Inter-cluster Separation Research Articles

Achieving Cluster Consensus in Continuous-Time Networks of Multi-Agents With Inter-Cluster Non-Identical Inputs

In this paper, cluster consensus in continuous-time networks of multi-agents with time-varying topologies via non-identical inter-cluster inputs is studied. The cluster consensus contains two aspects: intra-cluster synchronization, that the state differences between agents in the same cluster converge to zero, and inter-cluster separation, that the states of the agents in different clusters do not approach. $\delta$-cluster-spanning-tree in continuous-time networks of multi-agent systems plays essential role in analysis of cluster synchronization. Inter-cluster separation can be realized by imposing adaptive inputs that are identical within the same cluster but different in different clusters, under the inter-cluster common influence condition. Simulation examples demonstrate the effectiveness of the derived theoretical results.

Inter-cluster distance dependence of electrical conduction in nanocluster assembled films of silver: a new paradigm for design of nanostructures.

The transport properties of films assembled from metal nanoclusters can be significantly different from the metals in their bulk or thin film forms due to quantum confinement effects and several competing energy and length scales. For a film composed of metal nanoclusters as its building blocks, the cluster size and the inter-cluster separation are parameters that can be varied experimentally. Here we show that the electrical conductivity of a film composed of silver nanoclusters can be changed by 9 orders of magnitude as a function of the average inter-cluster separation while keeping the average cluster size same. For inter-cluster separations of 9 nanometres or more the conductivity is insulating type whereas for lesser inter-cluster separations the conductivity behaviour is metallic type with a positive temperature coefficient of resistance. In the intermediate range between the two regions, a very interesting temperature-independent conductivity is seen. Our work provides a new paradigm for design of artificial solid structures composed of nanoclusters. The properties of these nanostructures could be tuned by varying the inter-cluster distances to get the desired properties in the same material.

Extensions of kmeans-type algorithms: a new clustering framework by integrating intracluster compactness and intercluster separation.

Kmeans-type clustering aims at partitioning a data set into clusters such that the objects in a cluster are compact and the objects in different clusters are well separated. However, most kmeans-type clustering algorithms rely on only intracluster compactness while overlooking intercluster separation. In this paper, a series of new clustering algorithms by extending the existing kmeans-type algorithms is proposed by integrating both intracluster compactness and intercluster separation. First, a set of new objective functions for clustering is developed. Based on these objective functions, the corresponding updating rules for the algorithms are then derived analytically. The properties and performances of these algorithms are investigated on several synthetic and real-life data sets. Experimental studies demonstrate that our proposed algorithms outperform the state-of-the-art kmeans-type clustering algorithms with respect to four metrics: accuracy, RandIndex, Fscore, and normal mutual information.

DSKmeans: A new kmeans-type approach to discriminative subspace clustering

Most of kmeans-type clustering algorithms rely on only intra-cluster compactness, i.e. the dispersions of a cluster. Inter-cluster separation which is widely used in classification algorithms, however, is rarely considered in a clustering process. In this paper, we present a new discriminative subspace kmeans-type clustering algorithm (DSKmeans), which integrates the intra-cluster compactness and the inter-cluster separation simultaneously. Different to traditional weighting kmeans-type algorithms, a 3-order tensor is constructed to evaluate the importance of different features in order to integrate the aforementioned two types of information. First, a new objective function for clustering is designed. To optimize the objective function, the corresponding updating rules for the algorithm are then derived analytically. The properties and performance of DSKmeans are investigated on several numerical and categorical data sets. Experimental results corroborate that our proposed algorithm outperforms the state-of-the-art kmeans-type clustering algorithms with respects to four metrics: Accuracy, RandIndex, Fscore and Normal Mutual Information(NMI).

