Cluster Prototypes Research Articles

Intuitive-K-prototypes: A mixed data clustering algorithm with intuitionistic distribution centroid

Data sets are usually mixed with numerical and categorical attributes in the real world. Data mining of mixed data makes a lot of sense. This paper proposes an Intuitive-K-prototypes clustering algorithm with improved prototype representation and attribute weights. The proposed algorithm defines intuitionistic distribution centroid for categorical attributes. In our approach, a heuristic search for initial prototypes is performed. Then, we combine the mean of numerical attributes and intuitionistic distribution centroid to represent the cluster prototype. In addition, intra-cluster complexity and inter-cluster similarity are used to adjust attribute weights, with higher priority given to those with lower complexity and similarity. The membership and non-membership distance are calculated using the intuitionistic distribution centroid. These distances are then combined parametrically to obtain the composite distance. The algorithm is judged for its clustering effectiveness on the real UCI data set, and the results show that the proposed algorithm outperforms the traditional clustering algorithm in most cases.

The prototypical major cluster merger Abell 754

Context. Abell 754 is a rich galaxy cluster at z = 0.0543 and is considered the prototype of a major cluster merger. As many dynamically unrelaxed systems, it hosts diffuse radio emission on megaparsec-scales. Extended synchrotron sources in the intra-cluster medium (ICM) are commonly interpreted as evidence that a fraction of the gravitational energy released during cluster mergers is dissipated into nonthermal components. Aims. Here, we aim to use new MeerKAT UHF- and L-band observations to study nonthermal phenomena in Abell 754. These data are complemented with archival XMM-Newton observations to investigate the resolved spectral properties of both the radio and X-ray cluster emission. Methods. For the first time, we employed the pipeline originally developed to calibrate LOFAR data to MeerKAT observations. This allowed us to perform a direction-dependent calibration and obtain highly sensitive radio images in UHF and L bands that capture the extended emission with unprecedented detail. By using a large XMM-Newton mosaic, we produced thermodynamic maps of the ICM. Results. Our analysis reveals that the radio halo in the cluster center is bounded by the well-known shock in the eastern direction. Furthermore, in the southwest periphery, we discover an extended radio source that we classify as a radio relic that is possibly tracing a shock driven by the squeezed gas compressed by the merger, outflowing in perpendicular directions. The low-luminosity of this relic appears compatible with direct acceleration of thermal pool electrons. We interpret the observed radio and X-ray features in the context of a major cluster merger with a nonzero impact parameter. Conclusions. Abell 754 is a remarkable galaxy cluster showcasing exceptional features associated with the ongoing merger event. The high quality of the new MeerKAT data motivates further work on this system.

Cluster prototype earth mover’s distance adapters and alignment-guided prompt learning for vision–language models

Vision–language pre-trained models have focused on fine-tuning methods to enhance generalization in downstream tasks, such as CLIP. Recent research proposes fine-tuning these models using prompting and adapter techniques. However, prompting methods tend to overfit class-specific data distributions, and most adapters ignore the prototype representations as the weights, resulting in poor generalization. To tackle these challenges, we propose a novel method that integrates the cluster prototype Earth Mover’s Distance adapters and alignment-guided prompt learning (CPAAP) for vision–language models. Specifically, our adapter designs three components: graph convolutional network-based clusters, hierarchy prototype representations, and Earth Mover’s Distance similarity, providing a robust metric for measuring feature representations. Additionally, alignment-guided prompt learning enforces a constraint in the prediction of trainable and frozen models, enabling effective adaptation to downstream tasks. Extensive experiments are conducted on few-shot classification, base-to-novel generalization, cross-dataset evaluation, and domain generalization. In practice, CPAAP outperforms state-of-the-art methods on zero-shot tasks, achieving an absolute gain of 0.46% on the harmonic mean across 11 popular datasets.

PhiHER2: phenotype-informed weakly supervised model for HER2 status prediction from pathological images.

