New algorithm maximizes agreements in bipartite graphs.
problem Maximizing agreements in bipartite graphs with constraints.
method Combination of approximation algorithm and bilinear maximization.
result Achieves (1−δ)-approximation for k-BCC with O(δ−1) clusters. A new method assesses similarity in bipartite data using reflexive regular equivalence.
problem Challenges in clustering bipartite data, especially in validating co-similarity assumptions.
method Uses spectral properties of a bipartite adjacency matrix and reflexive regular equivalence to estimate similarity.
result The method outperforms other measures in correctly classifying genes in real-world data.
Refined analysis of Mitra's algorithm for discrete mixtures.
problem Classifying general discrete mixture distribution models.
method Spectral clustering tailored to bipartite stochastic block models.
result Improved separation conditions for probability distributions.
Clusters vehicle trajectories constrained by road networks.
problem Clustering trajectories of vehicles on road networks.
method Modelled trajectories and road segments as a bipartite graph, then clustered vertices.
result Demonstrated clustering on synthetic data, inferred flow dynamics and driver behavior.
A biclustering algorithm finds dense disjoint subgraphs in weighted bipartite graphs.
problem Finding dense disjoint bicliques in a weighted bipartite graph.
method Semidefinite programming-based branch-and-cut algorithm with upper and lower bounds.
result The algorithm can solve much larger instances than general-purpose solvers.
Study analyzes Colombian firms' export capabilities over 5 years.
problem Understanding specialization in Colombian firms' export products.
method Bipartite network analysis, modularity maximization, Louvain algorithm.
result Firms specialize in exporting specific product categories, forming clusters.
Two novel algorithms improve scalability and robustness of spectral clustering for large datasets.
problem Scalability and robustness of spectral clustering for large-scale datasets.
method Ultra-scalable spectral clustering (U-SPEC) and ultra-scalable ensemble clustering (U-SENC) algorithms.
result Robust and efficient clustering of ten-million-level datasets on a PC.
New model detects communities in bipartite networks with covariates.
problem Detecting communities in bipartite networks with covariates.
method Variational inference for fitting the model.
result Effectiveness of the model on simulated and real data.
New method clusters weighted directed networks using motifs.
problem Clustering directed networks fails to consider higher-order structure and edge weights.
method Motif-based weighted spectral clustering with new matrix formulae.
result Scalable and effective clustering on large graphs and real-world data.
New spectral clustering method improves community detection in sparse networks.
problem Community detection in sparse networks using spectral clustering.
method Data-driven regularization and novel spectral truncation for adjacency matrix.
result Consistency results for community detection in general SBM and beyond.
New method for clustering bipartite networks achieves optimal performance.
problem Bipartite network clustering problem.
method Two-stage procedure based on spectral initialization and pseudo-likelihood classifier.
result Optimal biclustering performance under general stochastic block model.
Improved bipartite link prediction using 2-hop paths.
problem Link prediction in bipartite networks without node attributes.
method Multiply reconstructed adjacency matrix with symmetrically normalized training adjacency matrix to form 2-hop paths.
result 2-hop paths improve link prediction performance.
The latent block model (LBM) is a flexible probabilistic tool to describe interactions between node sets in bipartite networks, but it does not account for interactions of time varying intensity between nodes in unknown classes. In this paper we propose a non stationary temporal extension of the LBM that clusters simul…
Algorithm aligns correlated Erdős-Rényi graphs efficiently.
problem Graph alignment in correlated Erdős-Rényi graphs.
method A canonical labeling algorithm with two steps: degree-based matching and bipartite graph alignment.
result The algorithm succeeds in aligning correlated Erdős-Rényi graphs in a specific time complexity region.
Spring-electrical models predict network links based on node proximity.
problem Predicting links in networks.
method Spring-electrical models applied to network layouts.
result The Euclidean distance in network layouts correlates with link probabilities.
A new model detects common patterns in pollination networks.
problem Comparing organization of bipartite networks to understand community structure.
method colBiSBM, a family of probabilistic models for collections of bipartite networks.
result The method uncovers shared ecological roles and partitions networks.