LEARNING DECISION REGIONS BASED ON ADAPTIVE ELLIPSOIDS

A fuzzy classifier using multiple ellipsoids to approximate decision regions for classification is designed in this paper. To learn the sizes and orientations of ellipsoids, an algorithm called evolutionary ellipsoidal classification algorithm (EECA) that integrates the genetic algorithm (GA) with the Gustafson-Kessel algorithm (GKA) is proposed. Within EECA the GA is employed to learn the size of every ellipsoid. With the size of every ellipsoid encoded and intelligently estimated in the GA chromosome, GKA is utilized to learn the corresponding ellipsoid. GKA is able to adapt the distance norm to the underlying distribution of the prototype data points for an assigned ellipsoid size. A process called directed initialization is proposed to improve EECA's learning efficiency. Because EECA learns the data point distribution in every cluster by adjusting an ellipsoid with suitable size and orientation, the information contained in the ellipsoid is further utilized to improve the cluster validity. A cluster validity measure based on the ratio of summation for each intra-cluster scatter with respect to the inter-cluster separation is defined in this paper. The proposed cluster validity measure takes advantage of EECA's learning capability and serves as an effective index for determining the adequate number of ellipsoids required for classification.

Cluster Consensus in Discrete-Time Networks of Multiagents With Inter-Cluster Nonidentical Inputs

In this paper, cluster consensus of multiagent systems is studied via inter-cluster nonidentical inputs. Here, we consider general graph topologies, which might be time-varying. The cluster consensus is defined by two aspects: intracluster synchronization, the state at which differences between each pair of agents in the same cluster converge to zero, and inter-cluster separation, the state at which agents in different clusters are separated. For intra-cluster synchronization, the concepts and theories of consensus, including the spanning trees, scramblingness, infinite stochastic matrix product, and Hajnal inequality, are extended. As a result, it is proved that if the graph has cluster spanning trees and all vertices self-linked, then the static linear system can realize intra-cluster synchronization. For the time-varying coupling cases, it is proved that if there exists T > 0 such that the union graph across any T-length time interval has cluster spanning trees and all graphs has all vertices self-linked, then the time-varying linear system can also realize intra-cluster synchronization. Under the assumption of common inter-cluster influence, a sort of inter-cluster nonidentical inputs are utilized to realize inter-cluster separation, such that each agent in the same cluster receives the same inputs and agents in different clusters have different inputs. In addition, the boundedness of the infinite sum of the inputs can guarantee the boundedness of the trajectory. As an application, we employ a modified non-Bayesian social learning model to illustrate the effectiveness of our results.

Clustered copper nanorod arrays: a new class of adhesive hydrophobic materials

Clustered copper nanorod arrays constitute single-component, two-level hierarchical structures that mimic rose petals by showing high contact angles as well as considerable contact angle hysteresis (CAH). The cluster morphology of the nanorod arrays – electrochemically grown within porous alumina templates – is determined by the template geometry and the drying conditions. The CAH (a measure of the adhesion) is a function of the nanorod length and the cluster size to inter-cluster separation ratio. The measured pinning force was 176 μN, among the highest reported. The first level of the hierarchical nano-microstructure consists of the nanorod clusters and the air trapped between them – leading to a Cassie–Baxter type hydrophobicity. The second level comprises the tips of the clustered copper nanorods which pin the water droplets due to the inherently hydrophilic nature of metals. This conjecture is supported by fluorescence imaging and surface polymerization experiments. Thus, a clustered metal nanorod array provides a simple model system for studying the coexistence and complex interplay of hydrophobicity and adhesion, while also providing some degree of control over these mutually contradictory properties.

A co-crystal of polyoxometalates exhibiting single-molecule magnet behavior: the structural origin of a large magnetic anisotropy

A polyoxometalate-based {Mn(III)(3)Mn(IV)} single-molecule magnet exhibits a large axial anisotropy (D = -0.86 cm(-1)) resulting from a near-parallel alignment of Jahn-Teller axes. Its rigorous three-fold symmetry (i.e. rhombicity E→ 0) and increased intercluster separation via co-crystallization effectively hamper quantum tunnelling of the magnetization.

