Intracluster Density Research Articles

Graph clustering with Boltzmann machines

Graph clustering is the process of labeling nodes so that nodes sharing common labels form densely connected subgraphs with sparser connections to the remaining vertices. Because of its difficult formulation, we translate the intra-cluster density maximization problem to a distance minimization problem. To achieve this reformulation, we use a novel vertex–vertex distance that accurately reflects density. Specifically, we extend the recent binary quadratic K-medoids formulation to graph clustering. We also generalize a quadratic formulation originally designed for partitioning complete graphs. Because binary quadratic optimization is an NP-hard problem, we obtain numerical solutions for these formulations through the use of two novel Boltzmann machine (meta-)heuristics. For benchmarking purposes, we compare solution quality and computational performances to those obtained using a commercial solver, Gurobi. We also compare clustering quality to the clusters obtained using the popular Louvain modularity maximization method. Our initial results clearly demonstrate the superiority of our problem formulations combined with our Boltzmann machines. In the case of smaller less complex graphs, our formulations solved using Boltzmann machines provide the same solutions as Gurobi, but with solution times that are orders of magnitude lower. In the case of larger and more complex graphs, Gurobi either fails to return meaningful results within a reasonable time frame or returns inferior results. Finally, we also note that both our clustering formulations, the distance minimization and K-medoids, when solved using our Boltzmann machines, yield clusters of superior quality to those obtained with the Louvain algorithm.

Wafer Image Preprocessing Based on Density Based Spatial Clustering of Application with Noise

With the development of microelectronic manufacturing technology, semiconductor manufacturing presents the trend of maximization of scale and miniaturization of process size. Even if the wafer production now has a high automation of the production process, high-precision production equipment and advanced production technology, wafer abnormal situation is still inevitable. Abnormal conditions in semiconductor manufacturing process will reduce the yield of wafer products and increase production costs. The later analysis becomes the necessary means to improve the wafer yield. With the rapid development of modern computing power, the application of machine learning-based automatic detection method in semiconductor production is irresistible. In addition to its spatial pattern, there are many noises that can affect the classification of defects, so it is necessary to preprocess the wafer diagram. The traditional density based spatial clustering of application with noise (DBSCAN) algorithm needs to determine two clustering parameters artificially, and the choice of parameters can affect the clustering effect easily, the parameter list was obtained by K-mean nearest neighbor algorithm and mathematical expectation method, and the integrated parameters of intra-cluster density and inter-cluster density after DBSCAN clustering were selected as evaluation indexes to select the optimal parameters. Finally, a self-adaptive (SA)-DBSCAN map is obtained by retaining the largest cluster, adding feature points and feature clusters, thus improving the yield of wafer.

Machine Learning-Based Multipath Components Clustering and Cluster Characteristics Analysis in High-Speed Railway Scenarios

Channel multipath components (MPCs) clustering and cluster characterization are the prerequisite for the development of cluster based channel models. This article investigates the MPCs clustering based on machine learning (ML) and analyzes the cluster characteristics in typical high-speed railway (HSR) scenarios. A variational Bayesian Gaussian mixture model (GMM)-based algorithm is introduced to achieve the space–time clustering of MPCs, which incorporates the statistical characteristics of MPCs and can automatically determine the optimum number of clusters. Moreover, a novel density-based validity index is proposed for evaluating the MPCs clustering performance. The proposed validity index improves the traditional index by considering the intracluster density, which can be calculated according to the Graham scanning method and Green’s formula. In addition to synthetic datasets, realistic MPCs datasets collected in an HSR obstructed viaduct scenario are used for the performance evaluation of the clustering algorithm and clustering validity index. Based on clustering results in the measured scenario, static cluster characteristics, including cluster number, intercluster and intracluster delay spreads (DSs) and angle spreads (ASs), and dynamic cluster characteristics such as cluster lifetime and birth and death property of clusters, are extracted and analyzed. These results will be useful for cluster-based channel modeling in future HSR mobile communication systems.

