in unreliable estimates.

An Open-Source COVID-19 CT Dataset with Automatic Lung Tissue Classification for Radiomics.

The coronavirus disease 19 (COVID-19) pandemic is having a dramatic impact on society and healthcare systems. In this complex scenario, lung computerized tomography (CT) may play an important prognostic role. However, datasets released so far present limitations that hamper the development of tools for quantitative analysis. In this paper, we present an open-source lung CT dataset comprising information on 50 COVID-19-positive patients. The CT volumes are provided along with (i) an automatic threshold-based annotation obtained with a Gaussian mixture model (GMM) and (ii) a scoring provided by an expert radiologist. This score was found to significantly correlate with the presence of ground glass opacities and the consolidation found with GMM. The dataset is freely available in an ITK-based file format under the CC BY-NC 4.0 license. The code for GMM fitting is publicly available, as well. We believe that our dataset will provide a unique opportunity for researchers working in the field of medical image analysis, and hope that its release will lay the foundations for the successfully implementation of algorithms to support clinicians in facing the COVID-19 pandemic.

PAM-4 eye-opening monitoring techniques based on Gaussian mixture model fitting

PAM-4 eye-opening monitoring techniques based on Gaussian mixture model fitting

Improving patient classification and biomarker assessment using Gaussian Mixture Models and Bayes' rule.

In clinical research, determining cutoff values for continuous variables in test results remains challenging, particularly when considering candidate biomarkers or therapeutic targets for disease. Distribution of a continuous variable into two populations is known as dichotomization and has been commonly used in clinical studies. We recently reported a new method for determining multiple cutoffs for continuous variables. The development of this original approach was based on fitting Gaussian Mixture Models (GMM) onto real-world clinical data. We also explored how to leverage Bayesian probability to minimize uncertainty while classifying individual patients into respective subpopulations. In addition, we investigated the performance of the proposed method for the distribution of classical prognostic markers in breast cancer. Finally, we applied the proposed method to analyze a candidate marker and a target for cancer therapy. Here, we present an overview of this method and our prospects for its implementation in biomedical and clinical research.

Reduced-Degrees-of-Freedom Gaussian-Mixture-Model Fitting for Large-Scale History-Matching Problems

Summary It has been demonstrated that the Gaussian-mixture-model (GMM) fitting method can construct a GMM that more accurately approximates the posterior probability density function (PDF) by conditioning reservoir models to production data. However, the number of degrees of freedom (DOFs) for all unknown GMM parameters might become huge for large-scale history-matching problems. A new formulation of GMM fitting with a reduced number of DOFs is proposed in this paper to save memory use and reduce computational cost. The performance of the new method is benchmarked against other methods using test problems with different numbers of uncertain parameters. The new method performs more efficiently than the full-rank GMM fitting formulation, reducing the memory use and computational cost by a factor of 5 to 10. Although it is less efficient than the simple GMM approximation dependent on local linearization (L-GMM), it achieves much higher accuracy, reducing the error by a factor of 20 to 600. Finally, the new method together with the parallelized acceptance/rejection (A/R) algorithm is applied to a synthetic history-matching problem for demonstration.

Gaussian mixture model fitting method for uncertainty quantification by conditioning to production data

For most history matching problems, the posterior probability density function (PDF) may have multiple local maxima, and it is extremely challenging to quantify uncertainty of model parameters and production forecasts by conditioning to production data. In this paper, a novel method is proposed to improve the accuracy of Gaussian mixture model (GMM) approximation of the complex posterior PDF by adding more Gaussian components. Simulation results of all reservoir models generated during the history matching process, e.g., using the distributed Gauss-Newton (DGN) optimizer, are used as training data points for GMM fitting. The distance between the GMM approximation and the actual posterior PDF is estimated by summing up the errors calculated at all training data points. The distance is an analytical function of unknown GMM parameters such as covariance matrix and weighting factor for each Gaussian component. These unknown GMM parameters are determined by minimizing the distance function. A GMM is accepted if the distance is reasonably small. Otherwise, new Gaussian components will be added iteratively to further reduce the distance until convergence. Finally, high-quality conditional realizations are generated by sampling from each Gaussian component in the mixture, with the appropriate relative probability. The proposed method is first validated using nonlinear toy problems and then applied to a history-matching example. GMM generates better samples with a computational cost comparable to or less than other methods we tested. GMM samples yield production forecasts that match production data reasonably well in the history-matching period and are consistent with production data observed in the blind test period.

Soft clustering of GPS velocities from a homogeneous permanent network in Turkey

Global positioning system (GPS) velocities have long and widely been used on various scales in revealing the deformations of the continental lithosphere. We present a homogeneous geodetic velocity field with high precision derived from ~ 10-year-long permanent GPS observations throughout Turkey. Without any apriori information or assumption, the cluster analysis might be applied upon the velocity fields for inspection, before going further in the analyses used prevalently in tectonic studies. We first “hard clustered” the velocities using k-means, hierarchical agglomerative clustering and Gaussian mixture models and examined how the cluster assignments change by tuning the algorithm-specific parameters. The Eurasian and the Arabian blocks which are separated from the Anatolian block with the strike-slip North and East Anatolian faults have been detected immediately. The Anatolian block itself has been divided into three blocks where the cluster assignments of the velocities at the transition zones might differ according to the chosen hard clustering algorithm. We then applied soft clustering using an appropriate Gaussian mixture model fit and created a probability map exhibiting the credibility of the cluster assignments. The detection capability of the cluster analysis has been demonstrated by comparison to various previously published block models of western Turkey. Cluster analysis detected the most pronounced blocks in western Turkey successfully, especially when the initially chosen number of clusters is not too large. The probability map of soft clustering can be used to modify the block boundaries together with the external validation.