CPCQ: Contrast pattern based clustering quality index for categorical data

Clustering validation is concerned with assessing the quality of clustering solutions. Since clustering is unsupervised and highly explorative, clustering validation has been an important and long standing research problem. Existing validity measures, including entropy-based and distance-based indices, have significant shortcomings. Indeed, for many datasets from the UCI repository, they fail to recognize that the expert-determined classes are the best clusters and they frequently give preference to clusterings with larger number of clusters. Their weakness reflects their inability to accurately capture intra-cluster coherence and inter-cluster separation. This paper proposes a novel Contrast Pattern based Clustering Quality index (CPCQ) for categorical data, by utilizing the quality and diversity of the contrast patterns, which contrast the clusters in given clusterings. High quality contrast patterns can serve to characterize the clusters and discriminate one cluster against the others. The CPCQ index is based on the rationale that a high-quality clustering should have many diversified high-quality contrast patterns among its clusters. The quality of individual contrast patterns is defined in terms of their length, support, and the length of their corresponding closed pattern. The quality measure concerning ''many diversified'' contrast patterns is defined in terms of the quality and diversity of some selected groups of contrast patterns with minimal overlap among contrast patterns and groups in terms of items and matching transactions. Experiments show that the CPCQ index (1) does not require a user to provide a distance function; (2) does not give inappropriate preference to larger number of clusters; (3) can recognize that expert-determined classes are the best clusters for many datasets from the UCI repository.

Mixed fuzzy inter-cluster separation clustering algorithm

Based on inter-cluster separation clustering (ICSC) fuzzy inter-cluster separation clustering (FICSC) deals with all the distances between the cluster centers, maximizes these distances and obtains the better performances of clustering. However, FICSC is sensitive to noises the same as fuzzy c-means (FCM) clustering. Possibilistic type of FICSC is proposed to combine FICSC and possibilistic c-means (PCM) clustering. Mixed fuzzy inter-cluster separation clustering (MFICSC) is presented to extend possibilistic type of FICSC because possibilistic type of FICSC is sensitive to initial cluster centers and always generates coincident clusters. MFICSC can produce both fuzzy membership values and typicality values simultaneously. MFICSC shows good performances in dealing with noisy data and overcoming the problem of coincident clusters. The experimental results with data sets show that our proposed MFICSC holds better clustering accuracy, little clustering time and the exact cluster centers.

Electrical behavior of silver particulate films deposited on 8 MeV electron beam irradiated softened polystyrene substrates

Results of the investigations carried out on the electrical behavior of silver particulate films deposited on electron beam irradiated polystyrene (PS) coated substrates held at a temperature of 455 K in a vacuum of 8 × 10−6 torr at a constant deposition rate of 0.4 nm/s are reported. It is known that when metals are evaporated on to softened polymer substrates, subsurface particulate structures are formed whose morphology is dependent on deposition parameters. Further, it was shown that the morphology is dependent on polymer-metal interaction. The present work demonstrates that the polymer-metal interaction can be brought about in inert polymers like PS by electron irradiation. The results indicate that the films deposited on PS irradiated to a dose of 20 and 25 kGy gives rise to smaller clusters with smaller inter-cluster separation, better suited for sensor applications. The induced polymer-metal interaction is attributed to the creation of free radicals due to the 8 MeV electron irradiation.

Engineering Nanoparticle Cluster Arrays for Bacterial Biosensing: The Role of the Building Block in Multiscale SERS Substrates

AbstractNoble metal nanoparticle cluster arrays (NCAs) are a novel class of engineered substrates for surface enhanced Raman spectroscopy (SERS), in which the noble metal nanoparticles interact on multiple length scales to create a multiscale E‐field cascade enhancement. In this work the role of the building block for the NCA performance is quantified. Periodic NCAs with constant cluster diameter (D = 200 nm) but variable nanoparticle diameter (d) and intercluster separation (Λ) were assembled on glass and their optical response and SERS enhancement were systematically characterized as a function of D, Λ, and d. An increase of d from 40 to 80 nm and simultaneous decrease of Λ from 200 to 50 nm led to an improvement of the ensemble averaged SERS enhancement factor by a factor of up to ∼8. The coefficient of variation (cv) of the enhancement factors (G) is significantly lower for the d = 80 nm NCAs than for the d = 40 nm and d = 60 nm NCAs. Optimized (D = 200 nm, Λ = 50 nm, d = 80 nm) NCAs show the overall highest signal reproducibility of all investigated NCAs and random nanoparticle substrates and achieve effective single cell detection sensitivity.

Improved Inter-Cluster Separation Algorithm

The inter-cluster separation (ICS) algorithm adds the separation item into the objective function to minimize the fuzzy Euclidean distance and maximize the inter-cluster separation. However, ICS is sensitive to noisy data, so an improved inter-cluster separation (IICS) algorithm is proposed to deal with this problem. It is claimed that IICS is an incorporation of ICS and improved possibilistic c-means (IPCM) clustering. IICS can produce both possibilities and memberships simultaneously, and it overcomes the noise sensitivity problem of ICS and the coincident clusters problem of possibilistic c-means (PCM) clustering. Further, IICS does not depend on the parameters that exist in IPCM. The experimental results show that IICS compares favorably with ICS.