Human epidermal growth factor receptor 2 (HER2) status identification enables physicians to assess the prognosis risk and determine the treatment schedule for patients. In clinical practice, pathological slides serve as the gold standard, offering morphological information on cellular structure and tumoral regions. Computational analysis of pathological images has the potential to discover morphological patterns associated with HER2 molecular targets and achieve precise status prediction. However, pathological images are typically equipped with high-resolution attributes, and HER2 expression in breast cancer (BC) images often manifests the intratumoral heterogeneity. We present a phenotype-informed weakly supervised multiple instance learning architecture (PhiHER2) for the prediction of the HER2 status from pathological images of BC. Specifically, a hierarchical prototype clustering module is designed to identify representative phenotypes across whole slide images. These phenotype embeddings are then integrated into a cross-attention module, enhancing feature interaction and aggregation on instances. This yields a phenotype-based feature space that leverages the intratumoral morphological heterogeneity for HER2 status prediction. Extensive results demonstrate that PhiHER2 captures a better WSI-level representation by the typical phenotype guidance and significantly outperforms existing methods on real-world datasets. Additionally, interpretability analyses of both phenotypes and WSIs provide explicit insights into the heterogeneity of morphological patterns associated with molecular HER2 status. Our model is available at https://github.com/lyotvincent/PhiHER2.

Adaptive weighted multi-view evidential clustering with feature preference

Multi-view clustering has attracted substantial attention thanks to its ability to integrate information from diverse views. However, the existing methods can only generate hard or fuzzy partitions, which cannot effectively represent the uncertainty and imprecision when facing objects in overlapping clusters, thus increasing the risk of error. To solve the above problems, in this paper, we propose an adaptive weighted multi-view evidential clustering (WMVEC) method based on the theory of belief functions to characterize the uncertainty and imprecision in cluster assignment. Technically, we integrate view weight assignments and credal partition between objects and cluster prototypes into a joint learning framework. The credal partition offers a more comprehensive insight into the data by enabling objects to be associated with not only singleton clusters but also subsets of these clusters (termed meta-clusters) and the empty set, which represents a noise cluster. To avoid the interference of irrelevant and redundant features, we further present a weighted multi-view evidential clustering with feature preference (WMVEC-FP) to learn the importance of each feature under different views. We suggest the objective functions of WMVEC and WMVEC-FP and design alternating optimization schemes to obtain the optimal solutions, respectively. Through an extensive array of experiments, it has been demonstrated that our proposed clustering methods outperform other related and state-of-the-art methods in terms of their advantages and overall effectiveness.

Cluster analysis via projection onto convex sets

This paper proposes a data clustering algorithm that is inspired by the prominent convergence property of the Projection onto Convex Sets (POCS) method, termed the POCS-based clustering algorithm. For disjoint convex sets, the form of simultaneous projections of the POCS method can result in a minimum mean square error solution. Relying on this important property, the proposed POCS-based clustering algorithm treats each data point as a convex set and simultaneously projects the cluster prototypes onto respective member data points, the projections are convexly combined via adaptive weight values in order to minimize a predefined objective function for data clustering purposes. The performance of the proposed POCS-based clustering algorithm has been verified through a large scale of experiments and data sets. The experimental results have shown that the proposed POCS-based algorithm is competitive in terms of both effectiveness and efficiency against some of the prevailing clustering approaches such as the K-Means/K-Means+⁣+ and Fuzzy C-Means (FCM) algorithms. Based on extensive comparisons and analyses, we can confirm the validity of the proposed POCS-based clustering algorithm for practical purposes.

