Combinatorial Clustering Research Articles

Combinatorial clustering with a coherent XY machine.

We propose and numerically study the performance of an all-optical machine for tackling combinatorial clustering, one of the unsupervised machine learning problems. A problem instance is encoded into the phase of time-multiplexed optical pulses, which are coupled repulsively through optical delay lines. To maintain uniform pulse amplitudes, we utilize a nonlinear amplifier with gain saturation, enabling our optical architecture to emulate the classical XY-spin system. This solver, called the coherent XY machine, leads to the formation of clusters in an optical phase space and allows us to efficiently identify the solution with post-processing. Additionally, we implement momentum in our solver to provide a powerful mechanism for escaping local minima and searching for the global optimum. Benchmarking our approach with a most advanced Ising-spin-based solver reveals a two-orders-of-magnitude improvement in the time-to-solution of the algorithm. Furthermore, our approach exhibits scaling advantages for larger problems, which will facilitate time- and energy-efficient data clustering.

Method of compression and ensuring the fidelity of video images in infocommunication networks

Subject research in the article is the methods of compressing video images under conditions of ensuring the desired level of their fidelity in the delivery process using infocommunication networks. The goal is to develop methods of encoding video images for increasing the level of their compression in the conditions of ensuring required reliability. Task: to substantiate the approach regarding the structural clusterization of transformed video segments in the conditions of preserving their reliability; to develop a method of structural and statistical coding of transformants in the spectral-cluster space; conduct a comparative evaluation of the effectiveness of various methods of encoding video segments. The methods used: mathematical models for estimating the amount of statistical and structural redundancy in the clustered spectral space of video segments; methods of statistical coding. The following results have been obtained. The potential effectiveness of representing a transformant in clustered space by the number of series of units in binary description of their components has been substantiated. A method of structural-statistical coding in the spectral-cluster space has been created. The basic component of this technological approach is the evaluation of the estimates regarding the potential ability to eliminate various types of redundancy in the current cluster. Here, the amount of redundancy is reduced considering the statistical and structural features of the cluster. The comparative evaluation revealed the advantages of the created method over coding methods in standardized platforms. The advantage is achieved in terms of the peak signal-to-noise ratio by at least 30%. and in terms of a compression ratio by an average of 12 %. Conclusions. The scientific novelty of the obtained results is as follows: for the first time, a method of structural-statistical coding of video segments in spectral space based on their clusterization has been created. The differences of the method lie in the fact that the component of the transformant is simultaneously interpreted as an element of the statistical and combinatorial cluster space; the potential capabilities of eliminating various types of redundancy in the clustered transformant are considered. This provides an increase in the level of compression of video images for a given level of reliability.

Combinatorial clustering of distinct DNA motifs directs synergistic binding of Caenorhabditis elegans dosage compensation complex to X chromosomes

Organisms that count X-chromosome number to determine sex utilize dosage compensation mechanisms to balance X-gene expression between sexes. Typically, a regulatory complex is recruited to X chromosomes of one sex to modulate gene expression. A major challenge is to determine the mechanisms that target regulatory complexes specifically to X. Here, we identify critical X-sequence motifs in Caenorhabditis elegans that act synergistically in hermaphrodites to direct X-specific recruitment of the dosage compensation complex (DCC), a condensin complex. We find two DNA motifs that collaborate with a previously defined 12-bp motif called MEX (motif enriched on X) to mediate binding: MEX II, a 26-bp X-enriched motif and Motif C, a 9-bp motif that lacks X enrichment. Inserting both MEX and MEX II into a new location on X creates a DCC binding site equivalent to an endogenous recruitment site, but inserting only MEX or MEX II alone does not. Moreover, mutating MEX, MEX II, or Motif C in endogenous recruitment sites with multiple different motifs dramatically reduces DCC binding invivo to nearly the same extent as mutating all motifs. Changing the orientation or spacing of motifs also reduces DCC binding. Hence, synergy in DCC binding via combinatorial clustering of motifs triggers DCC assembly specifically on X chromosomes. Using an invitro DNA binding assay, we refine the features of motifs and flanking sequences that are critical for DCC binding. Our work reveals general principles by which regulatory complexes can be recruited across an entire chromosome to control its gene expression.

