Geometric Clustering Research Articles

Accelerating Global Search of Large-Sized Silver Clusters Using Cluster Graph Attention Network.

Great efforts have been devoted to understanding the stability and reactivity of silver clusters, which usually depend on geometric structures, electronic configuration, and cluster size. Despite the fact that the jellium model and Wulff construction rule have successfully rationalized the stable clusters with "magic number" behavior, some experiments imply that silver clusters with 48 valence electrons also possess puzzling enhanced stability. In this work, using a recently developed deep learning technology, i.e., cluster graph attention network (CGANet), combined with a homemade comprehensive genetic algorithm (CGA) program, we searched the global minimum (GM) structures of Agn (n = 30-60) clusters with graphics processing unit acceleration, whose efficiency is about 2 orders of magnitude higher than that of the conventional density functional theory (DFT) calculations. GM structures and some representative isomers are reported at each size, revealing the competitive structural patterns based on truncated octahedra and icosahedra as well as the icosahedra-based layer-by-layer growth mode of large-sized Ag clusters. Most importantly, the size-dependent evolution behavior of structural and electronic properties of Agn (n = 30-60) clusters can successfully explain the observed stability at Ag48. Therefore, CGANet provides a powerful tool for rapidly exploring the potential energy surface of atoms with an accuracy comparable to that of DFT.

Design optimization of geometrically confined cardiac organoids enabled by machine learning techniques

Stem cell organoids are powerful models for studying organ development, disease modeling, drug screening, and regenerative medicine applications. The convergence of organoid technology, tissue engineering, and artificial intelligence (AI) could potentially enhance our understanding of the design principles for organoid engineering. In this study, we utilized micropatterning techniques to create a designer library of 230 cardiac organoids with 7 geometric designs. We employed manifold learning techniques to analyze single organoid heterogeneity based on 10 physiological parameters. We clustered and refined the cardiac organoids based on their functional similarity using unsupervised machine learning approaches, thus elucidating unique functionalities associated with geometric designs. We also highlighted the critical role of calcium transient rising time in distinguishing organoids based on geometric patterns and clustering results. This integration of organoid engineering and machine learning enhances our understanding of structure-function relationships in cardiac organoids, paving the way for more controlled and optimized organoid design.

FPDclustering: a comprehensive R package for probabilistic distance clustering based methods

AbstractData clustering has a long history and refers to a vast range of models and methods that exploit the ever-more-performing numerical optimization algorithms and are designed to find homogeneous groups of observations in data. In this framework, the probability distance clustering (PDC) family methods offer a numerically effective alternative to model-based clustering methods and a more flexible opportunity in the framework of geometric data clustering. Given nJ-dimensional data vectors arranged in a data matrix and the number K of clusters, PDC maximizes the joint density function that is defined as the sum of the products between the distance and the probability, both of which are measured for each data vector from each center. This article shows the capabilities of the PDC family, illustrating the package .

Algebraic model studies of the structure and reactions of 12C and 16O

The role of algebraic models and geometric cluster models of alpha clusters in the structure of ground and first excited 0+ and second excited 2+ states in 12C are evaluated with the aim of establishing if the rotational bands are compatible with rigid structures or if they are instead overlaps of different configurations. A rigid equilateral triangle shape is assumed in Ref.[2, 3]: the energy spectrum, electromagnetic observables are calculated and the transition densities are compared with elastic and inelastic cross-sections for various processes. In a different approach [4, 5], we solve the three-body quantum problem for 3 alphas using the orthogonality condition and the stochastic variational method with correlated Gaussian basis functions. The two-body density distributions indicate that the main configurations of both the second 0+ and 2+ states are acute iscosceles triangle shapes with a 8Be(0+)+α configuration. We also find clues that the second 2+ state is probably not a member of the rigid rotational band built on the Hoyle state.

Nonequilibrium critical dynamics of the two-dimensional ±J Ising model.