Cluster-based Adversarial Decision Boundary for domain-adaptive open set recognition

Domain adaptation has achieved significant progress recently by adapting models trained on a source domain to an unlabeled target domain. Open Set Domain adaptation (OSDA) has drawn much attention nowadays, where the target domain contains some exclusive categories other than the source domain’s known classes. With no label in the target data, existing OSDA methods often suffer from negative transfer. Conventional methods for unknown class rejection require an empirical setting of the confidence threshold, which lacks flexibility since the model confidence may vary during the training process, and our motivation is to omit the effort of setting the rejection threshold manually. Based on the idea that latent features of the same class should be in the same cluster to address this issue, we propose a domain adaptive open set recognition framework: Cluster-based Adversarial Decision Boundary (CADB). Specifically, we design an end-to-end unknown class rejection model consisting of three components: known class prototype estimation under the cluster assumption; known class similarity score estimation; and adaptive unknown class rejection threshold generation with adversarial feature suppression. These three components work as one entity to give a similarity score for each sample. Those samples that are less similar to the cluster prototype compared with the counterfactual features are rejected as the unknown class. Extensive evaluations are conducted to verify the effectiveness and robustness of the proposed boundary generation procedure.

MACHINE LEARNING CAN PREDICT DIFFICULTY IN ANTERIOR APPROACH TOTAL HIP ARTHROPLASTY TO IMPROVE PATIENT SAFETY AND SURGICAL TRAINING

Anterior approach total hip arthroplasty (AA-THA) has a steep learning curve, with higher complication rates in initial cases. Proper surgical case selection during the learning curve can reduce early risk. This study aims to identify patient and radiographic factors associated with AA-THA difficulty using Machine Learning (ML).Consecutive primary AA-THA patients from two centres, operated by two expert surgeons, were enrolled (excluding patients with prior hip surgery and first 100 cases per surgeon). K- means prototype clustering – an unsupervised ML algorithm – was used with two variables - operative duration and surgical complications within 6 weeks - to cluster operations into difficult or standard groups.Radiographic measurements (neck shaft angle, offset, LCEA, inter-teardrop distance, Tonnis grade) were measured by two independent observers. These factors, alongside patient factors (BMI, age, sex, laterality) were employed in a multivariate logistic regression analysis and used for k-means clustering. Significant continuous variables were investigated for predictive accuracy using Receiver Operator Characteristics (ROC).Out of 328 THAs analyzed, 130 (40%) were classified as difficult and 198 (60%) as standard. Difficult group had a mean operative time of 106mins (range 99–116) with 2 complications, while standard group had a mean operative time of 77mins (range 69–86) with 0 complications. Decreasing inter-teardrop distance (odds ratio [OR] 0.97, 95% confidence interval [CI] 0.95–0.99, p = 0.03) and right-sided operations (OR 1.73, 95% CI 1.10–2.72, p = 0.02) were associated with operative difficulty. However, ROC analysis showed poor predictive accuracy for these factors alone, with area under the curve of 0.56. Inter-observer reliability was reported as excellent (ICC >0.7).Right-sided hips (for right-hand dominant surgeons) and decreasing inter-teardrop distance were associated with case difficulty in AA-THA. These data could guide case selection during the learning phase. A larger dataset with more complications may reveal further factors.

Anti-Forgetting Adaptation for Unsupervised Person Re-Identification.

Regular unsupervised domain adaptive person re-identification (ReID) focuses on adapting a model from a source domain to a fixed target domain. However, an adapted ReID model can hardly retain previously-acquired knowledge and generalize to unseen data. In this paper, we propose a Dual-level Joint Adaptation and Anti-forgetting (DJAA) framework, which incrementally adapts a model to new domains without forgetting source domain and each adapted target domain. We explore the possibility of using prototype and instance-level consistency to mitigate the forgetting during the adaptation. Specifically, we store a small number of representative image samples and corresponding cluster prototypes in a memory buffer, which is updated at each adaptation step. With the buffered images and prototypes, we regularize the image-to-image similarity and image-to-prototype similarity to rehearse old knowledge. After the multi-step adaptation, the model is tested on all seen domains and several unseen domains to validate the generalization ability of our method. Extensive experiments demonstrate that our proposed method significantly improves the anti-forgetting, generalization and backward-compatible ability of an unsupervised person ReID model.