Clustering Optimization for Triple-Frequency Combined Observations of BDS-3 Based on Improved PSO-FCM Algorithm

The triple-frequency linear combination method can provide combinations with different characteristics and is one of the important methods to improve the performance of navigation services. Due to the large number of combinations and different combination performances, combinatorial clustering optimization is very important, and the efficiency of manual screening is very low. Firstly, based on the basic model, the objective equations are derived. Secondly, based on the fuzzy c-means (FCM) algorithm, three improved PSO-FCM algorithms are proposed, namely the S-PSO-FCM algorithm, L-PSO-FCM algorithm, and LOG-PSO-FCM algorithm. Thirdly, according to the different combination characteristics, the two datasets whose combined coefficients sum to 0 and 1 are emphatically discussed. Finally, the effectiveness of the improved PSO-FCM algorithms is studied based on the public dataset and the measured BeiDou-3 navigation satellite system (BDS-3) data of short baseline, long baseline, and ultra-long baseline. The results show that the performance of the proposed algorithm is better than that of the FCM algorithm, especially in short baseline and long baseline cases.

Digitalization as a Tool for Ensuring Innovative Development of Restaurant Business

The aim of the study is to identify and systematize innovations in the restaurant business in the context of digitalization of business process management. The article proves that the globalization of crisis phenomena in the national and world economy, in particular complicated by the COVID19 pandemic, the variability of the market environment necessitates an innovative orientation of the restaurant business. The definition of “innovation in the restaurant business” as a creative entrepreneurial process of creating and/or improving and commercializing a new product, service or technology with the appropriate transformation of management methods, which increase the efficiency of business processes while bifurcating quality management parameters and form the basis for further development. The classification of the combination of innovations in the restaurant business according to the criteria on the basis of the results of the transformation of the combinatorial clustering of innovations is given. It is proved that digitalization creates a basis for innovative business process management formats of restaurants, which allow to form their own ecosystem of information and communication interaction with consumers and other stakeholders, based on customer orientation, innovation, partnership and synergy. Factors of gradual and rapid digitalization of the restaurant business are highlighted, the combined effect of which necessitates the introduction of adaptive models of innovative digital management by restaurant business owners.

An External Definition of the One-Hot Constraint and Fast QUBO Generation for High-Performance Combinatorial Clustering

Recently, a clustering method using a combinatorial optimization problem, called combinatorial clustering, has been drawing attention due to the rapid spreads of quantum annealing and simulated annealing. Combinatorial clustering is performed by minimizing an objective function under a condition to satisfy a one-hot constraint. The objective function and the constraint function are generally formulated to a unified objective function of a QUBO (Quadratic Unconstrained Binary Optimization) problem using the method of the Lagrange multiplier. The coefficients of the QUBO function can be represented by a square matrix, which is called the QUBO matrix. Although the Lagrange multiplier needs to be large enough to avoid violating the constraint, it is usually hard to be set appropriately due to the limitation of the bit precision. For example, the latest quantum annealer can handle values represented by only six or fewer bits. Even conventional computing systems cannot control the larger value of the Lagrange multiplier as the number of data points increases. Besides, the execution time for combinatorial clustering increases exponentially as the problem size increases. This is because the time for the QUBO matrix generation is long and a dominant factor of the total execution time when the problem size is large. To solve these problems, this paper proposes combinatorial clustering that overcomes the limitation of the method of the Lagrange multiplier. The proposed method uses a QUBO solver that can externally define the one-hot constraint independent from the objective function, and the externally-defined constraint is satisfied by the operations with multiple bit-flips. As the QUBO function contains only the objective function, the method of the Lagrange multiplier is not necessary. The proposed method can optimize the objective function sufficiently even when the problem size is large. Since the constraint function is not included in the QUBO function, the proposed method also reduces the time for the QUBO matrix generation. The experimental results obtained using the artificial and real data show that the proposed method can improve the quality of annealing-based clustering results in all data sets. The experimental results also clarify that the quality of the proposed method is almost equal to or better than that of quasi-optimal clustering methods such as K-means. The evaluation using the multiple traveling salesman problem shows that the proposed method can obtain shorter tour lengths than the conventional annealing-based clustering in all 13 cases and K-means++ in 6 out of 12 cases with a significant difference. Furthermore, the proposed method can accelerate the execution time for combinatorial clustering because there is no need to calculate the coefficients of the constraint function.