An empirical comparison of connectivity-based distances on a graph and their computational scalability

Abstract In this study, we compare distance measures with respect to their ability to capture vertex community structure and the scalability of their computation. Our goal is to find a distance measure which can be used in an aggregate pairwise minimization clustering scheme. The minimization should lead to subsets of vertices with high induced subgraph density. Our definition of distance is rooted in the notion that vertices sharing more connections are closer to each other than vertices which share fewer connections. This definition differs from that of the geodesic distance typically used in graphs. It is based on neighbourhood overlap, not shortest path. We compare four distance measures from the literature and evaluate their accuracy in reflecting intra-cluster density, when aggregated (averaged) at the cluster level. Our tests are conducted on synthetic graphs, where clusters and intra-cluster densities are known in advance. We find that amplified commute, Otsuka–Ochiai and Jaccard distances display a consistent inverse relation to intra-cluster density. We also conclude that the computation of amplified commute distance does not scale as well to large graphs as that of the other two distances.

A self-adaptive DBSCAN-based method for wafer bin map defect pattern classification

The wafer map is obtained by testing each die in the wafer during semiconductor production for defects and marking the defective die. The classification of wafer maps can provide evidence for problems occurring in the production process, so as to solve the problems and reduce the costs. Before classifying the wafer map, the most important thing is feature extraction. In addition to a certain spatial pattern, the wafer map also has a lot of noise, which affects the process of feature extraction. When the traditional DBSCAN algorithm is used for filtering, it is necessary to manually determine the value of Eps and MinPts parameters, and the selection of the parameters directly affects the accuracy of the clustering. Therefore, this paper proposes an automatic parameter filtering method based on DBSCAN, which can solve the traditional drawbacks of manually parameters setting, the algorithm is a Self-Adaptive DBSCAN-based method for wafer bin map, we call it SA-DBSCANWBM. This method selects a comprehensive index of cluster intra-cluster density and inter-cluster density to evaluate the optimal parameters. The experimental results show that the algorithm proposed in this paper can automatically and reasonably select better parameters and has a good clustering effect, which helpful for subsequent feature extraction and classification.

Exploring the step function distribution of the threshold fraction of adopted neighbors versus minimum fraction of nodes as initial adopters to assess the cascade blocking intra-cluster density of complex real-world networks

We first propose a binary search algorithm to determine the minimum fraction of nodes in a network to be used as initial adopters (f_{IA}^{min }) for a particular threshold fraction (q) of adopted neighbors (related to the cascade capacity of the network) leading to a complete information cascade. We observe the q versus f_{IA}^{min } distribution for several complex real-world networks to exhibit a step function pattern wherein there is an abrupt increase in f_{IA}^{min } beyond a certain value of q (qstep); the f_{IA}^{min } values at qstep and the next measurable value of q are represented as underline{{f_{IA}^{min } }} and overline{{f_{IA}^{min } }} respectively. The difference overline{{f_{IA}^{min } }} - underline{{f_{IA}^{min } }} is observed to be significantly high (a median of 0.44 for a suite of 40 real-world networks studied in this paper) such that we claim the 1 − qstep value (we propose to refer 1 − qstep as the Cascade Blocking Index, CBI) for a network could be perceived as a measure of the intra-cluster density of the blocking cluster of the network that cannot be penetrated without including an appreciable number of nodes from the cluster to the set of initial adopters (justifying a relatively larger overline{{f_{IA}^{min } }} value).

Three dimensional cluster analysis for atom probe tomography using Ripley’s K-function and machine learning

The size and structure of spatial molecular and atomic clustering can significantly impact material properties and is therefore important to accurately quantify. Ripley’s K-function (K(r)), a measure of spatial correlation, can be used to perform such quantification when the material system of interest can be represented as a marked point pattern. This work demonstrates how machine learning models based on K(r)-derived metrics can accurately estimate cluster size and intra-cluster density in simulated three dimensional (3D) point patterns containing spherical clusters of varying size; over 90% of model estimates for cluster size and intra-cluster density fall within 11% and 18% error of the true values, respectively. These K(r)-based size and density estimates are then applied to an experimental APT reconstruction to characterize MgZn clusters in a 7000 series aluminum alloy. We find that the estimates are more accurate, consistent, and robust to user interaction than estimates from the popular maximum separation algorithm. Using K(r) and machine learning to measure clustering is an accurate and repeatable way to quantify this important material attribute.

A density-based statistical analysis of graph clustering algorithm performance

Abstract We introduce graph clustering quality measures based on comparisons of global, intra- and inter-cluster densities, an accompanying statistical significance test and a step-by-step routine for clustering quality assessment. Our work is centred on the idea that well-clustered graphs will display a mean intra-cluster density that is higher than global density and mean inter-cluster density. We do not rely on any generative model for the null model graph. Our measures are shown to meet the axioms of a good clustering quality function. They have an intuitive graph-theoretic interpretation, a formal statistical interpretation and can be tested for significance. Empirical tests also show they are more responsive to graph structure, less likely to breakdown during numerical implementation and less sensitive to uncertainty in connectivity than the commonly used measures.