A simulated-to-real transfer fault diagnosis method based on prototype clustering subdomain adversarial adaptation network for HST bogie bearing

A simulated-to-real transfer fault diagnosis method based on prototype clustering subdomain adversarial adaptation network for HST bogie bearing

Longitudinal Clusters of Long-Term Trajectories in Patients with Early-Onset Chronic Depression: 2 Years of Naturalistic Follow-Up after Extensive Psychological Treatment

Introduction: In clinical trials, mostly group-level treatment effects of repeated cross-sectional measures are analyzed. However, substantial heterogeneity regarding individual symptom profiles and the variability of treatment effects are often neglected, especially over the long-term course. To provide effective personalized treatments, investigations of these characteristics are urgently needed. Methods: Depression severity ratings over 104 weeks of follow-up after year-long treatment with the Cognitive Behavioral Analysis System of Psychotherapy (CBASP) or Supportive Psychotherapy (SP) were analyzed. Longitudinal cluster analysis and multinomial logistic regression analysis were conducted to investigate intraindividual trajectories from one of the largest psychotherapy trials in early-onset chronic depression. Results: Two-year post-study-treatment trajectories of N = 188 patients with early-onset chronic depression were grouped into four prototypical clusters. Overall, 16.0% of patients remitted (cluster 1) and most of them did not receive any treatment during the 2-year follow-up. However, 84.0% of patients continued to experience subthreshold (37.2% cluster 2) or major depressive symptoms (46.8% clusters 3–4) and spent on average more than half of the follow-up in pharmacological and psychological treatment. Hierarchical regression analysis indicated that previous study treatment with CBASP or SP did not significantly predict cluster allocation, while baseline variables accounted for a large proportion of explained variance (R² _N = 0.64). Conclusion: While some patients experienced stable remission over 2 years of follow-up, the majority of patients experienced subthreshold or major depressive symptoms regardless of former study treatment with CBASP or SP. This calls for a long-term perspective implementing staging and innovative treatment approaches such as the sequential model or modular psychotherapy.

Real-time Pedestrian Tracking Based on YOLOv3 and Prototype Clustering

Although the accuracy of existing neural network models is high, in pedestrian tracking tasks, due to the uncertainty of targets, when tracking new targets, it is necessary to fine-tune the model, which further requires large computing and storage resource overhead. Therefore, its application on some lightweight platforms, such as robots and UAVs, is limited. Pedestrian tracking by robots and UAVs still faces great challenges in occlusion, multi-target, target loss, etc. This paper mainly solves the problem of real-time pedestrian tracking by object detection model of robot lightweight, which is mainly based on YOLO network to detect pedestrians, and then proposes a novel lightweight model and prototype clustering algorithm. Numerous experiments on the ETH dataset validate the superiority and effectiveness of our approach.

Linear Fuzzy Information-Granule-Based Fuzzy C-Means Algorithm for Clustering Time Series.

This article aims to design a trend-oriented-granulation-based fuzzy C -means (FCM) algorithm that can cluster a group of time series at an abstract (granular) level. To achieve a better trend-oriented granulation of a time series, l1 trend filtering is firstly carried out to result in segments which are then optimized by the proposed segment merging algorithm. By constructing a linear fuzzy information granule (LFIG) on each segment, a granular time series which well reflects the linear trend characteristic of the original time series is produced. With the novel designed distance that can well measure the trend similarity of two LFIGs, the distance between two granular time series is calculated by the modified dynamic time warping (DTW) algorithm. Based on this distance, the LFIG-based FCM algorithm is developed for clustering time series. In this algorithm, cluster prototypes are iteratively updated by the specifically designed granule splitting and merging algorithm, which allows the lengths of prototypes to change in the process of iteration. This overcomes the serious drawback of the existing approaches, where the lengths of prototypes cannot be changed. Experimental studies demonstrate the superior performance of the proposed algorithm in clustering time series with different shapes or trends.

