Prior Probability Estimates Research Articles

Abstract 7414: Claire: a search engine leveraging deep databases for reliable detection of peptides, with a special focus on proteogenomic applications

Abstract As the field of cancer diagnostics and treatment evolves, the significance of peptides characterized by post-translational modifications and amino acid substitutions is becoming increasingly prominent. These molecular alterations frequently offer critical insights into tumor biology, aiding the development of targeted therapies and methods for personalized medicine. However, despite ongoing advances in shotgun proteomics, the field still faces multiple challenges for the reliable detection of rare peptide forms, for instance, amino acid substitutions when the corresponding DNA or RNA sequencing is unavailable. As a response to these challenges, our group has developed Claire—a probabilistic search engine employing large peptide databases for detection. These databases, often on the terabyte scale, further incorporate the estimates of peptides' prior probabilities to improve detection accuracy and utilize several optimizations to allow fast interpretation of tandem mass spectra. Claire outperformed state-of-the-art software, such as MSFragger and TagGraph when evaluated on the protein-level detection of single nucleotide variants in the public NCI60 proteome dataset. Further, Claire's analysis of a range of NCI60 datasets revealed high protein-level mutational burdens in genomically unstable cancer cell lines and detected mislabeling and contamination across several omics datasets. In a clinical domain, Claire discerned the hypermutation status of colorectal cancer patients' tumors, identifying candidates suitable for immunotherapy. Protein-level variation in peripheral blood mononuclear cells also recognized individuals, monozygotic twins aside, revealing the pseudonymous nature of germline proteome datasets, and raising the need for their protection. From a computational perspective, Claire can be run as a standalone software in the Linux operating system, or its capabilities accessed remotely using an interface on our cloud computing infrastructure. Claire has thus shown remarkable potential in enhancing peptide detection, offers substantial advancements for both clinical and research applications, and allows direct incorporation of its capabilities into various computational workflows. Citation Format: Miroslav Hruska, Petr Dzubak, Marian Hajduch. Claire: a search engine leveraging deep databases for reliable detection of peptides, with a special focus on proteogenomic applications [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 7414.

Spike synchrony as a measure of Gestalt structure

The function of spike synchrony is debatable: some researchers view it as a mechanism for binding perceptual features, others – as a byproduct of brain activity. We argue for an alternative computational role: synchrony can estimate the prior probability of incoming stimuli. In V1, this can be achieved by comparing input with previously acquired visual experience, which is encoded in plastic horizontal intracortical connections. V1 connectivity structure can encode the acquired visual experience in the form of its aggregate statistics. Since the aggregate statistics of natural images tend to follow the Gestalt principles, we can assume that V1 is more often exposed to Gestalt-like stimuli, and this is manifested in its connectivity structure. At the same time, the connectivity structure has an impact on spike synchrony in V1. We used a spiking model with V1-like connectivity to demonstrate that spike synchrony reflects the Gestalt structure of the stimulus. We conducted simulation experiments with three Gestalt laws: proximity, similarity, and continuity, and found substantial differences in firing synchrony for stimuli with varying degrees of Gestalt-likeness. This allows us to conclude that spike synchrony indeed reflects the Gestalt structure of the stimulus, which can be interpreted as a mechanism for prior probability estimation.

Reasoning from background knowledge: Evaluating and explaining behaviour in Finnish rape judgments

According to explanationist theories of evidence, fact-finders reason by evaluating the ‘goodness’ of different narratives that explain the evidence. One standard is external coherence: does the narrative fit with what the fact-finder knows or assumes about the world? This study uses qualitative content analysis to examine how District Court judges draw inferences directly from ‘background knowledge’ in 119 Finnish rape cases and how these inferences are contested by dissenting and appellate judges. The results show that especially the complainant's behaviour was frequently evaluated against behavioural scripts and other background beliefs. Outspoken reliance on rape myths was relatively rare, and myths were explicitly resisted as often as they were relied upon. Where judges used stereotypical behaviour to support the rape complainant's testimony, this reasoning could be explained by the search for optimum (explanatory) coherence or the Finnish legal principle that a rape complainant's testimony requires supporting evidence. Judges also used estimates of prior probabilities to inform their reasoning; few behaviours are impossible, but some actions are ‘more coherent’ with rape than with non-rape, or vice versa. Accruing the type of knowledge necessary (and usually unavailable) for probabilistic reasoning is therefore necessary also for explanationist reasoning.