Overlapping community detection using superior seed set selection in social networks

Community discovery in the social network is one of the tremendously expanding areas which earn interest among researchers for past one decade. There are many already existing algorithms. However, new seed-based algorithms establish an emerging drift in this area. The basic idea behind these strategies is to identify exceptional nodes in the given network, called seeds, around which communities can be located. This paper proposes a blended strategy for locating suitable superior seed set by applying various centrality measures and using them to find overlapping communities. The examination of the algorithm has been performed regarding the goodness of the identified communities with the help of intra-cluster density and inter-cluster density. Finally, the runtime of the proposed algorithm has been compared with the existing community detection algorithms showing remarkable improvement.

Column-like Ca2 + clusters in the mouse neonatal neocortex revealed by three-dimensional two-photon Ca2 + imaging in vivo

Neuronal network activity in the developing brain is generated in a discontinuous manner. In the visual cortex during the period of physiological blindness of immaturity, this activity mainly comprises retinally triggered spindle bursts or Ca2+ clusters thought to contribute to the activity-dependent construction of cortical circuits. In spite of potentially important developmental functions, the spatial structure of these activity patterns remains largely unclear. In order to address this issue, we here used three-dimensional two-photon Ca2+ imaging in the visual cortex of neonatal mice at postnatal days (P) 3–4 in vivo. Large-scale voxel imaging covering a cortical depth of 200μm revealed that Ca2+ clusters, identified as spindle bursts in simultaneous extracellular recordings, recruit cortical glutamatergic neurons of the upper cortical plate (CP) in a column-like manner. Specifically, the majority of Ca2+ clusters exhibit prominent horizontal confinement and high intra-cluster density of activation involving the entire depth of the upper CP. Moreover, using simultaneous Ca2+ imaging from hundreds of neurons at single-cellular resolution, we demonstrate that the degree of neuronal co-activation within Ca2+ clusters displays substantial heterogeneity. We further provide evidence that co-activated cells within Ca2+ clusters are spatially distributed in a non-stochastic manner. In summary, our data support the conclusion that dense coding in the form of column-like Ca2+ clusters is a characteristic property of network activity in the developing visual neocortex. Such knowledge is expected to be relevant for a refined understanding of how specific spatiotemporal characteristics of early network activity instruct the development of cortical circuits.

Galactic energetic particles and their radiative yields in clusters

As energetic particles diffuse out of radio and star-forming galaxies (SFGs), their intracluster density builds up to a level that could account for a substantial part or all the emission from a radio halo. We calculate the particle time-dependent, spectro-spatial distributions from a solution of a diffusion equation with radio galaxies as sources of electrons and SFGs as sources of both electrons and protons. Whereas strong radio galaxies are typically found in the cluster (e.g., Coma) core, the fraction of SFGs increases with distance from the cluster center. Scaling particle escape rates from their sources to the reasonably well determined Galactic rates, and for realistic gas density and magnetic field spatial profiles, we find that predicted spectra and spatial profiles of radio emission from primary and secondary electrons are roughly consistent with those deduced from current measurements of the Coma halo (after subtraction of emission from the relic Coma A). Nonthermal x-ray emission is predicted to be mostly by Compton scattering of electrons from radio galaxies off the CMB, whereas $\ensuremath{\gamma}$-ray emission is primarily from the decay of neutral pions produced in interactions of protons from SFGs with protons in intracluster gas.

Synthetic extinction maps around intermediate-mass black holes in Galactic globular clusters

During the last decades, much effort has been devoted to explain the discrepancy between the amount of intracluster medium (ICM) estimated from stellar evolution theories and that emerging from observations in globular clusters (GCs). One possible scenario is the accretion of this medium by an intermediate-mass black hole (IMBH) at the centre of the cluster. In this work, we aim at modelling the cluster colour-excess profile as a tracer of the ICM density, both with and without an IMBH. Comparing the profiles with observations allows us to test the existence of IMBHs and their possible role in the cleansing of the ICM. We derive the intracluster density profiles from hydrodynamical models of accretion onto a central IMBH in a GC and we determine the corresponding dust density. This model is applied to a list of 25 Galactic GCs. We find that central IMBHs decrease the ICM by several orders of magnitude. In a subset of 9 clusters, the absence of the black hole combined with a low intracluster medium temperature would be at odds with present gas mass content estimations. As a result, we conclude that IMBHs are an effective cleansing mechanism of the ICM of GCs. We construct synthetic extinction maps for M 62 and {\omega} Cen, two clusters in the small subset of 9 with observed 2D extinction maps. We find that under reasonable assumptions regarding the model parameters, if the gas temperature in M 62 is close to 8000 K, an IMBH needs to be invoked. Further ICM observations regarding both the gas and dust in GCs could help to settle this issue.