The ±J Ising model is a simple frustrated spin model, where the exchange couplings independently take the discrete value -J with probability p and +J with probability 1-p. It is especially appealing due to its connection to quantum error correcting codes. Here, we investigate the nonequilibrium critical behavior of the two-dimensional ±J Ising model, after a quench from different initial conditions to a critical point T_{c}(p) on the paramagnetic-ferromagnetic (PF) transition line, especially above, below, and at the multicritical Nishimori point (NP). The dynamical critical exponent z_{c} seems to exhibit nonuniversal behavior for quenches above and below the NP, which is identified as a preasymptotic feature due to the repulsive fixed point at the NP, whereas for a quench directly to the NP, the dynamics reaches the asymptotic regime with z_{c}≃6.02(6). We also consider the geometrical spin clusters (of like spin signs) during the critical dynamics. Each universality class on the PF line is uniquely characterized by the stochastic Loewner evolution with corresponding parameter κ. Moreover, for the critical quenches from the paramagnetic phase, the model, irrespective of the frustration, exhibits an emergent critical percolation topology at the large length scales.

Flow box decomposition for gradients of univariate polynomials, billiards on the Riemann sphere, tree-like configurations of vanishing cycles for $A_n$ curve singularities and geometric cluster monodromy

The base space of the universal unfolding of A_n -curve singularities is equipped with a stratification such that the geometric monodromy group is generated by wall-crossing mapping classes.

DIG-SLAM: an accurate RGB-D SLAM based on instance segmentation and geometric clustering for dynamic indoor scenes

Simultaneous localization and mapping (SLAM) has emerged as a critical technology enabling robots to navigate in unknown environments, drawing extensive attention within the robotics research community. However, traditional visual SLAM ignores the presence of dynamic objects in indoor scenes, and dynamic point features of dynamic objects can lead to incorrect data correlation, making the traditional visual SLAM is difficult to accurately estimate the camera’s pose when the objects in the scenes are moving. Using only point features cannot fully extract geometric information in dynamic indoor scenes, reducing the system’s robustness. To solve this problem, we develop a RGB-D SLAM system called DIG-SLAM. Firstly, the objects’ contour regions are extracted using the YOLOv7 instance segmentation method, serving as a prerequisite for determining dynamic objects and constructing a semantic information map. Meanwhile, the line features are extracted using the line segment detector algorithm, and the redundant line features are optimized via K-means clustering. Secondly, moving consistency checks combined with instance partitioning determine dynamic regions, and the point and line features of the dynamic regions are removed. Finally, the combination of static line features and point features optimizes the camera pose. Meanwhile, a static semantic octree map is created to provide richer and higher-level scene understanding and perception capabilities for robots or autonomous systems. The experimental results on the Technische Universität München dataset show that the average absolute trajectory error of the developed DIG-SLAM is reduced by 28.68% compared with the dynamic semantic SLAM. Compared with other dynamic SLAM methods, the proposed system shows better camera pose estimation accuracy and system’s robustness in dynamic indoor environments and better map building in real indoor scenes.

SiteFerret: Beyond Simple Pocket Identification in Proteins.

We present a novel method for the automatic detection of pockets on protein molecular surfaces. The algorithm is based on an ad hoc hierarchical clustering of virtual probe spheres obtained from the geometrical primitives used by the NanoShaper software to build the solvent-excluded molecular surface. The final ranking of putative pockets is based on the Isolation Forest method, an unsupervised learning approach originally developed for anomaly detection. A detailed importance analysis of pocket features provides insight into which geometrical (clustering) and chemical (amino acidic composition) properties characterize a good binding site. The method also provides a segmentation of pockets into smaller subpockets. We prove that subpockets are a convenient representation to pinpoint the binding site with great precision. SiteFerret is outstanding in its versatility, accurately predicting a wide range of binding sites, from those binding small molecules to those binding peptides, including difficult shallow sites.

Towards the Application of Purely Inorganic Icosahedral Boron Clusters in Emerging Nanomedicine.