Multi-Label Radar Compound Jamming Signal Recognition Using Complex-Valued CNN with Jamming Class Representation Fusion

In the complex battlefield electromagnetic environment, multiple jamming signals can enter the radar receiver simultaneously due to the development of jammers and modulation technology. The received compound jamming signals aggravate the difficulty of recognition and subsequent counter-countermeasure. In the face of strong overlapping signals and unseen jamming signal combinations, the performance of existing recognition methods usually seriously degrades. In this paper, an end-to-end multi-label classification framework combining a complex-valued convolutional neural network (CV-CNN) and jamming class representations is proposed to automatically recognize the jamming signal components of compound jamming signals. A basic multi-label CV-CNN (ML-CV-CNN) is first designed to directly process time–domain complex signals and fully retain jamming signal information. Then, the jamming class representations are generated using prototype clustering implemented by learning vector quantization, and they are fused with the ML-CV-CNN using class decoupling implemented by the attention mechanism to construct a multi-label class representation CV-CNN (ML-CR-CV-CNN), which can better learn the class-related features required for recognition. Finally, an adaptive threshold calibration is adopted to obtain optimal recognition results by multi-threshold discrimination. Simulation results verify that the proposed method has superior recognition performance, which is reflected in the strong robustness to the varying jamming-to-noise ratio (JNR) and power ratio, faster convergence speed with high JNRs, and better generalization for unseen jamming signal combinations.

Beyond [formula omitted]-Means++: Towards better cluster exploration with geometrical information

Although k-means and its variants are known for their remarkable efficiency, they suffer from a strong dependence on the prior knowledge of K and the assumption of a circle-like pattern, which can result in the algorithms dividing the input space instead of discovering non-predetermined data patterns. Thus, we propose beyond k-means++ that infers and utilizes explicit clusters by emphasizing local geometrical information for better cluster exploration. To avoid the K dependence, a novel framework of iterative division and aggregation (IDA) over k-means++ is presented. It begins with any K≥1, then increases and reduces K along with the procedure of clusters’ division and aggregation, respectively. To break through the circle-like pattern limitation, we introduce a reasonability checking strategy (RCS) for cluster division. Given local geometrical information, RCS achieves arbitrary cluster shape support by rejecting edge patterns with distinguished convergence direction and merging adjacent clusters with pseudo-edge patterns. Furthermore, we design an edge shrinkage strategy (ESS). Taking edge patterns as the cluster prototype, it benefits accuracy by effectively avoiding representability reduction due to irregular distribution. To compensate for the loss of efficiency, a near maximin and random sampling algorithm is suggested for large-scale data with high dimensionality. Experimental results confirm that beyond k-means++ is featured by handling arbitrary cluster shapes with remarkable accuracy.

Discriminative feature constraints via supervised contrastive learning for few-shot forest tree species classification using airborne hyperspectral images