A new measure k-variance captures local distributional shape.
problem Summarizing distributional shape with local information.
method Random bipartite matchings and stochastic approximation.
result Easily approximated k-variance measures capture local distributional properties. Improved model for grouping nodes in bipartite networks.
problem Challenges in grouping nodes in bipartite graphs.
method Introduced DC-LBM and developed variational EM algorithm.
result Significantly enhanced performance on real-world data.
A new multi-view clustering method that is fast, scalable, and easy to use.
problem High computational complexity, one-stage fusion, and dataset-specific hyperparameter tuning in multi-view clustering.
method Random view groups, hybrid early-late fusion, diversified base clusterings, and unified bipartite graph.
result Almost linear time and space complexity, no dataset-specific tuning required.
Algorithm extracts meaningful projections from bipartite networks.
problem Devising projections that preserve bipartite network structure.
method Entropy-based approach using four null models for statistical significance.
result Validated projections reveal non-trivial communities in real-world networks.
Using a model of wealth distribution where traders are characterized by quenched random saving propensities and trade among themselves by bipartite transactions, we mimic the enhanced rates of trading of the rich by introducing the preferential selection rule using a pair of continuously tunable parameters. The biparti…
We use statistically validated networks, a recently introduced method to validate links in a bipartite system, to identify clusters of investors trading in a financial market. Specifically, we investigate a special database allowing to track the trading activity of individual investors of the stock Nokia. We find that …
Much of the data being created on the web contains interactions between users and items. Stochastic blockmodels, and other methods for community detection and clustering of bipartite graphs, can infer latent user communities and latent item clusters from this interaction data. These methods, however, typically ignore t…
Integrable dynamics explained via geometric maps and cluster algebras.
problem Integrable dynamics in projective geometry.
method Twisted triple crossing diagram maps and cluster integrable systems.
result Cross-ratio dynamics described by geometric R-matrices. Proposes a hierarchical clustering method for positive and negative dissimilarities.
problem Clustering dissimilarities, especially positive and negative.
method Hierarchical correlation clustering followed by tree preserving embedding.
result Performance on various datasets.
Clusters of highly correlated stocks are identified for better asset selection.
problem Identifying a small set of stocks to approximate the diversification of the whole stock universe.
method Data-driven correlation blockmodel clustering approach.
result The algorithm effectively detects clusters of highly correlated stocks.
New link polynomials linked to cluster theory.
problem Connecting link polynomials to cluster theory.
method Introducing new link polynomials and their expansion over perfect matchings.
result Bracket polynomials of certain links can be realized as specializations of cluster variables.
Clustering evaluation measures are frequently used to evaluate the performance of algorithms. However, most measures are not properly normalized and ignore some information in the inherent structure of clusterings. We model the relation between two clusterings as a bipartite graph and propose a general component-based …
The paper tackles fair correlation clustering with new algorithms and analysis.
problem Fair variants of correlation clustering under various constraints.
method Introducing a novel combinatorial optimization problem for fairlet decomposition.
result Approximation algorithms for fair correlation clustering under multiple fairness constraints.
We present an analysis of the credit market of Japan. The analysis is performed by investigating the bipartite network of banks and firms which is obtained by setting a link between a bank and a firm when a credit relationship is present in a given time window. In our investigation we focus on a community detection alg…
CCP clusters correlated features and projects them to 1D for efficient dimensionality reduction.
problem Efficiency in handling large datasets with high intrinsic dimensions.
method CCP partitions features into correlated clusters and projects them to 1D based on sample correlations.
result CCP achieves efficient dimensionality reduction without matrix diagonalization.
CSTS benchmarks time series clustering by evaluating correlation structures.
problem Lack of validated ground truth for objectively assessing clustering quality.
method Synthetic benchmark CSTS for evaluating correlation structures in multivariate time series data.
result CSTS enables precise diagnosis of methodological limitations in correlation-based time series clustering.