Efficient reliability updating methods based on Bayesian inference and sequential learning Kriging

Reliability updating is an effective tool for reappraising reliability level of system when new observation information is obtained. The adaptive Kriging based reliability updating method (RUAK) inserts the adaptive Kriging into traditional simulation method to improve the efficiency of reliability updating. However, an identical candidate sampling pool is used to simultaneously estimate the prior failure probability and the posterior one in RUAK, which leads to a waste of computational resources in case of significant difference between the importance regions in estimation of prior and posterior failure probabilities. To overcome this disadvantage, an efficient reliability updating framework based on Bayesian inference and sequential learning Kriging is proposed in this paper. In the proposed method, two candidate sampling pools respectively for estimating the prior and posterior failure probabilities are separately constructed by prior probability density function (PDF) and posterior PDF obtained by Bayesian inference. Then, the Kriging model is established and sequentially refined in these two candidate sampling pools to accurately estimate the corresponding failure probabilities. Through combining different simulation methods with the proposed framework, the Monte Carlo simulation based and importance sampling based sequential learning Kriging methods are respectively developed for reliability updating.

Analysis of alternative strategies applied to Naïve-Bayes classifier into the recognition of electrofacies: Application in well-log data at Recôncavo Basin, North-East Brazil

This paper is concerned with the applicability of different strategies to improve the definition of prior probabilities and/or likelihoods of naïve Bayes (NB) classifiers. Standard NB method computes likelihoods and priors by means of normal distributions and evaluation of the entire training data-set, respectively. NB is one of the most prolific classification methods in data mining and machine learning. Despite decent efficiency facing good training data, NB classifiers present the intriguing assumption of conditional independence between the attributes. Several algorithms have been proposed to improve the effectiveness of NB classifiers by inserting discriminant approaches into its generative structure. From a reliability perspective, the standard NB approach might not explore the real capabilities of NB classifiers facing the lithologic classification problem. To cover such distrust, a novel approach considering four particular strategies are suggested and compared to the standard NB classification outcomes. At first, a kernel density estimation (KDE) is considered to ameliorate the likelihood models. We also apply the NB classifier in parts by separating the training data-set in individual wells in a committee architecture framework. A tuning strategy is also considered for automatic estimation of prior probabilities in an optimization-scheme. Another novel alternative, named as CRC, adapted to the standard NB classifier consists in defining priors based on depth zones from regional stratigraphic information in which to apply NB classifier. We prepare an extensive statistical investigation, based on precision, recall, classification errors, fscores and confusion matrices to bespeak the most relevant NB strategy for classification of electrofacies. Despite the decent classification outcomes for all above-mentioned strategies, CRC can be considered, by a narrow margin, the most prolific method to be applied as an improvement of the standard NB to classify rock units. Tests are performed on a validation well (i.e., 7-MP-50D-BA) of Massapê Field, in Recôncavo Basin, northeast Brazil to highlight the classification particularities provided by the improved strategy. A significant improvement in the classification of sandstones (i.e., from 68 % to 83 % accuracy) is observed, according to the confusion matrix analysis. Additionally, a minimal decreasing is observed into the classification of shales and slurries (i.e., from 92% to 90% and to 63% to 56%, respectively), which is acceptable according to the fscores and errors. This aspect reinforces the relevance of using the NB classifier jointly with previous geologic information to optimize the lithologic classification.