In scenarios where sample collection is limited, studying few-shot learning algorithms such as prototypical networks (P-Net) is a keynote topic for supervised multiple tree species classification. In a previous study, we improved the P-Net by combining the feature enhancement algorithm based on the convolutional block attention module and several popular data augmentation methods in the computer vision domain, the classification accuracy can be significantly increased, and the degree of model overfitting can be reduced. However, there is a clear boundary between the data augmentations and the feature enhancement algorithm, which is manifested in that data augmentations are only used to enrich the diversity of the learned samples, but cannot directly affect the construction of the objective function, thus limiting the ability of data augmentations. In fact, in the supervised contrastive learning research, data augmentation methods are often used to generate positive samples of an anchor image to construct the objective function, i.e. supervised contrastive loss. The core idea for solving such a boundary problem is to use contrastive learning to make the anchor image close to its positive samples and the negative samples away from each other. Inspired by this, we introduced supervised contrastive learning in the P-Net, i.e., SCL-P-Net, which takes the discriminative feature representations as the constraints of the prototype clustering algorithm. In SCL-P-Net, data augmentation methods can not only extend the sample distribution, but also be used to construct the supervised contrastive loss directly. The study involves four airborne hyperspectral image datasets related to tree species classification, including the GFF-A and GFF-B datasets collected from Gaofeng Forest Farm in Nanning City, Guangxi Province, South China, the Xiongan dataset from Matiwan Village in Xiongan New Area, Hebei Province, North China, and the Tea Farm dataset from Fanglu Tea Farm in Changzhou City, Jiangsu Province, East China. The highest overall accuracy (OA) for the four datasets is 99.23% for GFF-A, 98.39% for GFF-B, 99.30% for Xiongan, and 99.54% for Tea Farm. It is concluded that the proposed SCL-P-Net classification framework can achieve multiple tree species classification with high-precision. Without changing the basic classification framework of P-Net, the introduction of supervised contrastive learning makes the combination of the data augmentations and the feature enhancement algorithm and plays a positive role in improving the distinguishability between samples.

The Role of BIA Analysis in Osteoporosis Risk Development: Hierarchical Clustering Approach.

Osteoporosis is a common musculoskeletal disorder among the elderly and a chronic condition which, like many other chronic conditions, requires long-term clinical management. It is caused by many factors, including lifestyle and obesity. Bioelectrical impedance analysis (BIA) is a method to estimate body composition based on a weak electric current flow through the body. The measured voltage is used to calculate body bioelectrical impedance, divided into resistance and reactance, which can be used to estimate body parameters such as total body water (TBW), fat-free mass (FFM), fat mass (FM), and muscle mass (MM). This study aims to find the tendency of osteoporosis in obese subjects, presenting a method based on hierarchical clustering, which, using BIA parameters, can group patients who show homogeneous characteristics. Grouping similar patients into clusters can be helpful in the field of medicine to identify disorders, pathologies, or more generally, characteristics of significant importance. Another added value of the clustering process is the possibility to define cluster prototypes, i.e., imaginary patients who represent models of "states", which can be used together with clustering results to identify subjects with similar characteristics in a classification context. The results show that hierarchical clustering is a method that can be used to provide the detection of states and, consequently, supply a more personalized medicine approach. In addition, this method allowed us to elect BIA as a potential prognostic and diagnostic instrument in osteoporosis risk development.

An MDS-based unifying approach to time series K-means clustering: application in the dynamic time warping framework

Partitioning algorithms, and in particular K-means clustering, are widely used in time series analysis. K-means clustering is intrinsically related to the use of the Euclidean distance as a measure of dissimilarity. When other dissimilarity measures, such as dynamic time warping, are involved, K-means clustering is usually replaced by the optimisation of a sums-of-the-stars clustering criterion, giving rise to an algorithm other than that of K-means, such as K-medoids. Another common restriction in the implementation of K-means concerns the need to estimate the average as the cluster prototype, which may represent a drawback for this method in time series when elastic measures such as dynamic time warping are used. In this paper, we propose a multidimensional scaling based K-means clustering algorithm that enables the use of K-means clustering together with any dissimilarity measure, and in particular with dynamic time warping, without requiring us to estimate cluster prototypes for the time series. This procedure is a true K-means clustering algorithm that searches for the partition in an equivalent auxiliary configuration, usually in a dimension lower than the time series length. The approach proposed is of particular interest when dynamic time warping is used in the analysis of series of unequal length and/or when some data are missing, and hence Euclidean distances cannot be used. The performance of our procedure is tested by conducting an extensive Monte Carlo experiment, comparing the results with those obtained by K-medoids. The procedure is also illustrated with the analysis of carbon dioxide emissions from 133 countries.

