Cluster analysis which focuses on the grouping and categorization of similar elements is widely used in various fields of research. Inspired by the phenomenon of atomic fission, a novel density-based clustering algorithm is proposed in this paper, called fission clustering (FC). It focuses on mining the dense families …
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48 results for “dense clusters”
Finding "densely connected clusters" in a graph is in general an important and well studied problem in the literature \cite{Schaeffer}. It has various applications in pattern recognition, social networking and data mining \cite{Duda,Mishra}. Recently, Ames and Vavasis have suggested a novel method for finding cliques i…
A new method for clustering high-dimensional data into subspaces efficiently and accurately.
problem Inaccurate clustering due to poor intra-subspace similarity in existing methods.
method Iterative Maximum Correlation (IMC) for affinity matrix learning and Piecewise Correlation Estimation (PCE) for densification.
result SDSC framework improves clustering accuracy and efficiency for large-scale data.
Clustering of solutions in the symmetric binary perceptroncond-mat.dis-nn
The study finds dense clusters of solutions in a simple neural network model, providing bounds for their existence.
problem Exploring the existence of minimizers in a simple neural network model with binary weights.
method Formulating the learning problem as a constraint satisfaction problem and computing moment bounds for the existence of solutions.
result First rigorous steps toward proving the existence of dense clusters of solutions in certain parameter regimes.
Proposes SAG-DBSCAN for clustering with self-adaptation.
problem Clustering analysis in data mining.
method Uses grey relational matrix and DBSCAN for clustering.
result Demonstrates superior performance compared to other methods.
SpaPool combines dense and sparse techniques for efficient graph pooling.
problem Efficiently processing large graphs in graph neural networks.
method Adaptive clustering of graph vertices into clusters.
result SpaPool outperforms existing methods on small-scale graphs.
Supervised Multivariate Learning with Simultaneous Feature Auto-grouping and Dimension Reductionstat.ML
CRL framework groups features for multivariate learning with sparse and dense problems.
problem Sparse and dense problems in supervised multivariate learning.
method Clustered reduced-rank learning (CRL) with joint matrix regularizations.
result CRL framework is more interpretable and relaxes sparsity assumption.
We present two related methods for deriving connectivity-based brain atlases from individual connectomes. The proposed methods exploit a previously proposed dense connectivity representation, termed continuous connectivity, by first performing graph-based hierarchical clustering of individual brains, and subsequently a…
A new algorithm reduces graph complexity for better dense subgraph analysis.
problem Mining dense subgraphs in large graphs for better analysis.
method Multi-stage graph peeling algorithm (M-PA) with two-stage data screening.
result M-PA produces similar dense subgraphs to the previous PA but with reduced graph complexity.
Spectral clustering is widely used to partition graphs into distinct modules or communities. Existing methods for spectral clustering use the eigenvalues and eigenvectors of the graph Laplacian, an operator that is closely associated with random walks on graphs. We propose a new spectral partitioning method that exploi…
Solves Riemann-Hilbert problems on surface triangulations.
problem Riemann-Hilbert problems in Donaldson-Thomas theory.
method Map from stability conditions to cluster variety.
result Constructs solutions to Riemann-Hilbert problems.
ViCE uses superpixels to enhance self-supervised learning for better dense visual embeddings.
problem Lack of high-resolution feature maps from self-supervised models.
method Superpixels for dense representation learning, contrasting over regions.
result Improves unsupervised semantic segmentation on benchmarks like Cityscapes and COCO.
Paper proposes efficient methods for clustering and signal recovery in high-dimensional data with block structures.
problem High-dimensional clustering and signal recovery under block signal structures.
method CFA-PCA and MA-PCA methods for sparse and dense block signals.
result Proposed methods achieve computational minimax optimality for clustering and signal recovery.
Study of -vector cones in cluster algebras from weighted orbifolds.
problem Determine the closure of -vector cones in cluster algebras.
method Analyzing -vector cones in a cluster algebra defined from a weighted orbifold.
result Closure of the union of -vector cones is except for specific weighted orbifolds.
Rare dense solutions clusters in asymmetric binary perceptrons -- local entropy via fully lifted RDTstat.ML
New method finds rare dense clusters in asymmetric binary perceptrons, resolving algorithmic hardness.
problem Resolving algorithmic hardness in asymmetric binary perceptrons.
method Fully lifted random duality theory (fl RDT) and large deviation upgrade (sfl LD RDT).
result Local entropy breaks down for constraint densities in (0.77, 0.78) interval, matching current solver limits.
