Clustering Constraints Research Articles

Categorizing and Determining of BI-RAD Breast Cancer Score by Using Deep Learning Techniques

Breast cancer is second only to skin cancer in prevalence. Failure to detect and treat breast cancer early could be fatal. Breast cancer is more common in underdeveloped countries due to low health awareness and limited early detection methods. However, detecting equipment and radiography advances have helped solve this difficulty and suggest a drop in mortality. Along with ultrasounds, mammography, Magnetic Resonance Imaging (MRI), Computed tomography (CT) scan, and Positron emission tomography (PET) scans are used for diagnosis. These devices add data to test findings for greater accuracy. Diagnosticians determine breast cancer stage by examining tumor size, shape, and spread. Artificial intelligence users employ these factors as fixed values to classify the illness using region of interest (RIO), Gray Level Co-Occurrence Matrix (GLCAM), clustering, or mass constraints like diameter and volume. Artificial intelligence algorithms have created many techniques to extract features from massive volumes of data through training, such as deep learning. The study investigated DL algorithms (Attention mechanism and efficintNetB7 ) to determine the breast imaging-reporting and data system (BI-RADS) score by categorizing mammography images. The dataset Digital Database for Screening Mammography (DDSM) used in this study, acquired from Kaggle, contains 55,890 training samples, of which 86% are negative, and 14% are positive, categorized into classes C1, C2, C3, C4, and C5. This work utilized deep learning techniques and algorithms to accurately categorize breast cancer at 93%, 92%, 90%, and 93% for each category (C2, C3, C4, and C5). We developed the BI-RADS classifier model using the bycharm framework, an integrated development environment (IDE) for Python programming, and using multiple libraries, namely NumPy, Pandas, TensorFlow, Keras, Matplotlib, and Seaborn. This study used a laptop with the following specifications: an Intel Core i7 CPU, 16GB of RAM, and Intel RTX integrated graphics.

Self-Supervised Spatiotemporal Clustering of Vehicle Emissions With Graph Convolutional Network.

Spatiotemporal clustering of vehicle emissions, which reveals the evolution pattern of air pollution from road traffic, is a challenging representation learning task due to the lack of supervision. Some recent work building upon graph convolutional network (GCN) models the intrinsic spatiotemporal correlations among the nodes in road networks as graph representations for clustering. However, these existing methods ignore the interactions between spatial and temporal variations in vehicle emissions, resulting in incomplete descriptions and inaccurate detection of the evolution pattern of air pollution. To address this issue, this article proposes a two-way self-supervised spatiotemporal representation learning scheme, in which the temporal and spatial features are progressively learned in a mutually reinforced manner. Our proposed method is based on the observation that though the variation in vehicle emissions in the road network is consistent in the spatial and temporal domains, its expression is more distinct in temporal sequences. To this end, the input emission data are first projected into an initial temporal representation space spanned by the captured features from a pretrained BiLSTM network. Then the generated distribution of temporal features is used to construct an objective constraint for high-purity clustering through a two-way self-supervised mechanism, which is leveraged as a constraint for the feature clustering of a GCN. Furthermore, to eliminate the initial errors, a joint optimization scheme is presented to generate the decoupled clustering results through the progressive refinement of representation and clustering. Our proposed method is evaluated on the traffic emission dataset of Xian city in 2020, and the experimental results have demonstrated the superiority against the state-of-the-art.

Probing Populations of Dark Stellar Remnants in the Globular Clusters 47 Tuc and Terzan 5 Using Pulsar Timing

We present a new method to combine multimass equilibrium dynamical models and pulsar timing data to constrain the mass distribution and remnant populations of Milky Way globular clusters (GCs). We first apply this method to 47 Tuc, a cluster for which there exists an abundance of stellar kinematic data and which is also host to a large population of millisecond pulsars. We demonstrate that the pulsar timing data allow us to place strong constraints on the overall mass distribution and remnant populations even without fitting on stellar kinematics. Our models favor a small population of stellar-mass black holes (BHs) in this cluster (with a total mass of 446−72+75M⊙ ), arguing against the need for a large (>2000 M ⊙) central intermediate-mass BH. We then apply the method to Terzan 5, a heavily obscured bulge cluster that hosts the largest population of millisecond pulsars of any Milky Way GC and for which the collection of conventional stellar kinematic data is very limited. We improve existing constraints on the mass distribution and structural parameters of this cluster and place stringent constraints on its black hole content, finding an upper limit on the mass in BHs of ∼4000 M ⊙. This method allows us to probe the central dynamics of GCs even in the absence of stellar kinematic data and can be easily applied to other GCs with pulsar timing data, for which data sets will continue to grow with the next generation of radio telescopes.