Validation indices for projective clustering

Cluster validation is a major issue in cluster analysis of data mining, which is the process of evaluating performance of clustering algorithms under varying input conditions. Many existing validity indices address clustering results of low-dimensional data. Within high-dimensional data, many of the dimensions are irrelevant, and the clusters usually only exist in some projected subspaces spanned by different combinations of dimensions. This paper presents a solution to the problem of cluster validation for projective clustering. We propose two new measurements for the intracluster compactness and intercluster separation of projected clusters. Based on these measurements and the conventional indices, three new cluster validity indices are presented. Combined with a fuzzy projective clustering algorithm, the new indices are used to determine the number of projected clusters in high-dimensional data. The suitability of our proposal has been demonstrated through an empirical study using synthetic and real-world datasets.

NIFTI: An evolutionary approach for finding number of clusters in microarray data

BackgroundClustering techniques are routinely used in gene expression data analysis to organize the massive data. Clustering techniques arrange a large number of genes or assays into a few clusters while maximizing the intra-cluster similarity and inter-cluster separation. While clustering of genes facilitates learning the functions of un-characterized genes using their association with known genes, clustering of assays reveals the disease stages and subtypes. Many clustering algorithms require the user to specify the number of clusters a priori. A wrong specification of number of clusters generally leads to either failure to detect novel clusters (disease subtypes) or unnecessary splitting of natural clusters.ResultsWe have developed a novel method to find the number of clusters in gene expression data. Our procedure evaluates different partitions (each with different number of clusters) from the clustering algorithm and finds the partition that best describes the data. In contrast to the existing methods that evaluate the partitions independently, our procedure considers the dynamic rearrangement of cluster members when a new cluster is added. Partition quality is measured based on a new index called Net InFormation Transfer Index (NIFTI) that measures the information change when an additional cluster is introduced. Information content of a partition increases when clusters do not intersect and decreases if they are not clearly separated. A partition with the highest Total Information Content (TIC) is selected as the optimal one. We illustrate our method using four publicly available microarray datasets.ConclusionIn all four case studies, the proposed method correctly identified the number of clusters and performs better than other well known methods. Our method also showed invariance to the clustering techniques.

Testing the High Spin MnII9WV6 Cluster as Building Block for Three-Dimensional Coordination Networks

Pentadecanuclear high spin cyano-bridged {M' II 9 M v 6 (CN)48(solv)24) (M' = 3d metal ions; M = Mo, W; solv = H 2 O, alcohol) clusters are considered as building blocks for three-dimensional open networks. Self-assembly of Mn II 9 W v 6 clusters (S = 39/2) with 4,4'-bipyridine leads to their organization into an organic-inorganic hybrid coordination network {Mn II 9 (4,4'-bpy) 4 [W v (CN) 8 ] 6 (EtOH) 12 (H 2 O) 4 } ·10EtOH 1 (System, triclinic; space group: P1, a = 17.1569(2) A, b = 17.3835(2) A, c = 19.2530(2) A, a = 103.5520(10)°, P = 115.3950(10)°, y = 98.3060(10)°, Z = 1). The clusters are connected through 4,4'-bpy spacers into a two-dimensional square-grid coordination framework extended in the ab crystallographic plane with the smallest intercluster separation along the a (Mn···W = 7.12 A) and b (Mn···W = 7.15 A) directions significantly lower than that along the c crystallographic direction (Mn···W = 8.64 A). Direct current magnetic measurements suggest strong dominance of intracluster antiferromagnetic Mn II -W v coupling over a very weak intercluster antiferromagnetic interaction.