Experiments on Density-Constrained Graph Clustering

Clustering a graph means identifying internally dense subgraphs that are only sparsely interconnected. Formalizations of this notion lead to measures that quantify the quality of a clustering and to algorithms that actually find clusterings. Since, most generally, corresponding optimization problems are hard, heuristic clustering algorithms are used in practice, or other approaches that are not based on an objective function. In this work, we conduct a comprehensive experimental evaluation of the qualitative behavior of greedy bottom-up heuristics driven by cut-based objectives and constrained by intracluster density, using both real-world data and artificial instances. Our study documents that a greedy strategy based on local movement is superior to one based on merging. We further reveal that the former approach generally outperforms alternative setups and reference algorithms from the literature in terms of its own objective, while a modularity-based algorithm competes surprisingly well. Finally, we exhibit which combinations of cut-based inter- and intracluster measures are suitable for identifying a hidden reference clustering in synthetic random graphs and discuss the skewness of the resulting cluster size distributions. Our results serve as a guideline to the usage of bicriterial, cut-based measures for graph clusterings.

An Improved Semi-Supervised Clustering Algorithm for Multi-Density Datasets with Fewer Constraints

Semi-supervised clustering algorithms aim to significantly improve the clustering results using limited supervision in the form of labelled instances or pairwise constraints. But few of these algorithms are specially and well-designed both for multi-density and complex shape datasets. However, such complex data are usual in the real world. In this paper, an improved semi-supervised clustering algorithm is proposed based on SCMD algorithm. Our new algorithm can deal with the multi-density problems, including not only the inter-cluster density variety but also the intra-cluster density difference; and it can yield superior performance with fewer constraints. We test our new algorithm on several synthetic datasets of varying shapes, sizes, and densities. Experimental results show that our algorithm has manifest superior performance in comparison with SCMD algorithm, even when the constraints are not sufficient.

Density-based hierarchical clustering for streaming data

For streaming data that arrive continuously such as multimedia data and financial transactions, clustering algorithms are typically allowed to scan the data set only once. Existing research in this domain mainly focuses on improving the accuracy of clustering. In this paper, a novel density-based hierarchical clustering scheme for streaming data is proposed in order to improve both accuracy and effectiveness; it is based on the agglomerative clustering framework. Traditionally, clustering algorithms for streaming data often use the cluster center to represent the whole cluster when conducting cluster merging, which may lead to unsatisfactory results. We argue that even if the data set is accessed only once, some parameters, such as the variance within cluster, the intra-cluster density and the inter-cluster distance, can be calculated accurately. This may bring measurable benefits to the process of cluster merging. Furthermore, we employ a general framework that can incorporate different criteria and, given the same criteria, will produce similar clustering results for both streaming and non-streaming data. In experimental studies, the proposed method demonstrates promising results with reduced time and space complexity.

Statistical Analysis of High-Resolution Light Microscope Images Reveals Effects of Cytoskeleton-Disrupting Drugs on the Membrane Organization of the Nicotinic Acetylcholine Receptor

Extensive evidence supports the notion that the cytoskeleton participates in the immobilization and membrane clustering of the nicotinic acetylcholine receptor (AChR) at the neuromuscular junction. Stimulated emission depletion fluorescence microscopy has revealed the supramolecular organization of AChR nanoclusters at the surface of CHO-K1/A5 cells with subdiffraction resolution (Kellner et al., Neuroscience 144:135-143 2007). We studied the effect of two cytoskeletal-disrupting drugs (cytochalasin D and jasplakinolide) on the nanoscale distribution of muscle-type AChR expressed in these cells by means of mathematical and statistical analysis of images obtained with the same high-resolution microscopy. AChR nanoclusters were found to be randomly distributed in both controls and cells treated with either drug for distances larger than 500 nm. Treatments altered the distribution of AChR nanoclusters according to their brightness/size. Cytochalasin D and jasplakinolide produced a statistically significant increase in the proportion of medium-size nanoclusters and a diminution of small nanoclusters, indicating higher disrupting activity on the latter. This was further corroborated by the diminution of the brightness/diameter ratio of nanoclusters (a measure of the intracluster density of AChR molecules) and by Ripley's analysis applied to simulated patterns with intracluster aggregation of AChR molecules. The combined analytical tools bring out subtle changes in the two-dimensional organization of the AChR nanoaggregates on disruption of the cytoskeletal network and throw light on the possible link between the cytoskeleton and the distribution of the AChR at the cell surface.