Improving photometric galaxy clustering constraints with cross-bin correlations

Improving photometric galaxy clustering constraints with cross-bin correlations

A Low Transformed Tubal Rank Tensor Model Using a Spatial-Tubal Constraint for Sample Clustering with Cancer Multi-omics Data

Background: Since each dimension of a tensor can store different types of genomics data, compared to matrix methods, utilizing tensor structure can provide a deeper understanding of multi-dimensional data while also facilitating the discovery of more useful information related to cancer. However, in reality, there are issues such as insufficient utilization of prior knowledge in multi-omics data and limitations in the recovery of low-tubal-rank tensors. Therefore, the method proposed in this article was developed. Objective: In this paper, we proposed a low transformed tubal rank tensor model (LTTRT) using a spatial-tubal constraint to accurately partition different types of cancer samples and provide reliable theoretical support for the identification, diagnosis, and treatment of cancer. Method: In the LTTRT method, the transformed tensor nuclear norm based on the transformed tensor singular value decomposition is characterized by the low-rank tensor, which can explore the global low-rank property of the tensor, resolving the challenge of the tensor nuclear norm-based method not achieving the lowest tubal rank. Additionally, the introduction of weighted total variation regularization is conducive to extracting more information from sequencing data in both spatial and tubal dimensions, exploring cross-correlation features of multiple genomic data, and addressing the problem of overlooking prior knowledge from various perspectives. In addition, the L1-norm is used to improve sparsity. A symmetric Gauss‒Seidel-based alternating direction method of multipliers (sGS-ADMM) is used to update the LTTRT model iteratively. Results: The experiments of sample clustering on multiple integrated cancer multi-omics datasets show that the proposed LTTRT method is better than existing methods. Experimental results validate the effectiveness of LTTRT in accurately partitioning different types of cancer samples. result: The experiments of sample clustering on multiple integrated cancer multi-omics datasets show that the proposed LTTRT method is better than existing methods. Experimental results validate the effectiveness of LTTRT in accurately partitioning different types of cancer samples. Conclusion: The LTTRT method achieves precise segmentation of different types of cancer samples.

NeRF-Texture: Synthesizing Neural Radiance Field Textures.

Texture synthesis is a fundamental problem in computer graphics that would benefit various applications. Existing methods are effective in handling 2D image textures. In contrast, many real-world textures contain meso-structure in the 3D geometry space, such as grass, leaves, and fabrics, which cannot be effectively modeled using only 2D image textures. We propose a novel texture synthesis method with Neural Radiance Fields (NeRF) to capture and synthesize textures from given multi-view images. In the proposed NeRF texture representation, a scene with fine geometric details is disentangled into the meso-structure textures and the underlying base shape. This allows textures with meso-structure to be effectively learned as latent features situated on the base shape, which are fed into a NeRF decoder trained simultaneously to represent the rich view-dependent appearance. Using this implicit representation, we can synthesize NeRF-based textures through patch matching of latent features. However, inconsistencies between the metrics of the reconstructed content space and the latent feature space may compromise the synthesis quality. To enhance matching performance, we further regularize the distribution of latent features by incorporating a clustering constraint. In addition to generating NeRF textures over a planar domain, our method can also synthesize NeRF textures over curved surfaces, which are practically useful. Experimental results and evaluations demonstrate the effectiveness of our approach.

Constraining the Clustering and 21 cm Signature of Radio Galaxies at Cosmic Dawn

The efficiency of radio emission is an important unknown parameter of early galaxies at cosmic dawn, as models with high efficiency have been shown to modify the cosmological 21 cm signal substantially, deepening the absorption trough and boosting the 21 cm power spectrum. Such models have been previously directly constrained by the overall extragalactic radio background, as observed by Absolute Radiometer for Cosmology, Astrophysics, and Diffuse Emission 2 and Long Wavelength Array. In this work, we constrain the clustering of high-redshift radio sources by utilizing the observed upper limits on arcminute-scale anisotropy from the Very Large Array at 4.9 GHz and Australia Telescope Compact Array at 8.7 GHz. Using a seminumerical simulation of a plausible astrophysical model for illustration, we show that the clustering constraints on the radio efficiency are much stronger than those from the overall background intensity by a factor that varies between 18 and 55 in the redshift range of 7–22. As a result, the predicted maximum depth of the global 21 cm signal is lowered by a factor of 6 (to 1400 mK), and the maximum 21 cm power spectrum peak at cosmic dawn is lowered by a factor of 45 (to 1.3 × 105 mK2). We conclude that the observed clustering is the strongest current direct constraint on such models, but strong early radio emission from galaxies remains viable for producing a strongly enhanced 21 cm signal from cosmic dawn.