Network structural dependency in the human connectome across the life-span.

Principles of network topology have been widely studied in the human connectome. Of particular interest is the modularity of the human brain, where the connectome is divided into subnetworks from which changes with development, aging or disease can be investigated. We present a weighted network measure, the Network Dependency Index (NDI), to identify an individual region’s importance to the global functioning of the network. Importantly, we utilize NDI to differentiate four subnetworks (Tiers) in the human connectome following Gaussian mixture model fitting. We analyze the topological aspects of each subnetwork with respect to age and compare it to rich club-based subnetworks (rich club, feeder, and seeder). Our results first demonstrate the efficacy of NDI to identify more consistent, central nodes of the connectome across age groups, when compared with the rich club framework. Stratifying the connectome by NDI led to consistent subnetworks across the life-span, revealing distinct patterns associated with age where, for example, the key relay nuclei and cortical regions are contained in a subnetwork with highest NDI. The divisions of the human connectome derived from our data-driven NDI framework have the potential to reveal topological alterations described by network measures through the life-span.

A method to correct background phase offset for phase-contrast MRI in the presence of steady flow and spatial wrap-around artifact.

Background phase offsets in phase-contrast MRI are often corrected using polynomial regression; however, correction performance degrades when temporally invariant outliers such as steady flow or spatial wrap-around artifact are present. We describe and validate an iterative method called automatic rejection of temporally invariant outliers (ARTO), which excludes these outliers from the fitting process. The ARTO method iteratively removes pixels with large polynomial regression errors analyzed by a Gaussian mixture model fitting of the residual distribution. A total of 150 trials of a simulated phantom (75 with wrap-around artifact) and 125 phase-contrast MRI cines from 22 healthy subjects (48 with wrap-around artifact) were used for validation. Background phase offsets were corrected using second-order weighted regularized least squares (WRLS) with and without ARTO. Flow volumes after WRLS and WRLS+ARTO corrections were compared with the known truth (phantom) and stationary phantom reference (in vivo) using Bland-Altman analysis. The ratio between the pulmonary flow and the systemic flow was also computed in a subset of 6 subjects. In the simulated phantom, compared with WRLS and no correction, correction with WRLS+ARTO produced superior agreement in volumetric flow quantification with the known truth. In vivo, WRLS+ARTO also produced superior agreement with stationary phantom-corrected volumetric flow compared with WRLS and no correction. In data sets with wrap-around artifact, WRLS produced significantly larger variance in the pulmonary flow and systemic flow ratio than stationary phantom correction (P = .0008). The proposed method provides automatic exclusion of temporally invariant outliers and produces flow quantification results comparable to stationary phantom correction.

Modelling of interactions for the recognition of activities in groups of people

In this research study we adopt a probabilistic modelling of interactions in groups of people, using video sequences, leading to the recognition of their activities. Firstly, we model short smooth streams of localised movement. Afterwards, we partition the scene in regions of distinct movement, by using maximum a posteriori estimation, by fitting Gaussian Mixture Models (GMM) to the movement statistics. Interactions between moving regions are modelled using the Kullback–Leibler (KL) divergence between pairs of statistical representations of moving regions. Such interactions are considered with respect to the relative movement, moving region location and relative size, as well as to the dynamics of the movement and location inter-dependencies, respectively. The proposed methodology is assessed on two different data sets showing different categories of human interactions and group activities.

Estimating extinction using unsupervised machine learning

Dust extinction is the most robust tracer of the gas distribution in the interstellar medium, but measuring extinction is limited by the systematic uncertainties involved in estimating the intrinsic colors to background stars. In this paper we present a new technique, PNICER, that estimates intrinsic colors and extinction for individual stars using unsupervised machine learning algorithms. This new method aims to be free from any priors with respect to the column density and intrinsic color distribution. It is applicable to any combination of parameters and works in arbitrary numbers of dimensions. Furthermore, it is not restricted to color space. Extinction towards single sources is determined by fitting Gaussian Mixture Models along the extinction vector to (extinction-free) control field observations. In this way it becomes possible to describe the extinction for observed sources with probability densities. PNICER effectively eliminates known biases found in similar methods and outperforms them in cases of deep observational data where the number of background galaxies is significant, or when a large number of parameters is used to break degeneracies in the intrinsic color distributions. This new method remains computationally competitive, making it possible to correctly de-redden millions of sources within a matter of seconds. With the ever-increasing number of large-scale high-sensitivity imaging surveys, PNICER offers a fast and reliable way to efficiently calculate extinction for arbitrary parameter combinations without prior information on source characteristics. PNICER also offers access to the well-established NICER technique in a simple unified interface and is capable of building extinction maps including the NICEST correction for cloud substructure. PNICER is offered to the community as an open-source software solution and is entirely written in Python.

An Ensemble of Invariant Features for Person Reidentification

This paper proposes an ensemble of invariant features (EIFs), which can properly handle the variations of color difference and human poses/viewpoints for matching pedestrian images observed in different cameras with nonoverlapping field of views. Our proposed method is a direct reidentification (re-id) method, which requires no prior domain learning based on prelabeled corresponding training data. The novel features consist of the holistic and region-based features. The holistic features are extracted by using a publicly available pretrained deep convolutional neural network used in generic object classification. In contrast, the region-based features are extracted based on our proposed two-way Gaussian mixture model fitting, which overcomes the self-occlusion and pose variations. To make a better generalization during recognizing identities without additional learning, the ensemble scheme aggregates all the feature distances using the similarity normalization. The proposed framework achieves robustness against partial occlusion, pose, and viewpoint changes. Moreover, the evaluation results show that our method outperforms the state-of-the-art direct re-id methods on the challenging benchmark viewpoint invariant pedestrian recognition and 3D people surveillance data sets.