Ambiguity attitudes in qualitative contexts: The role of prior beliefs

AbstractMost studies of ambiguity aversion rely on experimental paradigms involving monetary bets. Thus, the extent to which ambiguity aversion occurs outside of such contexts is much less understood, particularly when the situation cannot easily be reduced to numerical terms. The present work seeks to understand whether people prefer to avoid ambiguous decisions in a variety of different qualitative domains (e.g., work, family, love, friendship, exercise, study, and health), and, if so, to determine the role played by prior beliefs in those domains. Across three studies, we presented participants with 24 vignettes and measured the degree to which they preferred risk to ambiguity in each. We also asked them for their prior probability estimates about the likely outcomes in the ambiguous events. Ambiguity aversion was observed in the vast majority of vignettes, but at different magnitudes. It was predicted by whether the vignette involved gain or loss as well as by people's prior beliefs; however, the heterogeneity between people meant that the role of prior beliefs was only evident in an individual‐level analysis (i.e., not at the group level). Our results suggest that the desire to avoid ambiguity occurs in a wide variety of qualitative contexts but to different degrees for different people and may be partially driven by unfavorable prior estimates of the likely outcomes of the ambiguous events.

Fluvoxamine for Outpatient Management of COVID-19 to Prevent Hospitalization

Widely available and affordable options for the outpatient management of COVID-19 are needed, particularly for therapies that prevent hospitalization. To perform a meta-analysis of the available randomized clinical trial evidence for fluvoxamine in the outpatient management of COVID-19. World Health Organization International Clinical Trials Registry Platform and ClinicalTrials.gov. Studies with completed outpatient trials with available results that compared fluvoxamine with placebo were included. The PRISMA 2020 guidelines were followed and study details in terms of inclusion criteria, trial demographics, and the prespecified outcome of all-cause hospitalization were extracted. Risk of bias was assessed by the Cochrane Risk of Bias 2 tool and a bayesian random effects meta-analysis with different estimates of prior probability was conducted: a weakly neutral prior (50% chance of efficacy with 95% CI for risk ratio [RR] between 0.5 and 2.0) and a moderately optimistic prior (85% chance of efficacy). A frequentist random-effects meta-analysis was conducted as a senstivity analysis, and the results were contextualized by estimating the probability of any association (RR ≤ 1) and moderate association (RR ≤ 0.9) with reduced hospitalization. All-cause hospitalization. This systematic review and meta-analysis of 3 randomized clinical trials and included 2196 participants. The RRs for hospitalization were 0.78 (95% CI, 0.58-1.08) for the bayesian weakly neutral prior, 0.73 (95% CI, 0.53-1.01) for the bayesian moderately optimistic prior, and 0.75 (95% CI, 0.58-0.97) for the frequentist analysis. Depending on the scenario, the probability of any association with reduced hospitalization ranged from 94.1% to 98.6%, and the probability of moderate association ranged from 81.6% to 91.8%. In this systematic review and meta-analysis of data from 3 trials, under a variety of assumptions, fluvoxamine showed a high probability of being associated with reduced hospitalization in outpatients with COVID-19. Ongoing randomized trials are important to evaluate alternative doses, explore the effectiveness in vaccinated patients, and provide further refinement to these estimates. Meanwhile, fluvoxamine could be recommended as a management option, particularly in resource-limited settings or for individuals without access to SARS-CoV-2 monoclonal antibody therapy or direct antivirals.

Word Sense Disambiguation Using Prior Probability Estimation Based on the Korean WordNet