Evolution-aware Constraint Derivation Approach for Software Remodularization

Existing software clustering techniques tend to ignore prior knowledge from domain experts, leading to results (suggested big-bang remodularization actions) that can not acceptable to developers. Incorporating domain experts knowledge or constraints during clustering ensures the obtained modularization aligns with developers’ perspectives, enhancing software quality. However, manual review by knowledgeable domain experts for constraint generation is time-consuming and labor-intensive. In this paper, we propose an evolution-aware constraint derivation approach, Escort, which automatically derives clustering constraints based on the evolutionary history from the analyzed software. Specifically, Escort can serve as an alternative approach to derive implicit and explicit constraints in situations where domain experts are absent. In the subsequent constrained clustering process, Escort can be considered as a framework to help supplement and enhance various unconstrained clustering techniques to improve their accuracy and reliability. We evaluate Escort based on both quantitative and qualitative analysis. In quantitative validation, Escort, using generated clustering constraints, outperforms seven classic unconstrained clustering techniques. Qualitatively, a survey with developers from five IT companies indicates that 89% agree with Escort’s clustering constraints. We also evaluate the utility of refactoring suggestions from our constrained clustering approach, with 54% acknowledged by project developers, either implemented or planned for future releases.

Markov-Embedded Affinity Learning with Connectivity Constraints for Subspace Clustering

Subspace clustering algorithms have demonstrated remarkable success across diverse fields, including object segmentation, gene clustering, and recommendation systems. However, they often face challenges, such as omitting cluster information and the neglect of higher-order neighbor relationships within the data. To address these issues, a novel subspace clustering method named Markov-Embedded Affinity Learning with Connectivity Constraints for Subspace Clustering is proposed. This method seamlessly embeds Markov transition probability information into the self-expression, leveraging a fine-grained neighbor matrix to uncover latent data structures. This matrix preserves crucial high-order local information and complementary details, ensuring a comprehensive understanding of the data. To effectively handle complex nonlinear relationships, the method learns the underlying manifold structure from a cross-order local neighbor graph. Additionally, connectivity constraints are applied to the affinity matrix, enhancing the group structure and further improving the clustering performance. Extensive experiments demonstrate the superiority of this novel method over baseline approaches, validating its effectiveness and practical utility.

Ship trajectory segmentation and semisupervised clustering via geospatial background knowledge

Cluster analysis is a common application of maritime traffic pattern recognition. However, most current methods are unsupervised clustering algorithms that rely solely on the features of the trajectories themselves for clustering, making them susceptible to uneven density distributions. To address this issue, we propose a semisupervised clustering algorithm that utilizes geospatial data to segment trajectories and generate clustering constraints. First, shoreline and anchorage information are employed for trajectory segmentation to enhance the consistency of local trajectory features. Second, cannot-link constraints derived from shoreline data are used to modify the distance between two trajectories, thereby preventing the clustering of trajectories separated by nonnavigable waters into a single cluster. Last, experimental verification is conducted using automatic identification system data, and the results are compared with those of existing algorithms. The results demonstrate more concentrated trajectory segmentation points, easier selection of clustering parameters, and significantly improved evaluation outcomes based on external clustering validity indices.

Orthogonal graph regularized non-negative matrix factorization under sparse constraints for clustering

The standard NMF algorithm is not suitable for sampling data from low-dimensional manifolds embedded in high-dimensional environmental spaces, as the geometric information hidden in feature manifolds and sample manifolds is rarely learned. In order to obtain better clustering performance based on NMF, manifold and orthogonal constraint, a new type of model named Orthogonal Graph regularized Non-negative Matrix Factorization model under Sparse Constraints (OGNMFSC) is proposed. Firstly, this type of model constructs a nearest neighbor graph to encode the geometric information of the data space, in order to obtain more discriminative ability by preserving the structure of the graph. Secondly, this type of model adds orthogonal constraints to achieve better local representation and significantly reduce the inconsistency between the original matrix and the basis vectors. Thirdly, by adding sparse constraints to obtain a sparser representation matrix, the clustering performance of the model can be improved. The main conclusion of this paper is that two effective algorithms have been generated to solve the model, which not only provides theoretical convergence proof for these two algorithms, but also demonstrates significant clustering performance in experiments compared to classical models such as K-means, PCA, NMF, Semi-NMF, NMFSC, ONMF, GNMF, NeNMF.