Combinatorial Optimization-Based Clustering Algorithm for Wireless Sensor Networks

As node energy of wireless sensor networks (WSN) is limited and cannot be supplemented after exhaustion, clustering algorithm is frequently taken as an effective method to prolong the lifetime of WSN. However, the existing clustering algorithms have some drawbacks, either consuming excessive energy as a result of exchanging too much controlling information between nodes, or lacking a comprehensive perspective in terms of the balance among several conflicting objectives. In order to overcome these shortcomings, a novel combinatorial optimization-based clustering algorithm (COCA) for WSN is proposed in this paper. Different from the above mentioned algorithms which take clustering as a continuous optimization problem, COCA solves the clustering problem from the perspective of combinatorial optimization. Firstly, the clustering of WSN is abstracted into a combinatorial optimization problem. Then, the binary particle coding scheme of cluster head is proposed, which is based on the corresponding relationship between nodes and particle position vectors, and the fitness function is designed according to the parameters used in the process of cluster formation. Finally, the binary particle swarm optimization algorithm is applied to implement the clustering. COCA is validated under different scenarios compared with three other clustering algorithms. The simulation results show that COCA has better performance than its comparable algorithms.

HNCcorr: combinatorial optimization for neuron identification

We present a combinatorial algorithm for cell detection in two-photon calcium imaging. Calcium imaging is a modern technique used by neuroscientists for recording movies of in-vivo neuronal activity at cellular resolution. The proposed algorithm, named HNCcorr, builds on the combinatorial clustering problem Hochbaum’s Normalized Cut (HNC). HNC is a model that trades off two goals: One goal is that the cluster has low similarity to the remaining objects. The second goal is that the cluster is highly similar to itself. The HNC model is closely related to the Normalized Cut problem of Shi and Malik, a well-known problem in image segmentation. However, whereas Normalized Cut is an NP-hard problem, HNC is solvable in polynomial time. The neuronal cell detection in calcium imaging movies is viewed here as a clustering problem. HNCcorr utilizes HNC to detect cells in these movies as coherent clusters of pixels that are highly distinct from the remaining pixels. HNCcorr guarantees, unlike existing methodologies for cell identification, a globally optimal solution to the underlying optimization problem. Of independent interest is a novel method, named similarity-squared, that is devised here for measuring similarity. In an experimental study on data from the Neurofinder cell identification benchmark, HNCcorr is a top performer. In particular, it achieves a higher average score than two frequently used matrix factorization algorithms. The Python and Matlab implementations of HNCcorr used here are publicly available. The use of HNCcorr demonstrates that combinatorial optimization is a valuable tool for neuroscience and other biomedical disciplines.

Combinatorial Cluster Expansion Formulas from Triangulated Surfaces

We give a cluster expansion formula for cluster algebras with principal coefficients defined from triangulated surfaces in terms of maximal independent sets of angles. Our formula simplifies the cluster expansion formula given by Musiker, Schiffler and Williams in terms of perfect matchings of snake graphs. A key point of our proof is to give a bijection between maximal independent sets of angles in some triangulated polygon and perfect matchings of the corresponding snake graph. Moreover, they also correspond bijectively with perfect matchings of the corresponding bipartite graph and minimal cuts of the corresponding quiver with potential.

HNCcorr: A Novel Combinatorial Approach for Cell Identification in Calcium-Imaging Movies.

Calcium imaging is a key method in neuroscience for investigating patterns of neuronal activity in vivo. Still, existing algorithms to detect and extract activity signals from calcium-imaging movies have major shortcomings. We introduce the HNCcorr algorithm for cell identification in calcium-imaging datasets that addresses these shortcomings. HNCcorr relies on the combinatorial clustering problem HNC (Hochbaum’s Normalized Cut), which is similar to the Normalized Cut problem of Shi and Malik, a well known problem in image segmentation. HNC identifies cells as coherent clusters of pixels that are highly distinct from the remaining pixels. HNCcorr guarantees a globally optimal solution to the underlying optimization problem as well as minimal dependence on initialization techniques. HNCcorr also uses a new method, called “similarity squared”, for measuring similarity between pixels in calcium-imaging movies. The effectiveness of HNCcorr is demonstrated by its top performance on the Neurofinder cell identification benchmark. We believe HNCcorr is an important addition to the toolbox for analysis of calcium-imaging movies.