Physical Activity Patterns, Circadian Rhythms, and Aggressive and Suicidal Behavior among a Larger Sample of the General Population Aged 15 to 34 Years.

From a psychological perspective, aggressive behavior, non-suicidal self-injury and suicidal behavior could be considered dysfunctional coping strategies. Poor sleep patterns may further increase such dysfunctional coping. In contrast, regular physical activity may have the power to counteract such dysfunctional coping. Given this background, the aim of the present study was to combine categories of circadian rhythms as a proxy of normative sleep patterns and categories of physical activity patterns, and to associate these categories with aggressive behavior, non-suicidal self-injury and suicidal behavior among a larger sample of adolescents and young adults, aged 15 to 34 years. A total of 2991 (55.6% females) individuals aged 15 to 34 years of the so-called Ravansar non-communicable disease cohort study (RaNCD) took part in this study. Participants completed self-rating questionnaires covering circadian-related sleep patterns, regular physical activity, socio-demographic information and dimensions of aggression, non-suicidal self-injury and suicidal behavior. In a first step, both sleep patterns (circadian rhythm disorder: yes vs. no) and physical activity patterns (high vs. low) were dichotomized. Next, participants were assigned to one of four prototypical clusters: No circadian sleep disorders and high physical activity ("Hi-Sleep-Hi-PA"); no circadian sleep disorders and low physical activity ("Hi-Sleep-Lo-PA"); circadian sleep disorders and high physical activity ("Lo-Sleep-Hi-PA"); circadian sleep disorders and low physical activity ("Lo-Sleep-Lo-PA"). Projecting these four clusters on dimensions of aggressive behavior, non-suicidal self-injury and suicidal behavior, the following findings were observed: Participants of the "Hi-Sleep-Hi-PA" reported the lowest scores for aggressive behavior, self-injury and suicidal behavior, compared to participants of the "Lo-Sleep-Lo-PA" cluster. No differences for aggressive behavior, self-injury and suicidal behavior were observed among participants of the "Hi-Sleep-Lo-PA" and the "Lo-Sleep-Hi-PA" clusters. It appeared that the combination of favorable circadian sleep patterns and high physical activity patterns was associated with lower aggressive behavior, lower self-injury and suicidal behavior as proxies of favorable psychological functioning. In contrast, persons reporting high circadian sleep disorders and low physical activity patterns appeared to demand particular attention and counseling for both their lifestyle issues (sleep and physical activity) and their dysfunctional coping strategies.

Uncertainty parameter weighted entropy-based fuzzy c-means algorithm using complemented membership functions for noisy volumetric brain MR image segmentation

In this paper, we propose an uncertainty parameter weighted entropy-based fuzzy c-means clustering algorithm for noisy volumetric (3D) brain MR image segmentation using complemented global and spatially constraint local membership functions. Due to inherent noise and intensity inhomogeneity (IIH), the acquired MR images have blurry tissue boundaries. This leads to a situation where uncertainty arises while labeling a pixel/voxel into its proper tissue region. Further, it magnifies in the regions of different tissue boundaries. The proposed algorithm addresses this issue by introducing a class-level uncertainty parameter for each voxel and weightedly incorporating in the fuzzy objective function using complemented global and spatially constraint local fuzzy membership functions. It also incorporates total uncertainties in the 3D image domain by means of Shannon entropy. The complemented local fuzzy membership function estimates the degree of non-association, constraint by the local region-level intensity distribution. This framework allows the algorithm to utilize the spatial intensity distribution both in locally and globally within the image domain and produce more accurate cluster prototypes. We validate the proposed algorithm qualitatively and quantitatively with 10 3D simulated brain MR images, contaminated by noise and intensity inhomogeneity, 4 volumes of clinical real patient 3D brain MR images and a synthetic 3D image with added Rician noise. The simulation results in several evaluation indices indicate its superiority over state-of-the-art algorithms developed in recent past.