Traditionally, drugs were obtained by extraction from medicinal plants, but more recently also by organic synthesis. Today, medicinal chemistry continues to focus on organic compounds and the majority of commercially available drugs are organic molecules, which can incorporate nitrogen, oxygen, and halogens, as well as carbon and hydrogen. Aromatic organic compounds that play important roles in biochemistry find numerous applications ranging from drug delivery to nanotechnology or biomarkers. We achieved a major accomplishment by demonstrating experimentally/theoretically that boranes, carboranes, as well as metallabis(dicarbollides), exhibit global 3D aromaticity. Based on the stability-aromaticity relationship, as well as on the progress made in the synthesis of derivatized clusters, we have opened up new applications of boron icosahedral clusters as key components in the field of novel healthcare materials. In this brief review, we present the results obtained at the Laboratory of Inorganic Materials and Catalysis (LMI) of the Institut de Ciència de Materials de Barcelona (ICMAB-CSIC) with icosahedral boron clusters. These 3D geometric shape clusters, the semi-metallic nature of boron and the presence of exo-cluster hydrogen atoms that can interact with biomolecules through non-covalent hydrogen and dihydrogen bonds, play a key role in endowing these compounds with unique properties in largely unexplored (bio)materials.

Longitudinal study investigating serum metabolites and their association with type 2 diabetes risk in a Korean population.

The lack of longitudinal metabolomics data and the statistical techniques to analyse them has limited the understanding of the metabolite levels related to type 2 diabetes (T2D) onset. Thus, we carried out logistic regression analysis and simultaneously proposed new approaches based on residuals of multiple logistic regression and geometric angle-based clustering for the analysis in T2D onset-specific metabolic changes. We used the sixth, seventh and eighth follow-up data from 2013, 2015 and 2017 among the Korea Association REsource (KARE) cohort data. Semi-targeted metabolite analysis was performed using ultraperformance liquid chromatography/triple quadrupole-mass spectrometry systems. As the results from the multiple logistic regression and a single metabolite in a logistic regression analysis varied dramatically, we recommend using models that consider potential multicollinearity among metabolites. The residual-based approach particularly identified neurotransmitters or related precursors as T2D onset-specific metabolites. By using geometric angle-based pattern clustering studies, ketone bodies and carnitines are observed as disease-onset specific metabolites and separated from others. To treat patients with early-stage insulin resistance and dyslipidaemia when metabolic disorders are still reversible, our findings may contribute to a greater understanding of how metabolomics could be used in disease intervention strategies during the early stages of T2D.

GULLY EXTRACTION AND MAPPING IN KAJOO-GARGAROO WATERSHED – COMPARATIVE EVALUATION OF DEM-BASED AND IMAGE-BASED MACHINE LEARNING ALGORITHM

Abstract. Monitoring and mapping eroded lands by gully erosion is an essential step to control gully networks. Advances in remote sensing and aerial photography have enabled users to capture data with variant temporal and spatial resolution that is needed in different fields. In addition, introducing different types of unmanned aerial vehicles (UAV) enabled to carry imaging payload. The orthophoto and digital elevation model (DTM) produced from aerial images taken by Aeria-X camera mounted on Sensefly eBee-X drone was employed to identify and map eroded areas by gully in Kajoo-Gargaroo watershed in Chabahar, south-eastern part of Iran. Digitizing gully boarders manually is a tiring and time-consuming process for the operators. Maximum likelihood algorithm as one of the machine learning algorithm was also used to classify orthophoto in order to extract gully borders in the study area. In this study a new algorithm based on analysing geometric features and clustering of the DTM was used to map gullies automatically. The results of the proposed method and machine learning algorithm were compared with the manually digitized gully map. Quantitative evaluation demonstrates that our proposed method reaches better overall accuracy compared to machine learning algorithm with the increase of 7.2 percent in overall accuracy.

Geometric consistent fuzzy cluster ensemble with membership reconstruction for image segmentation

In recent years, to handle the ubiquitous uncertainty and unknown noise, different fuzzy clustering methods have been introduced to solve image segmentation problem for various applications, such as natural image, satellite image, multichannel (typically remote sensing) image. In fact, it is hard to know which one is the best for specified task. Cluster ensemble method is proposed to solve the problem of choosing a particular fuzzy clustering algorithm, or a special image processing before clustering, that best suits the given image segmentation task. In fuzzy cluster ensemble, membership vectors generated from different fuzzy clustering methods are merged into one vector as an input object, which is also a combination of data partitions. However, this kind of input object may lose detail information from original target image and may cause inaccurate edges in segmentation results. Moreover, by means of treating it as a new representation of original data, the membership vector of fuzzy cluster ensemble should be intuitively geometric consistent with the original target image. In this paper, by holding this view, we develop a geometric consistent fuzzy cluster ensemble model for spatial data, which involves a constraint between the membership and its reconstruction, to improve the clustering performance on image segmentation. In the proposed model, a pre-determined gradient-preserving weight is used in the membership reconstruction item to make the membership matrix be geometric consistent with the original target image. A semi-implicit optimization iterative algorithm is adopted to solve the proposed geometric consistent model. Experimental results demonstrate the effectiveness of proposed model in synthetic and real-world image segmentation problems over several state-of-the-art methods.