Zonotope approximation based flexible cluster division method for load‐side resource scheduling

AbstractIn view of the insufficient flexibility and adjustment capabilities caused by the high proportion of renewable energy connected to the distribution network and the limitations of the source‐side adjustment method, a load‐side resource flexibility cluster partitioning method based on zonotope approximation is proposed to cope with the flexibility adjustment requirements brought by uncertain resources. First, the constraint space of load‐side resources such as energy storage, multi‐source mobile energy storage, electric vehicles, and temperature‐controlled loads is described as a convex polyhedral form general model based on the virtual battery framework, and the zonotope approximation is used to integrate its constraint space with the Minkowski sum. Secondly, modularity and flexibility supply and demand balance index are proposed to perform flexibility clustering of load‐side resources. Then, the minimum comprehensive operating cost of the cluster aggregator is set as the optimization goal, the cluster constraint space is equivalent to the cost function, and the optimal charging and discharging power and flexibility adjustment capacity of the load‐side resources are obtained. Finally, the method proposed here is verified through numerical example simulation to effectively balance aggregation accuracy and calculation speed.

Balancing exploration and exploitation: Unleashing the adaptive power of automatic cuckoo search for meta-heuristic optimization

Meta-heuristic optimization algorithms are versatile and efficient techniques for solving complex optimization problems. When applied to clustering algorithms, these algorithms offer numerous advantages over traditional optimization methods, including global search capabilities, iterative refinement processes, robustness to initial conditions, and flexibility in handling diverse clustering objectives and constraints. Employing meta-heuristic optimization in clustering algorithms leads to improved accuracy, scalability, robustness, and flexibility in finding optimal or near-optimal clustering solutions. These algorithms generate new individuals iteratively using nature-inspired operations to obtain high-quality results. However, they often suffer from slower convergence and lack guarantees of finding the best solution for every problem, posing ongoing challenges in algorithm development. This study focuses on addressing the issue of premature convergence in metaheuristic algorithms by introducing an automatic cuckoo search (AuCS) algorithm. The AuCS algorithm aims to strike a balance between exploration and exploitation by dynamically updating the step size in each generation, thereby avoiding premature convergence. To evaluate the effectiveness of the proposed algorithm, experiments were conducted on 13 standard benchmark functions and 14 CEC 2005 benchmark functions. In overall performance, AuCS has the best optimum value in 72.22% of cases. This demonstrates the efficacy of the proposed algorithm in achieving improved clustering accuracy and minimizing intra-cluster distance. The proposed AuCS algorithm was applied to data clustering and compared with four swarm optimization algorithms. Here, AuCS outperforms these well-known algorithms in 5 out of 7 datasets. The experimental evaluations in both benchmark functions and clustering problems confirm the promising results of the proposed algorithm, suggesting that AuCS could be considered as a potential improvement over the cuckoo search algorithm.

A Theoretical Analysis of Density Peaks Clustering and the Component-Wise Peak-Finding Algorithm.

Density peaks clustering detects modes as points with high density and large distance to points of higher density. Each non-mode point is assigned to the same cluster as its nearest neighbor of higher density. Density peaks clustering has proved capable in applications, yet little work has been done to understand its theoretical properties or the characteristics of the clusterings it produces. Here, we prove that it consistently estimates the modes of the underlying density and correctly clusters the data with high probability. However, noise in the density estimates can lead to erroneous modes and incoherent cluster assignments. A novel clustering algorithm, Component-wise Peak-Finding (CPF), is proposed to remedy these issues. The improvements are twofold: 1) the assignment methodology is improved by applying the density peaks methodology within level sets of the estimated density; 2) the algorithm is not affected by spurious maxima of the density and hence is competent at automatically deciding the correct number of clusters. We present novel theoretical results, proving the consistency of CPF, as well as extensive experimental results demonstrating its exceptional performance. Finally, a semi-supervised version of CPF is presented, integrating clustering constraints to achieve excellent performance for an important problem in computer vision.

Dynamic Generation of Subordinate Clusters Based on Bayesian Information Criterion for Must-Link Constrained K-Means

This paper proposes a constrained K-means clustering method that dynamically generates subordinate clusters based on Bayesian information criterion (BIC). COP K-means, which considers a pairwise constraints in partition-based clustering, have difficulty in handling the case that a must-link is given to instances located far away from each other. To address this problem, the proposed method generates subordinate clusters that have a must-link to a master cluster during a clustering process. The final clustering result is obtained by merging the subordinate clusters. The proposed method determines whether to generate subordinate clusters or not based on the BIC. This paper also introduces an idea of mitigating the sensitivity to initial position of subordinate clusters. The effectiveness of the proposed methods is shown through the experiment with two synthetic datasets.