A new algorithm removes unexpected correlations in biased data for better clustering.
problem Clustering with selection bias in data.
method Decorrelation regularized K-Means (DCKM) algorithm.
result DCKM achieves significant performance gains on real-world datasets.
Active learning optimizes correlation clustering by querying the most informative pairwise comparisons.
problem Efficiently clustering data with limited pairwise similarity information.
method Developed principled active learning approach using information-theoretic acquisition functions.
result Significantly outperforms existing baselines in clustering accuracy and query efficiency.
Researchers analyze tagging patterns on Stack Exchange communities.
problem Understanding the structure and evolution of tags in Q&A platforms.
method Empirical analysis and development of a generative model for tag co-occurrence.
result The model can reproduce statistical properties of co-tagging graphs.
DynMSA detects market clusters for better portfolio allocation.
problem Identifying stable market clusters for effective portfolio management.
method Combining Random Matrix Theory with modularity optimization and spectral clustering.
result DynMSA outperforms baseline models in intra- and inter-cluster correlation differences.
Clustering analysis by nonnegative low-rank approximations has achieved remarkable progress in the past decade. However, most approximation approaches in this direction are still restricted to matrix factorization. We propose a new low-rank learning method to improve the clustering performance, which is beyond matrix f…
Automates machine learning of correlations between knot invariants.
problem Discovering and validating new relationships between knot invariants.
method Trained a neural network on 200,000 sets of knot invariants to predict an output invariant.
result Found novel correlations not explained by known results in knot theory.
The paper tackles fair correlation clustering with fairness constraints.
problem Minimizing disagreements while adhering to fairness constraints for clustering.
method Two variants of fairness constraints are considered: equal distribution and relative bounds. Approximation algorithms are developed for these constraints.
result Approximation algorithms for fair correlation clustering with theoretical guarantees and empirical validation.
This study examines clustering of correlated random variables using k-means and spectral methods.
problem Clustering of correlated random variables.
method Used k-means and spectral algorithms, analyzed different similarity measures.
result Impact of initial points on k-means efficiency was analyzed.
This paper analyzes correlations in patterns of trading of different members of the London Stock Exchange. The collection of strategies associated with a member institution is defined by the sequence of signs of net volume traded by that institution in hour intervals. Using several methods we show that there are signif…
Study explores properties of bipartite knots.
problem None explicitly stated; focuses on properties of bipartite knots.
method Exploration of combinatorial structure.
result Rich combinatorial structure of bipartite knots.
New method extends knot theory to non-bipartite knots, revealing PDs.
problem Extending knot theory to non-bipartite knots.
method Developed a new positive decomposition (PD) for HOMFLY polynomials of non-bipartite knots.
result PD exists for non-bipartite knots, not just bipartite ones.
This work optimizes clustering with adaptive queries to minimize disagreements.
problem Minimizing disagreements in clustering with adaptive similarity queries.
method Active learning algorithms and information-theoretical bounds.
result Achieves an almost optimal trade-off between queries and clustering error.
Paper uses HPCA for better stock correlation modeling.
problem Challenges in modeling cross-sectional correlations between thousands of stocks.
method Hierarchical Principal Component Analysis (HPCA) and statistical clustering.
result HPCA provides better cross-sectional correlations than classic PCA.
Paper uses clustering to diversify stocks, reducing risk.
problem Diversifying stock portfolios to reduce risk.
method Applied correlation clustering to a stock correlation matrix.
result Portfolio diversification using clustering reduces risk.
Clusters of financial market states identified over 2006-2019.
problem Understanding the statistical properties of financial markets.
method Clustering analysis of correlation matrices constructed from sliding epochs.
result Financial markets can be classified into distinct states with transitions indicating precursors to catastrophic events.
Simplified Khovanov polynomials for bipartite links.
problem Computing Khovanov polynomials for bipartite links.
method Reduced Khovanov-Rozansky technique to Kauffman-Khovanov cycle calculus.
result Consistency demonstrated between reduced technique and bipartite Khovanov polynomials.