GeoWaVe: geometric median clustering with weighted voting for ensemble clustering of cytometry data.

Clustering is an unsupervised method for identifying structure in unlabelled data. In the context of cytometry, it is typically used to categorize cells into subpopulations of similar phenotypes. However, clustering is greatly dependent on hyperparameters and the data to which it is applied as each algorithm makes different assumptions and generates a different 'view' of the dataset. As such, the choice of clustering algorithm can significantly influence results, and there is often not one preferred method but different insights to be obtained from different methods. To overcome these limitations, consensus approaches are needed that directly address the effect of competing algorithms. To the best of our knowledge, consensus clustering algorithms designed specifically for the analysis of cytometry data are lacking. We present a novel ensemble clustering methodology based on geometric median clustering with weighted voting (GeoWaVe). Compared to graph ensemble clustering methods that have gained popularity in single-cell RNA sequencing analysis, GeoWaVe performed favourably on different sets of high-dimensional mass and flow cytometry data. Our findings provide proof of concept for the power of consensus methods to make the analysis, visualization and interpretation of cytometry data more robust and reproducible. The wide availability of ensemble clustering methods is likely to have a profound impact on our understanding of cellular responses, clinical conditions and therapeutic and diagnostic options. GeoWaVe is available as part of the CytoCluster package https://github.com/burtonrj/CytoCluster and published on the Python Package Index https://pypi.org/project/cytocluster. Benchmarking data described are available from https://doi.org/10.5281/zenodo.7134723. Supplementary data are available at Bioinformatics online.

MDSCAN: RMSD-based HDBSCAN clustering of long molecular dynamics.

The term clustering designates a comprehensive family of unsupervised learning methods allowing to group similar elements into sets called clusters. Geometrical clustering of molecular dynamics (MD) trajectories is a well-established analysis to gain insights into the conformational behavior of simulated systems. However, popular variants collapse when processing relatively long trajectories because of their quadratic memory or time complexity. From the arsenal of clustering algorithms, HDBSCAN stands out as a hierarchical density-based alternative that provides robust differentiation of intimately related elements from noise data. Although a very efficient implementation of this algorithm is available for programming-skilled users (HDBSCAN*), it cannot treat long trajectories under the de facto molecular similarity metric RMSD. Here, we propose MDSCAN, an HDBSCAN-inspired software specifically conceived for non-programmers users to perform memory-efficient RMSD-based clustering of long MD trajectories. Methodological improvements over the original version include the encoding of trajectories as a particular class of vantage-point tree (decreasing time complexity), and a dual-heap approach to construct a quasi-minimum spanning tree (reducing memory complexity). MDSCAN was able to process a trajectory of 1 million frames using the RMSD metric in about 21 h with <8 GB of RAM, a task that would have taken a similar time but more than 32 TB of RAM with the accelerated HDBSCAN* implementation generally used. The source code and documentation of MDSCAN are free and publicly available on GitHub (https://github.com/LQCT/MDScan.git) and as a PyPI package (https://pypi.org/project/mdscan/). Supplementary data are available at Bioinformatics online.

Self-supervised deep geometric subspace clustering network

Graph mining has been widely studied to analyze real-world graph properties and applied to various applications. In particular, graph subspace clustering performance, defined as partitioning high-dimensional graph data into several clusters by finding minimum weights for the edges, has been consistently improved by exploiting deep learning algorithms with Euclidean features extracted from Euclidean domains (image datasets). Most subspace clustering algorithms tend to extract features from the Euclidean domain to identify graph characteristics and structures, and hence are limited for real-world data applications in non-Euclidean domains. This paper proposes a self-supervised deep geometric subspace clustering algorithm optimized for non-Euclidean high-dimensional graph data by emphasizing spatial features and geometric structures while simultaneously reducing redundant nodes and edges. Quantitative and qualitative experimental results verified the proposed approach is effective for graph clustering compared with previous state-of-the-art algorithms on public datasets.