Direct Atomic Scale Observation of Linkage Isomerization of As4S4 Clusters during the Photoinduced Transition of Realgar to Pararealgar

The reaction mechanism underlying the photoinduced linkage isomerization of discrete arsenic-sulfur clusters in the realgar form of tetraarsenic tetrasulfide (alpha-As4S4) to its pararealgar form was studied on a natural specimen of the mineral with a combination of in situ single-crystal X-ray photodiffraction and Fourier transform infrared spectroscopy. The photodiffraction technique provided direct atomic resolution evidence of formation of intermediate As4S5 phase in which half of the realgar molecule is retained in its envelope-type conformation, while the other half is transformed by effective switching of positions of one sulfur and one arsenic atom. The initiation and propagation stages of the process are studied under light and dark conditions, during and after photoexcitation with polychromatic visible light. In the "light" reaction stage, the interatomic and cell parameters averaged over the crystal volume and photoexcitation time remain almost unchanged. The residual electron density features are indicative for formation of a small amount of As4S5 clusters, which at this stage do not affect the overall crystalline order. In the "dark" reaction stage, a set of self-sustainable autocatalytic reactions results in strong and nearly isotropic expansion of the unit cell. The structure in the dark stage represents direct evidence of formation of pararealgar which was obtained in yield of about 5% in the single crystal of realgar. The cell expansion is due to increased mole ratio of clusters of pararealgar relative to realgar and to increased intercluster separation. Due to lattice incompatibility, a higher content of the product results in progressive decrease of crystal quality. Creation of small amount of arsenolite (As2O3) which appears as byproduct in the light stage and remains unreacted in the product mixture was confirmed by far-IR spectroscopy.

Ostwald Ripening in Rarefied Systems

Mass exchange between spherical molecular clusters is analyzed in the case when the mean free path of molecules in the intercluster space is much larger than the cluster sizes but much smaller than average intercluster separation. It is shown that there is a steady-state regime when big clusters grow at the expense of the smaller ones (Ostwald ripening), which is characterized by a one-parametric family of self-similar cluster size distribution functions and by an exponentially growing average cluster size. The obtained self-similar cluster size distributions are entirely different from those given by the classical theory of Ostwald ripening. Implications of the obtained results are discussed.

Ion-beam induced transformations in nanoscale multilayers: Evolution of clusters with preferred length scales

Ion-irradiation-induced modifications of a periodic Pt∕C multilayer system containing a small amount of Fe have been analyzed by transmission electron microscopy and grazing incidence x-ray diffraction (GIXRD) studies. The multilayer stack with 16 Pt∕C layer pairs (period of 4.23nm) was fabricated on a glass substrate. A 2MeV Au2+ ion beam was rastered on the sample to obtain uniformly irradiated strips with fluences from 1×1014to1×1015ions∕cm2. Ion irradiation has been found to cause preferential migration of Fe towards Pt layers [Bera et al., Nucl. Instrum. Methods Phys. Res. B 212, 530 (2003)]. Cross-sectional transmission electron microscopy (XTEM) shows considerable atomic redistribution for irradiation at the highest ion fluence (1×1015ions∕cm2). This structure is composed of small clusters. Phase separation and cluster formation processes are discussed. Periodic multilayers have periodicity only in the direction normal to the multilayer surface. However, Fourier transform (FT) of the XTEM images of the sample irradiated at the highest fluence shows extra off-normal Fourier components of superlattice periodicities arising due to ion irradiation. These extra spots in the FT are due to preferential length scales in intercluster separation in three dimensions. With a proper understanding of this phenomenon it may be possible to fabricate useful three-dimensional self-assembled structures of nanoclusters. Our high resolution transmission electron microscopy and GIXRD results reveal the formation of an FePt alloy. As FePt is a magnetic alloy, our observation raises the possibility of fabrication of ion-beam induced magnetic nanocluster lattices.

A note on the ICS algorithm with corrections and theoretical analysis

In [1], Ozdemir and Akarun proposed an intercluster separation (ICS) fuzzy clustering algorithm. The ICS algorithm is useful in combined quantization and dithering. However, there are two errors in the update equations for the ICS algorithm. This correspondence first points out these errors and gives their corrections. Since the parameters m, c, and gamma are important factors in the performance of ICS, we also conduct a theoretical analysis of these ICS parameters. In order to analyze the parameters in ICS, we devise a theorem for the calculation of the Hessian matrix from the ICS objective function. We establish the fixed-point property of ICS based on the decomposition of the Hessian matrix and then analyze the effect of the parameters. Finally, we propose a numerical approach in choosing the appropriate parameters m and gamma for ICS. These experimental results give a better numerical perspective on the effect of parameters in ICS and have conclusions consistent with our theoretical analysis.