Engineering graph clustering

A promising approach to graph clustering is based on the intuitive notion of intracluster density versus intercluster sparsity. As for the weighted case, clusters should accumulate lots of weight, in contrast to their connection to the remaining graph, which should be light. While both formalizations and algorithms focusing on particular aspects of this rather vague concept have been proposed, no conclusive argument on their appropriateness has been given. In order to deepen the understanding of particular concepts, including both quality assessment as well as designing new algorithms, we conducted an experimental evaluation of graph-clustering approaches. By combining proved techniques from graph partitioning and geometric clustering, we also introduce a new approach that compares favorably.

Electron bubbles in helium clusters. I. Structure and energetics

In this paper we present a theoretical study of the structure, energetics, potential energy surfaces, and energetic stability of excess electron bubbles in ((4)He)(N) (N=6500-10(6)) clusters. The subsystem of the helium atoms was treated by the density functional method. The density profile was specified by a void (i.e., an empty bubble) at the cluster center, a rising profile towards a constant interior value (described by a power exponential), and a decreasing profile near the cluster surface (described in terms of a Gudermannian function). The cluster surface density profile width (approximately 6 A) weakly depends on the bubble radius R(b), while the interior surface profile widths (approximately 4-8 A) increase with increasing R(b). The cluster deformation energy E(d) accompanying the bubble formation originates from the bubble surface energy, the exterior cluster surface energy change, and the energy increase due to intracluster density changes, with the latter term providing the dominant contribution for N=6500-2 x 10(5). The excess electron energy E(e) was calculated at a fixed nuclear configuration using a pseudopotential method, with an effective (nonlocal) potential, which incorporates repulsion and polarization effects. Concurrently, the energy V(0) of the quasi-free-electron within the deformed cluster was calculated. The total electron bubble energies E(t)=E(e)+E(d), which represent the energetic configurational diagrams of E(t) vs R(b) (at fixed N), provide the equilibrium bubble radii R(b) (c) and the corresponding total equilibrium energies E(t) (e), with E(t) (e)(R(e)) decreasing (increasing) with increasing N (i.e., at N=6500, R(e)=13.5 A and E(t) (e)=0.86 eV, while at N=1.8 x 10(5), R(e)=16.6 A and E(t) (e)=0.39 eV). The cluster size dependence of the energy gap (V(0)-E(t) (e)) allows for the estimate of the minimal ((4)He)(N) cluster size of N approximately 5200 for which the electron bubble is energetically stable.

Clustering of the self-organizing map using a clustering validity index based on inter-cluster and intra-cluster density

The self-organizing map (SOM) has been widely used in many industrial applications. Classical clustering methods based on the SOM often fail to deliver satisfactory results, specially when clusters have arbitrary shapes. In this paper, through some preprocessing techniques for filtering out noises and outliers, we propose a new two-level SOM-based clustering algorithm using a clustering validity index based on inter-cluster and intra-cluster density. Experimental results on synthetic and real data sets demonstrate that the proposed clustering algorithm is able to cluster data better than the classical clustering algorithms based on the SOM, and find an optimal number of clusters.

Self-Organizing-Map Based Clustering Using a Local Clustering Validity Index

Classical clustering methods, such as partitioning and hierarchical clustering algorithms, often fail to deliver satisfactory results, given clusters of arbitrary shapes. Motivated by a clustering validity index based on inter-cluster and intra-cluster density, we propose that the clustering validity index be used not only globally to find optimal partitions of input data, but also locally to determine which two neighboring clusters are to be merged in a hierarchical clustering of Self-Organizing Map (SOM). A new two-level SOM-based clustering algorithm using the clustering validity index is also proposed. Experimental results on synthetic and real data sets demonstrate that the proposed clustering algorithm is able to cluster data in a better way than classical clustering algorithms on an SOM.