Supervised disambiguation using a large amount of corpus data delivers better performance than other word sense disambiguation methods. However, it is not easy to construct large-scale, sense-tagged corpora since this requires high cost and time. On the other hand, implementing unsupervised disambiguation is relatively easy, although most of the efforts have not been satisfactory. A primary reason for the performance degradation of unsupervised disambiguation is that the semantic occurrence probability of ambiguous words is not available. Hence, a data deficiency problem occurs while determining the dependency between words. This paper proposes an unsupervised disambiguation method using a prior probability estimation based on the Korean WordNet. This performs better than supervised disambiguation. In the Korean WordNet, all the words have similar semantic characteristics to their related words. Thus, it is assumed that the dependency between words is the same as the dependency between their related words. This resolves the data deficiency problem by determining the dependency between words by calculating the χ2 statistic between related words. Moreover, in order to have the same effect as using the semantic occurrence probability as prior probability, which is used in supervised disambiguation, semantically related words of ambiguous vocabulary are obtained and utilized as prior probability data. An experiment was conducted with Korean, English, and Chinese to evaluate the performance of our proposed lexical disambiguation method. We found that our proposed method had better performance than supervised disambiguation methods even though our method is based on unsupervised disambiguation (using a knowledge-based approach).

Estimating the class prior for positive and unlabelled data via logistic regression

In the paper, we revisit the problem of class prior probability estimation with positive and unlabelled data gathered in a single-sample scenario. The task is important as it is known that in positive unlabelled setting, a classifier can be successfully learned if the class prior is available. We show that without additional assumptions, class prior probability is not identifiable and thus the existing non-parametric estimators are necessarily biased in general if extra assumptions are not imposed. The magnitude of their bias is also investigated. The problem becomes identifiable when the probabilistic structure satisfies mild semi-parametric assumptions. Consequently, we propose a method based on a logistic fit and a concave minorization of its (non-concave) log-likelihood. The experiments conducted on artificial and benchmark datasets as well as on a large clinical database MIMIC indicate that the estimation errors for the proposed method are usually lower than for its competitors and that it is robust against departures from logistic settings.

Standardized and reproducible measurement of decision-making in mice.

Progress in science requires standardized assays whose results can be readily shared, compared, and reproduced across laboratories. Reproducibility, however, has been a concern in neuroscience, particularly for measurements of mouse behavior. Here, we show that a standardized task to probe decision-making in mice produces reproducible results across multiple laboratories. We adopted a task for head-fixed mice that assays perceptual and value-based decision making, and we standardized training protocol and experimental hardware, software, and procedures. We trained 140 mice across seven laboratories in three countries, and we collected 5 million mouse choices into a publicly available database. Learning speed was variable across mice and laboratories, but once training was complete there were no significant differences in behavior across laboratories. Mice in different laboratories adopted similar reliance on visual stimuli, on past successes and failures, and on estimates of stimulus prior probability to guide their choices. These results reveal that a complex mouse behavior can be reproduced across multiple laboratories. They establish a standard for reproducible rodent behavior, and provide an unprecedented dataset and open-access tools to study decision-making in mice. More generally, they indicate a path toward achieving reproducibility in neuroscience through collaborative open-science approaches.

Human online adaptation to changes in prior probability.

Optimal sensory decision-making requires the combination of uncertain sensory signals with prior expectations. The effect of prior probability is often described as a shift in the decision criterion. Can observers track sudden changes in probability? To answer this question, we used a change-point detection paradigm that is frequently used to examine behavior in changing environments. In a pair of orientation-categorization tasks, we investigated the effects of changing probabilities on decision-making. In both tasks, category probability was updated using a sample-and-hold procedure: probability was held constant for a period of time before jumping to another probability state that was randomly selected from a predetermined set of probability states. We developed an ideal Bayesian change-point detection model in which the observer marginalizes over both the current run length (i.e., time since last change) and the current category probability. We compared this model to various alternative models that correspond to different strategies—from approximately Bayesian to simple heuristics—that the observers may have adopted to update their beliefs about probabilities. While a number of models provided decent fits to the data, model comparison favored a model in which probability is estimated following an exponential averaging model with a bias towards equal priors, consistent with a conservative bias, and a flexible variant of the Bayesian change-point detection model with incorrect beliefs. We interpret the former as a simpler, more biologically plausible explanation suggesting that the mechanism underlying change of decision criterion is a combination of on-line estimation of prior probability and a stable, long-term equal-probability prior, thus operating at two very different timescales.