Deep metric learning algorithms have been utilized to learn discriminative and generalizable models which are effective for classifying unseen classes. In this paper, a novel noise tolerant deep metric learning algorithm is proposed. The proposed method, termed as Density Aware Metric Learning, enforces the model to le…
The binary symmetric stochastic block model deals with a random graph of vertices partitioned into two equal-sized clusters, such that each pair of vertices is connected independently with probability within clusters and across clusters. In the asymptotic regime of and for fixe…
The two most extended density-based approaches to clustering are surely mixture model clustering and modal clustering. In the mixture model approach, the density is represented as a mixture and clusters are associated to the different mixture components. In modal clustering, clusters are understood as regions of high d…
Regularized spectral methods improve clustering in signed graphs, especially for sparse data.
problem Clustering signed graphs with positive and negative edges.
method Developed regularized versions of SPONGE and Signed Laplacian methods for clustering signed graphs, especially for sparse data.
result Theoretical guarantees and empirical performance improvements for clustering signed graphs, especially in sparse regimes.
New algorithms reduce communication in GNN training.
problem Higher communication costs in GNNs due to sparse connectivity.
method Parallel algorithms for sparse-dense matrix multiplication.
result Asymptotic reduction in communication compared to previous methods.
Paper proposes MMC to avoid high-density bias in clustering.
problem High-density bias in density-based clustering.
method Introduces mass distribution as a better foundation for clustering, proposing mass-maximization clustering (MMC).
result MMC avoids high-density bias and discovers clusters of arbitrary shapes, sizes, and densities.
CDF Transform-and-Shift: An effective way to deal with datasets of inhomogeneous cluster densitiescs.LG
The problem of inhomogeneous cluster densities has been a long-standing issue for distance-based and density-based algorithms in clustering and anomaly detection. These algorithms implicitly assume that all clusters have approximately the same density. As a result, they often exhibit a bias towards dense clusters in th…
A new method clusters complex networks using topological and geometric structure.
problem Clustering complex networks with intricate topology.
method Centroid-based clustering strategy using Wasserstein distance and barycenter for persistence barcodes.
result Demonstrated effectiveness on simulated and real-world networks.
APLC-XLNet improves XMTC by clustering labels and reducing computational time.
problem Efficiently tagging texts with many labels from a large set.
method Fine-tunes XLNet with APLC to approximate cross entropy loss.
result Achieved state-of-the-art results on XMTC benchmarks.
Mixture models and topic models generate each observation from a single cluster, but standard variational posteriors for each observation assign positive probability to all possible clusters. This requires dense storage and runtime costs that scale with the total number of clusters, even though typically only a few clu…
CAST improves spectral clustering for multi-scale data by integrating reachability similarity.
problem Applying spectral clustering to multi-scale data where clusters vary in size and density.
method CAST integrates reachability similarity with distance-based similarity to derive a coefficient matrix, then applies trace Lasso regularization.
result CAST provides excellent performance and robustness across various multi-scale data test cases.
Graph clustering improved using Boltzmann machine heuristics.
problem Graph clustering to form densely connected clusters.
method Two mathematical programming formulations, two variations of Boltzmann machine heuristic.
result Boltzmann machine provides superior solutions and faster computation times.
Subdominant Dense Clusters Allow for Simple Learning and High Computational Performance in Neural Networks with Discrete Synapsescond-mat.dis-nn
We show that discrete synaptic weights can be efficiently used for learning in large scale neural systems, and lead to unanticipated computational performance. We focus on the representative case of learning random patterns with binary synapses in single layer networks. The standard statistical analysis shows that this…
We present a first procedure that can estimate -- with statistical consistency guarantees -- any local-maxima of a density, under benign distributional conditions. The procedure estimates all such local maxima, or , of any bounded shape or dimension, including usual point-modes. In practice, modal-…
Quantum GBS boosts asset clustering for robust statistical arbitrage portfolios.
problem Identifying co-moving assets from correlation matrices for statistical arbitrage.
method Mapping S&P 500 correlation data to GBS-compatible adjacency matrices, benchmarking classical and quantum clustering algorithms.
result Quantum GBS generates superior alpha during high volatility periods, persisting under low-loss conditions.