Geometrical modelling of neuronal clustering and development

The dynamic geometry of neuronal development is an essential concept in theoretical neuroscience. We aimed to design a mathematical model which outlines stepwise in an innovative form and designed to model neuronal development geometrically and modelling spatially the neuronal-electrical field interaction. We demonstrated flexibility in forming the cell and its nucleus to show neuronal growth from inside to outside that uses a fractal cylinder to generate neurons (pyramidal/sphere) in form of mathematically called ‘surface of revolution’. Furthermore, we verified the effect of the adjacent neurons on a free branch from one-side, by modelling a ‘normal vector surface’ that represented a group of neurons. Our model also indicated how the geometrical shapes and clustering of the neurons can be transformed mathematically in the form of vector field that is equivalent to the neuronal electromagnetic activity/electric flux. We further simulated neuronal-electrical field interaction that was implemented spatially using Van der Pol oscillator and taking Laplacian vector field as it reflects biophysical mechanism of neuronal activity and geometrical change. In brief, our study would be considered a proper platform and inspiring modelling for next more complicated geometrical and electrical constructions.

Geometric weighting subspace clustering on nonlinear manifolds

Geometric weighting subspace clustering on nonlinear manifolds

A Maritime Traffic Network Mining Method Based on Massive Trajectory Data

Intelligent ships are the future direction of maritime transportation. Route design and route planning of intelligent ships require high-precision, real-time maritime traffic network information, which changes dynamically as the traffic environment changes. At present, there is a lack of high-precision and accurate information extraction methods for maritime traffic networks. Based on the massive trajectory data of vessels, the adaptive waypoint extraction model (ANPG) is proposed to extract the critical waypoints on the traffic network, and the improved kernel density estimation method (KDE-T) is constructed to mine the spatial–temporal characteristics of marine lanes. Then, an automatic traffic network generation model (NNCM), based on the pix2pix network, is put forward to reconstruct the maritime traffic network. NNCM has been tested on the historical trajectory data of Humen waters and Dongping waters in China, the experimental results show that the NNCM model improves the extraction accuracy by 13% and 33% compared to the geometric analysis method and density clustering method. It is of great significance to improve the navigation accuracy of intelligent ships. This method can also provide important technical support for waterway design and monitoring and maritime traffic supervision.

Corrections to scaling in geometrical clusters of the 2D Ising model

We study the scaling of the average cluster size and percolation strength of geometrical clusters for the two-dimensional Ising model. By means of Monte Carlo simulations and a finite-size scaling analysis we discuss the appearance of corrections to scaling for different definitions of cluster sets. We find that including all percolating clusters, or excluding only clusters that percolate in one but not the other direction, leads to smaller corrections to scaling for the average cluster size as compared to the other definitions considered. The percolation strength is less sensitive to the definitions used.

PathDetect-SOM: A Neural Network Approach for the Identification of Pathways in Ligand Binding Simulations.

Understanding the process of ligand–protein recognition is important to unveil biological mechanisms and to guide drug discovery and design. Enhanced-sampling molecular dynamics is now routinely used to simulate the ligand binding process, resulting in the need for suitable tools for the analysis of large data sets of binding events. Here, we designed, implemented, and tested PathDetect-SOM, a tool based on self-organizing maps to build concise visual models of the ligand binding pathways sampled along single simulations or replicas. The tool performs a geometric clustering of the trajectories and traces the pathways over an easily interpretable 2D map and, using an approximate transition matrix, it can build a graph model of concurrent pathways. The tool was tested on three study cases representing different types of problems and simulation techniques. A clear reconstruction of the sampled pathways was derived in all cases, and useful information on the energetic features of the processes was recovered. The tool is available at https://github.com/MottaStefano/PathDetect-SOM.