Investigation on Land Cover Mapping Capability of Maximum Likelihood Classifier: A Case Study on North Canara, India

The success of a large number of real-world applications depends on the efficiency with which land use land cover classes are extracted from Remotely Sensed (RS) imagery. This study aims at analysing the performance of Maximum Likelihood Classifier (MLC) over multispectral remote sensor data characterized by the overlapping of spectral classes and presence of mixed pixels, investigating the impact of prior class probabilities on the overall classification performance, the impact of the number of land cover classes on classification accuracy, and identifying the decision parameters for assigning a pixel to a land cover class. A quantitative analysis of decision parameters of MLC for pixel assignment is presented for five randomly selected pixels in the study area. Landsat 8 multispectral data of North Canara District was collected from USGS website and is considered for the research. Seven land use land cover classes were identified over the study area. Results obtained indicate that use of prior probability estimates improves the classification accuracy. The study also presents the variation in classification accuracy for four different cases of total number of land cover classes. The conducted research is useful in understanding the performance of MLC under multiple scenarios.

Estimation of sensitivity and specificity of pregnancy diagnosis using transrectal ultrasonography and ELISA for pregnancy-associated glycoprotein in dairy cows using a Bayesian latent class model

AIMS: To determine the sensitivity (Se) and specificity (Sp) of pregnancy diagnosis using transrectal ultrasonography and an ELISA for pregnancy-associated glycoprotein (PAG) in milk, in lactating dairy cows in seasonally calving herds approximately 85–100 days after the start of the herd’s breeding period.METHODS: Paired results were used from pregnancy diagnosis using transrectal ultrasonography and ELISA for PAG in milk carried out approximately 85 and 100 days after the start of the breeding period, respectively, from 879 cows from four herds in Victoria, Australia. A Bayesian latent class model was used to estimate the proportion of cows pregnant, the Se and Sp of each test, and covariances between test results in pregnant and non-pregnant cows. Prior probability estimates were defined using beta distributions for the expected proportion of cows pregnant, Se and Sp for each test, and covariances between tests. Markov Chain Monte Carlo iterations identified posterior distributions for each of the unknown variables. Posterior distributions for each parameter were described using medians and 95% probability (i.e. credible) intervals (PrI). The posterior median estimates for Se and Sp for each test were used to estimate positive predictive and negative predictive values across a range of pregnancy proportions.RESULTS: The estimate for proportion pregnant was 0.524 (95% PrI = 0.485–0.562). For pregnancy diagnosis using transrectal ultrasonography, Se and Sp were 0.939 (95% PrI = 0.890–0.974) and 0.943 (95% PrI = 0.885–0.984), respectively; for ELISA, Se and Sp were 0.963 (95% PrI = 0.919–0.990) and 0.870 (95% PrI = 0.806–0.931), respectively. The estimated covariance between test results was 0.033 (95% PrI = 0.008–0.046) and 0.035 (95% PrI = 0.018–0.078) for pregnant and non-pregnant cows, respectively. Pregnancy diagnosis results using transrectal ultrasonography had a higher positive predictive value but lower negative predictive value than results from the ELISA across the range of pregnancy proportions assessed.CONCLUSIONS AND CLINICAL RELEVANCE: Pregnancy diagnosis using transrectal ultrasonography and ELISA for PAG in milk had similar Se but differed in predictive values. Pregnancy diagnosis in seasonally calving herds around 85–100 days after the start of the breeding period using the ELISA is expected to result in a higher negative predictive value but lower positive predictive value than pregnancy diagnosis using transrectal ultrasonography. Thus, with the ELISA, a higher proportion of the cows with negative results will be non-pregnant, relative to results from transrectal ultrasonography, but a lower proportion of cows with positive results will be pregnant.

Using a Bayesian Network to Predict L5/S1 Spinal Compression Force from Posture, Hand Load, Anthropometry, and Disc Injury Status.