CW-EDMD improves prediction accuracy by learning local Koopman models for different state-space regions.
problem Inefficient global Koopman operator approximation for distinct local dynamics.
method Cluster-Weighted EDMD (CW-EDMD) learns a soft phase-space partition and per-cluster EDMD operators using EM objective.
result CW-EDMD significantly reduces prediction errors across various systems and configurations.
Tangles improve clustering in various datasets.
problem Clustering diverse datasets efficiently and accurately.
method Tangles aggregate cuts to identify dense structures, leading to soft cluster characterization.
result Tangle framework generates hierarchical soft dendrograms for cluster exploration.
ARMED models improve deep learning interpretability and generalize better on clustered data.
problem Clustered data leads to spurious associations and poor model fitting.
method Adversarial regularization and mixed effects subnetworks.
result ARMED models outperform conventional methods in accuracy and generalization.
The Dehornoy order on braid groups is derived from a cluster algebra.
problem Deriving the Dehornoy order on braid groups from a cluster algebra.
method Using a tracial state on a cluster -algebra associated to a surface.
result The Dehornoy order on is recovered from the cluster algebra.
This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know whether or not there is an edge. We want to organize the nodes into disjoint cl…
Spectral clustering for geometric graphs achieves strong consistency in community recovery.
problem Community recovery in dense geometric graphs.
method Spectral clustering algorithm using eigenvectors of adjacency matrix.
result Strong consistency in community recovery proved.
New algorithm speeds up fair clustering by 12x.
problem Achieving fair clustering in scalable algorithms.
method s-FairSC algorithm incorporating nullspace projection and Hotelling's deflation.
result s-FairSC is 12x faster and maintains fairness.
Efficient algorithms find solutions in a rare well-connected cluster at low constraint densities.
problem Finding solutions in the symmetric binary perceptron at low density.
method Formal proof of existence of a subdominant connected cluster and application of an efficient multiscale majority algorithm.
result An efficient algorithm can find solutions in a subdominant connected cluster with high probability.
In this paper, we investigate community detection in networks in the presence of node covariates. In many instances, covariates and networks individually only give a partial view of the cluster structure. One needs to jointly infer the full cluster structure by considering both. In statistics, an emerging body of work …
Paper explores limits of high-order clustering with planted structures.
problem Statistical and computational limits of high-order clustering with planted structures.
method Developed methods for detection and recovery of clusters, identified signal-to-noise ratio boundaries.
result Sharp boundaries of signal-to-noise ratio for statistical and computational feasibility.
Paper perfect clusters sparse, diverse multilayer networks.
problem Clustering sparse, diverse multilayer networks.
method Tensor-based methodology pooling all layers' information.
result Achieves perfect clustering under sparser conditions than previous models.
In this paper, we propose a deep reinforcement learning (DRL) based mobility load balancing (MLB) algorithm along with a two-layer architecture to solve the large-scale load balancing problem for ultra-dense networks (UDNs). Our contribution is three-fold. First, this work proposes a two-layer architecture to solve the…
The paper introduces curvature-based clustering algorithms for graph analysis.
problem Identifying densely connected substructures in graphs for community detection.
method Discrete Ricci curvatures and geometric flows to reveal community structure.
result The curvature-based approach can identify overlapping communities in graphs.
Prototype model improves model auditing and understanding.
problem Auditing and understanding modern language models is expensive and approximate.
method Introduced a sparse, non-negative mixture of learned prototypes trained with clustering objectives.
result Prototype models either surpass or remain within 2.5 percentage points of dense baselines on downstream tasks.
Grouping objects into clusters based on similarities or weights between them is one of the most important problems in science and engineering. In this work, by extending message passing algorithms and spectral algorithms proposed for unweighted community detection problem, we develop a non-parametric method based on st…
We propose Rademacher complexity bounds for multiclass classifiers trained with a two-step semi-supervised model. In the first step, the algorithm partitions the partially labeled data and then identifies dense clusters containing predominant classes using the labeled training examples such that the proportion of t…
Generative model for hypergraph clustering improves detection of higher-order structure.
problem Detecting clusters in complex relational systems modeled as hypergraphs.
method Poisson degree-corrected hypergraph stochastic blockmodel (DCHSBM) and Louvain-type algorithms.
result AON hypergraph Louvain algorithm efficiently detects higher-order structure in large hypergraphs.
Partitioning a graph into groups of vertices such that those within each group are more densely connected than vertices assigned to different groups, known as graph clustering, is often used to gain insight into the organisation of large scale networks and for visualisation purposes. Whereas a large number of dedicated…