Multi-Dimensional Clustering Based on Restricted Distance-Dependent Mixture Dirichlet Process for Diffusion Tensor Imaging

Brain imaging research poses challenges due to the intricate structure of the brain and the absence of clearly discernible features in the images. In this study, we propose a technique for analyzing brain image data identifying crucial regions relevant to patients’ conditions, specifically focusing on Diffusion Tensor Imaging data. Our method utilizes the Bayesian Dirichlet process prior incorporating generalized linear models, that enhances clustering performance while it benefits from the flexibility of accommodating varying numbers of clusters. Our approach improves the performance of identifying potential classes utilizing locational information by considering the proximity between locations as clustering constraints. We apply our technique to a dataset from Transforming Research and Clinical Knowledge in Traumatic Brain Injury study, aiming to identify important regions in the brain’s gray matter, white matter, and overall brain tissue that differentiate between young and old age groups. Additionally, we explore a link between our discoveries and the existing outcomes in the field of brain network research.

Unknown DDoS Attack Detection with Fuzzy C-Means Clustering and Spatial Location Constraint Prototype Loss

Unknown DDoS Attack Detection with Fuzzy C-Means Clustering and Spatial Location Constraint Prototype Loss

Graph-Based Semi-Supervised Deep Image Clustering With Adaptive Adjacency Matrix.

Image clustering is a research hotspot in machine learning and computer vision. Existing graph-based semi-supervised deep clustering methods suffer from three problems: 1) because clustering uses only high-level features, the detailed information contained in shallow-level features is ignored; 2) most feature extraction networks employ the step odd convolutional kernel, which results in an uneven distribution of receptive field intensity; and 3) because the adjacency matrix is precomputed and fixed, it cannot adapt to changes in the relationship between samples. To solve the above problems, we propose a novel graph-based semi-supervised deep clustering method for image clustering. First, the parity cross-convolutional feature extraction and fusion module is used to extract high-quality image features. Then, the clustering constraint layer is designed to improve the clustering efficiency. And, the output layer is customized to achieve unsupervised regularization training. Finally, the adjacency matrix is inferred by actual network prediction. A graph-based regularization method is adopted for unsupervised training networks. Experimental results show that our method significantly outperforms state-of-the-art methods on USPS, MNIST, street view house numbers (SVHN), and fashion MNIST (FMNIST) datasets in terms of ACC, normalized mutual information (NMI), and ARI.

An adaptive clustering constraint inversion method for gravity data

Clustering constraint is one of the effective ways to improve reliability of the inversion results by incorporating petrophysical information based on some mathematical techniques, such as the Fuzzy C-means clustering (FCM) algorithm. However, for most practical geophysical works, enough reliable petrophysical information is not available. In this way, the FCM inversion method is difficult to be performed. In order to solve this problem to some extent, we proposed an adaptive FCM inversion method (AFCM) in this study, with which the cluster information contained in the gravity data can be extracted adaptively and automatically, and then the FCM inversion can be executed without prior petrophysical information. We presented the detailed steps of the proposed method and illustrated its effectiveness on synthetic and field example tests. The obtained inversion results demonstrate that the AFCM method yields much better results compared with the conventional inversion methods without clustering information, as well as those obtained by using the FCM methods with wrong petrophysical information.

Non-negative Tucker decomposition with graph regularization and smooth constraint for clustering

Non-negative Tucker decomposition (NTD) and its graph regularized extensions are the most popular techniques for representing high-dimensional non-negative data, which are typically found in a low-dimensional sub-manifold of ambient space, from a geometric perspective. Therefore, the performance of the graph-based NTD methods relies heavily on the low-dimensional representation of the original data. However, most existing approaches treat the last factor matrix in NTD as a low-dimensional representation of the original data. This treatment leads to the loss of the original data’s multi-linear structure in the low-dimensional subspace. To remedy this defect, we propose a novel graph regularized Lp smooth NTD (GSNTD) method for high-dimensional data representation by incorporating graph regularization and an Lp smoothing constraint into NTD. The new graph regularization term constructed by the product of the core tensor and the last factor matrix in NTD, and it is used to uncover hidden semantics while maintaining the intrinsic multi-linear geometric structure of the data. The addition of the Lp smoothing constraint to NTD may produce a more accurate and smoother solution to the optimization problem. The update rules and the convergence of the GSNTD method are proposed. In addition, a randomized variant of the GSNTD algorithm based on fiber sampling is proposed. Finally, the experimental results on four standard image databases show that the proposed method and its randomized variant have better performance than some other state-of-the-art graph-based regularization methods for image clustering.