Stochastic biomechanical modeling has become a useful tool most commonly implemented using Monte Carlo simulation, advanced mean value theorem, or Markov chain modeling. Bayesian networks are a novel method for probabilistic modeling in artificial intelligence, risk modeling, and machine learning. The purpose of this study was to evaluate the suitability of Bayesian networks for biomechanical modeling using a static biomechanical model of spinal forces during lifting. A 20-node Bayesian network model was used to implement a well-established static two-dimensional biomechanical model for predicting L5/S1 compression and shear forces. The model was also implemented as a Monte Carlo simulation in MATLAB. Mean L5/S1 spinal compression force estimates differed by 0.8%, and shear force estimates were the same. The model was extended to incorporate evidence about disc injury, which can modify the prior probability estimates to provide posterior probability estimates of spinal compression force. An example showed that changing disc injury status from false to true increased the estimate of mean L5/S1 compression force by 14.7%. This work shows that Bayesian networks can be used to implement a whole-body biomechanical model used in occupational biomechanics and incorporate disc injury.

Dynamic estimation of prior probabilities in an orientation-discrimination task

Dynamic estimation of prior probabilities in an orientation-discrimination task

A fast and high performance multiple data integration algorithm for identifying human disease genes.

BackgroundIntegrating multiple data sources is indispensable in improving disease gene identification. It is not only due to the fact that disease genes associated with similar genetic diseases tend to lie close with each other in various biological networks, but also due to the fact that gene-disease associations are complex. Although various algorithms have been proposed to identify disease genes, their prediction performances and the computational time still should be further improved.ResultsIn this study, we propose a fast and high performance multiple data integration algorithm for identifying human disease genes. A posterior probability of each candidate gene associated with individual diseases is calculated by using a Bayesian analysis method and a binary logistic regression model. Two prior probability estimation strategies and two feature vector construction methods are developed to test the performance of the proposed algorithm.ConclusionsThe proposed algorithm is not only generated predictions with high AUC scores, but also runs very fast. When only a single PPI network is employed, the AUC score is 0.769 by using F2 as feature vectors. The average running time for each leave-one-out experiment is only around 1.5 seconds. When three biological networks are integrated, the AUC score using F3 as feature vectors increases to 0.830, and the average running time for each leave-one-out experiment takes only about 12.54 seconds. It is better than many existing algorithms.

A Bayesian network highlighting the linkages between landscape structure and the local economy: the case of agritourism in lowland areas of Northern Italy

Linking landscapes to socio-economic benefits necessarily requires considering the usability of landscape structure. To do so, however, depends on the interaction between users and producers of landscape-related services. We illustrate this interaction with a Bayesian Belief Network (BBN) in a case study analysing the connection between residents' perceptions of landscape structure and agritourism restaurants in the eastern lowlands of Ferrara (Italy). We use estimates of prior and conditional probabilities from a mix of different data: land use, survey data, regional statistics, and expert judgements to show the likely effects of the landscape structure on the local economy by using intermediate forms of services (i.e. second-order services). The second-order service is highly influenced by the agritourism density and by the frequency with which customers dine at agritourism restaurants and less by landscape attractiveness, confirming the importance of the supply and demand of second-order services in the provision of landscape-related services.

Segmentation of myocardium from cardiac MR images using a novel dynamic programming based segmentation method.