Research on Transformation Characteristics of Binomial Coefficient Formula and Its Extended Model

Combinatorial methods are used to give specific mathematics, and the proof of combinatorial identities is the hot spot research of combinatorial mathematics. Binomial coefficients play an important role in the fields of physics, mathematics and computer science. In variances of rotation and reflection is the core characteristic for combinatorial systems. This paper uses different parameters to form reflection, rotation and specific features by using variant construction model and method, meanwhile the quantitative distribution characteristics of binomial coefficient formula are analyzed by three-dimensional maps. Using variant construction, the combinatorial clustering properties are investigated to apply binomial formulas and sample distributions, and various combinatorial patterns are illustrated. It is proved that the basic binomial coefficient formula and its extended model have obvious properties of reflection and rotation invariance.

Research on Reflection and Rotation Features of Binomial Coefficient Distributions

With the rapid development of frontier neural network, artificial intelligence and big data technology, the related theory and application research of combinatorial mathematics are more and more extensive. The application of binomial coefficient in combinatorial mathematics is an effective way to solve the research of information coding and quantum computation. Binomial coefficients and its distributions are the core topic in probability statistics, and there are many theories and applications related to them.In this paper, the quantification of binomial coefficients and the characteristic of reflection rotation transformation are studied using three-dimensional diagrams. Using variant construction, the combinatorial clustering properties are investigated applying binomial formulas and sample distributions and their combinatorial patterns are illustrated. It is proved that the basic binomial coefficient formula and its extended model have obvious properties of reflection and rotation invariance.

Identification of high-confidence RNA regulatory elements by combinatorial classification of RNA\u2013protein binding sites

Crosslinking immunoprecipitation sequencing (CLIP-seq) technologies have enabled researchers to characterize transcriptome-wide binding sites of RNA-binding protein (RBP) with high resolution. We apply a soft-clustering method, RBPgroup, to various CLIP-seq datasets to group together RBPs that specifically bind the same RNA sites. Such combinatorial clustering of RBPs helps interpret CLIP-seq data and suggests functional RNA regulatory elements. Furthermore, we validate two RBP–RBP interactions in cell lines. Our approach links proteins and RNA motifs known to possess similar biochemical and cellular properties and can, when used in conjunction with additional experimental data, identify high-confidence RBP groups and their associated RNA regulatory elements.

Channel-Dependent Constrained Combinatorial Clustering

Constrained combinatorial clustering (CCC) is a new approach for grouping multiple features where the clustering metric depends on an unknown communication channel assignment. Features assigned to the same channel cannot be from the same source and, conversely, channels assigned to the same source must be distinct. While the number of sources and their states are unknown, the channels are assumed to be known except for additive noise. Potential clustering assignments are checked for compatibility with the constraints in a structured way that results in significant computational savings with respect to exhaustive enumeration, especially when combined with a $K$ -best channel assignment algorithm that has polynomial complexity. By combining two channel assignment methods (exhaustive and $K$ -best) with two clustering techniques (CCC and greedy), four new algorithms are presented to solve this novel problem, along with detailed computational complexity analyses. The main algorithm (CCC) is a top-down clustering strategy based on assignment aggregation in a channel constrained environment. The approaches are compared on a one-dimensional simulation. Significant performance differences in source estimation accuracy and estimated number of sources are observed at low signal-to-noise ratios (SNRs) and for low values of $K$ . Some novel permutation symmetry properties arising from the study, which lead to a new type of self-affine set or discrete fractal, are also presented.

On dynamic combinatorial clustering

The paper addresses dynamic combinatorial clustering. First, a systematic literature survey on dynamic/online clustering is presented (problems, methods, applications). Second, restructuring approach to clustering is described (one-stage clustering, multi-stage clustering, sorting). Third, two network application examples of dynamic/multistage clustering are examined: (a) multi-stage connection of users to access points, (b) partition coloring problem in optical networks (wavelength routing and assignment).