Myocardium segmentation in cardiac magnetic resonance (MR) images plays a vital role in clinical diagnosis of the cardiovascular diseases. Because of the low contrast and large variation in intensity and shapes, myocardium segmentation has been a challenging task. A dynamic programming (DP) based segmentation method, incorporating the likelihood and shape information of the myocardium, is developed for segmenting myocardium in cardiac MR images. The endocardium, i.e., the left ventricle blood cavity, is segmented for initialization, and then the optimal epicardium contour is determined using the polar-transformed image and DP scheme. In the DP segmentation scheme, three techniques are proposed to improve the segmentation performance: (1) the likelihood image of the myocardium is constructed to define the external cost in the DP, thus the cost function incorporates prior probability estimation; (2) the adaptive search range is introduced to determine the polar-transformed image, thereby excluding irrelevant tissues; (3) the connectivity constrained DP algorithm is developed to obtain an optimal closed contour. Four metrics, including the Dice metric (Dice), root mean squared error (RMSE), reliability, and correlation coefficient, are used to assess the segmentation accuracy. The authors evaluated the performance of the proposed method on a private dataset and the MICCAI 2009 challenge dataset. The authors also explored the effects of the three new techniques of the DP scheme in the proposed method. For the qualitative evaluation, the segmentation results of the proposed method were clinically acceptable. For the quantitative evaluation, the mean (Dice) for the endocardium and epicardium was 0.892 and 0.927, respectively; the mean RMSE was 2.30 mm for the endocardium and 2.39 mm for the epicardium. In addition, the three new techniques in the proposed DP scheme, i.e., the likelihood image of the myocardium, the adaptive search range, and the connectivity constrained DP algorithm, improved the segmentation performance for the epicardium with 0.029, 0.047, and 0.007 in terms of the Dice and 0.98, 1.31, and 0.21 mm in terms of the RMSE, respectively. The three techniques (the likelihood image of the myocardium, the adaptive search range, and the connectivity constrained DP algorithm) can improve the segmentation ability of the DP method, and the proposed method with these techniques has the ability to achieve the acceptable segmentation result of the myocardium in cardiac MR images. Therefore, the proposed method would be useful in clinical diagnosis of the cardiovascular diseases.

Effective fuzzy clustering algorithm with Bayesian model and mean template for image segmentation

Fuzzy c-means (FCMs) with spatial constraints have been considered as an effective algorithm for image segmentation. The well-known Gaussian mixture model (GMM) has also been regarded as a useful tool in several image segmentation applications. In this study, the authors propose a new algorithm to incorporate the merits of these two approaches and reveal some intrinsic relationships between them. In the authors model, the new objective function pays more attention on spatial constraints and adopts Gaussian distribution as the distance function. Thus, their model can degrade to the standard GMM as a special case. Our algorithm is fully free of the empirically pre-defined parameters that are used in traditional FCM methods to balance between robustness to noise and effectiveness of preserving the image sharpness and details. Furthermore, in their algorithm, the prior probability of an image pixel is influenced by the fuzzy memberships of pixels in its immediate neighbourhood to incorporate the local spatial information and intensity information. Finally, they utilise the mean template instead of the traditional hidden Markov random field (HMRF) model for estimation of prior probability. The mean template is considered as a spatial constraint for collecting more image spatial information. Compared with HMRF, their method is simple, easy and fast to implement. The performance of their proposed algorithm, compared with state-of-the-art technologies including extensions of possibilistic fuzzy c-means (PFCM), GMM, FCM, HMRF and their hybrid models, demonstrates its improved robustness and effectiveness.

A Robust Fuzzy Algorithm Based on Student's t-Distribution and Mean Template for Image Segmentation Application

Fuzzy c-means (FCM) with spatial constraints has been considered as an effective algorithm for image segmentation. Student's t-distribution has come to be regarded as an alternative to Gaussian distribution, as it is heavily tailed and more robust for outliers. In this letter, we propose a new algorithm to incorporate the merits of these two approaches. The advantages of our method are as follows: First, we incorporate the local spatial information and pixel intensity value by considering the labeling of an image pixel influenced by the labels in its immediate neighborhood. Second, we introduce additional parameter <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</i> to control the extent of this influence. The larger <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</i> indicates heavier extent of influence in the neighborhoods. Finally, we utilize a mean template instead of the traditional hidden Markov random field (HMRF) model for estimation of prior probability. Compared with HMRF, our method is simple, easy and fast to implement. Experimental results on synthetic and real images demonstrate the improved robustness and effectiveness of our approach.