Optimized combinatorial clustering for stochastic processes

As a new data processing era like Big Data, Cloud Computing, and Internet of Things approaches, the amount of data being collected in databases far exceeds the ability to reduce and analyze these data without the use of automated analysis techniques, data mining. As the importance of data mining has grown, one of the critical issues to emerge is how to scale data mining techniques to larger and complex databases so that it is particularly imperative for computationally intensive data mining tasks such as identifying natural clusters of instances. In this paper, we suggest an optimized combinatorial clustering algorithm for noisy performance which is essential for large data with random sampling. The algorithm outperforms conventional approaches through various numerical and qualitative thresholds like mean and standard deviation of accuracy and computation speed.

Combinatorial clustering and Its Application to 3D Polygonal Traffic Sign Reconstruction From Multiple Images

Abstract. The 3D reconstruction of similar 3D objects detected in 2D faces a major issue when it comes to grouping the 2D detections into clusters to be used to reconstruct the individual 3D objects. Simple clustering heuristics fail as soon as similar objects are close. This paper formulates a framework to use the geometric quality of the reconstruction as a hint to do a proper clustering. We present a methodology to solve the resulting combinatorial optimization problem with some simplifications and approximations in order to make it tractable. The proposed method is applied to the reconstruction of 3D traffic signs from their 2D detections to demonstrate its capacity to solve ambiguities.

A novel fuzzy hybrid quantum artificial immune clustering algorithm based on cloud model

In this paper we propose a novel fuzzy hybrid quantum artificial immune clustering algorithm based on cloud model (C-FHQAI) to solve the stochastic problem. Fuzzy hybrid quantum artificial immune algorithm can be developed with some of the advantages of information processing where there is a certain amount of indeterminism with qubits, i.e. quantum bits, replacing classical neurons having deterministic states and also in place of the classical artificial immune algorithm with quantum operators.The fuzzy combinatorial fuzzy hybrid quantum artificial immune clustering algorithm (C-FHQAI) is more expressive than the other fuzzy theories and methods. Finally, numerical examples show that the clustering effectiveness of the C-FHQAI algorithm is fast convergence and improves the accuracy of the fuzzy calculation. We find that the C-FHQAI clustering algorithm has the perspective of widespread application.

Combinatorial Clustering of Residue Position Subsets Predicts Inhibitor Affinity across the Human Kinome

The protein kinases are a large family of enzymes that play fundamental roles in propagating signals within the cell. Because of the high degree of binding site similarity shared among protein kinases, designing drug compounds with high specificity among the kinases has proven difficult. However, computational approaches to comparing the 3-dimensional geometry and physicochemical properties of key binding site residue positions have been shown to be informative of inhibitor selectivity. The Combinatorial Clustering Of Residue Position Subsets (ccorps) method, introduced here, provides a semi-supervised learning approach for identifying structural features that are correlated with a given set of annotation labels. Here, ccorps is applied to the problem of identifying structural features of the kinase atp binding site that are informative of inhibitor binding. ccorps is demonstrated to make perfect or near-perfect predictions for the binding affinity profile of 8 of the 38 kinase inhibitors studied, while only having overall poor predictive ability for 1 of the 38 compounds. Additionally, ccorps is shown to identify shared structural features across phylogenetically diverse groups of kinases that are correlated with binding affinity for particular inhibitors; such instances of structural similarity among phylogenetically diverse kinases are also shown to not be rare among kinases. Finally, these function-specific structural features may serve as potential starting points for the development of highly specific kinase inhibitors.

A Genome-wide Map of CTCF Multivalency Redefines the CTCF Code

The "CTCF code" hypothesis posits that CTCF pleiotropic functions are driven by recognition of diverse sequences through combinatorial use of its 11 zinc fingers (ZFs). This model, however, is supported by invitro binding studies of a limited number of sequences. To study CTCF multivalency invivo, we define ZF binding requirements at ∼50,000 genomic sites in primary lymphocytes. We find that CTCF reads sequence diversity through ZF clustering. ZFs 4-7 anchor CTCF to ∼80% of targets containing the core motif. Nonconserved flanking sequences are recognized by ZFs 1-2 and ZFs 8-11 clusters, which also stabilize CTCF broadly. Alternatively, ZFs 9-11 associate with a second phylogenetically conserved upstream motif at ∼15% of its sites. Individually, ZFs increase overall binding and chromatin residence time. Unexpectedly, we also uncovered a conserved downstream DNA motif that destabilizes CTCF occupancy. Thus, CTCF associates with a wide array of DNA modules via combinatorial clustering of its 11 ZFs.