We establish basic properties of cluster algebras associated with oriented bordered surfaces with marked points. In particular, we show that the underlying cluster complex of such a cluster algebra does not depend on the choice of coefficients, describe this complex explicitly in terms of "tagged triangulations" of the…
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48 results for “cluster complex”
We try to give a cluster algebraic interpretation of complex volume of knots. We construct the R-operator from the cluster mutations, and we show that it is regarded as a hyperbolic octahedron. The cluster variables are interpreted as edge parameters used by Zickert in computing complex volume.
A clustering algorithm for natural hierarchical clusters with near-linear time complexity.
problem Hierarchical clustering with near-linear time complexity.
method Nearest neighbor based clustering algorithm that defines clusters naturally.
result Near-linear time and space complexity for certain datasets.
Proposes a constraint for deep clustering to handle both simple and complex topologies.
problem Limited prior knowledge for deep clustering methods to perform well on complex topologies.
method Introduces a constraint using symmetric InfoNCE to enhance deep clustering performance.
result The constraint improves deep clustering methods' performance on both simple and complex topologies.
A fundamental property of complex networks is the tendency for edges to cluster. The extent of the clustering is typically quantified by the clustering coefficient, which is the probability that a length-2 path is closed, i.e., induces a triangle in the network. However, higher-order cliques beyond triangles are crucia…
We outline a novel clustering scheme for simplicial complexes that produces clusters of simplices in a way that is sensitive to the homology of the complex. The method is inspired by, and can be seen as a higher-dimensional version of, graph spectral clustering. The algorithm involves only sparse eigenproblems, and is …
New concept of mixture complexity helps detect gradual clustering changes.
problem Determining the number of clusters in mixture models with overlaps and weight biases.
method Introducing mixture complexity (MC) as a new measure of cluster size, defined from information theory.
result MC can detect gradual clustering changes, allowing earlier detection and finer distinction.
This paper proposes a spectral clustering algorithm for hyperbolic spaces, improving efficiency over Euclidean methods.
problem Inefficient clustering in Euclidean spaces for complex data structures.
method Developed a spectral clustering algorithm using hyperbolic similarity matrices.
result The algorithm converges at least as fast as Euclidean spectral clustering and performs better on complex datasets.
We propose a framework for Semi-Supervised Active Clustering framework (SSAC), where the learner is allowed to interact with a domain expert, asking whether two given instances belong to the same cluster or not. We study the query and computational complexity of clustering in this framework. We consider a setting where…
SPINEX improves clustering with explainable neighbors, outperforming other methods.
problem Improving clustering performance and explainability.
method Leverages similarity and higher-order interactions for clustering.
result SPINEX outperforms 13 clustering algorithms across various datasets.
DIVA clusters dynamic data without needing cluster count, outperforming baselines.
problem Clustering complex, dynamic data without prior knowledge of cluster count.
method Nonparametric Dirichlet Process Mixtures with memoized online variational inference.
result DIVA outperforms state-of-the-art in classifying complex data with changing features.
New method reduces clustering time and improves accuracy.
problem High time and space complexity in spectral clustering.
method Approximate spectral clustering using GNG network topology.
result Equal or better clustering performance than traditional SC.
Clustered attention improves transformer efficiency for large sequences.
problem Quadratic complexity of transformer attention matrix for large sequences.
method Group queries into clusters, compute attention only for centroids, and use centroids to approximate key/query dot products.
result Linear complexity with respect to sequence length for a fixed number of clusters.
Study clusters distributions with known or unknown clusters using distribution testing.
problem Cluster distributions that are -far in total variation.
method Distribution testing approach to establish upper and lower bounds on sample complexity.
result Achieves tight sample complexity bounds for all regimes (up to a logarithmic factor).
Spectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to reuse information of past cluster assignments to expedite computation. Our approach builds on a recent idea of sidestepping the main bottleneck of spectral clusterin…
Study examines how cluster number affects short-text clustering, introducing a stability metric.
problem Challenges in finding meaningful clusters in short-text data.
method Introduces a stability metric to determine cluster robustness and visualizes cluster subdivisions.
result Choosing a cluster number involves balancing informativeness and complexity, not seeking a single 'optimal' solution.
FCA improves fair clustering by optimizing utility and fairness.
problem Balancing fairness and utility in clustering.
method FCA alternates between aligning data and optimizing cluster centers in an aligned space.
result FCA achieves a superior trade-off between fairness and utility.
This study evaluates clustering algorithms on high-dimensional data.
problem Comparing clustering algorithms on high-dimensional datasets.
method Evaluation of K-means, DBSCAN, and Spectral Clustering using PCA, t-SNE, UMAP, and multiple metrics.
result UMAP preprocessing improves clustering quality across all algorithms, with Spectral Clustering excelling.
CLASSIX is a fast and explainable clustering method that sorts data and merges groups.
problem Clustering of data with various shapes and dimensions.
method Greedy aggregation followed by cluster merging with scalar parameters.
result CLASSIX performs competitively with state-of-the-art algorithms and provides intuitive explanations.
New interpretation reconciles country and product complexity.
problem Difficulty in interpreting Economic and Product Complexity Indices.
method Spectral clustering algorithm to separately group similar countries and products.
result Indices identify two co-clusters of similar countries and products.
Kernel methods obtain superb performance in terms of accuracy for various machine learning tasks since they can effectively extract nonlinear relations. However, their time complexity can be rather large especially for clustering tasks. In this paper we define a general class of kernels that can be easily approximated …
A new hierarchical clustering method selects representative points from sub-minimum-spanning-trees.
problem Selecting representative points for hierarchical clustering to improve robustness and reliability.
method Identify representative points using reciprocal nearest data points in sub-minimum-spanning-trees.
result The proposed algorithm outperforms other methods in accuracy and efficiency.
Study exact partition recovery with same-cluster oracle, bounded error.
problem Exact recovery of partitions with same-cluster oracle in adversarial error.
method Novel connection to correlation clustering, Rényi-Ulam framework, upper and lower bounds, randomized algorithm analysis, adaptivity-query complexity study.
result Upper and lower bounds on worst-case query complexity, expected performance bounds of randomized algorithm.
A new clustering algorithm reduces density peaks clustering's computational complexity.
problem High computational complexity of density peaks clustering.
method Sparse distance matrix, sparse search, K-d tree, second-order difference method.
result Reduced computational complexity from to .
A Bernoulli Mixture Model (BMM) is a finite mixture of random binary vectors with independent dimensions. The problem of clustering BMM data arises in a variety of real-world applications, ranging from population genetics to activity analysis in social networks. In this paper, we analyze the clusterability of BMMs from…
SASE improves attributed graph clustering for large graphs with linear time and space complexity.
problem Challenges in clustering large attributed graphs due to high computational and memory costs.
method SASE combines node features smoothing, scalable spectral clustering, and adaptive order selection.
result SASE achieves a 6.9% improvement in ACC and a 5.87x speedup on the ArXiv dataset.
Paper detects gradual changes in cluster structure using MC fusion.
problem Detecting gradual changes in cluster structure over time.
method MC fusion for multiple mixture numbers, examining MC transition.
result Accurately captures cluster structure during transitional periods.
This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is first applied to a sub-matrix of the graph's adjacency matrix associated with a re…
This paper represents a preliminary (pre-reviewing) version of a sublinear variational algorithm for isotropic Gaussian mixture models (GMMs). Further developments of the algorithm for GMMs with diagonal covariance matrices (instead of isotropic clusters) and their corresponding benchmarking results have been published…
New SDP algorithm recovers large clusters in SBM with small clusters of any size.
problem Graph clustering in SBM with large and small clusters.
method Semidefinite programming (SDP) with novel techniques to handle small clusters.
result Proves exact recovery of large clusters regardless of small cluster sizes.
Exact cluster recovery with same-cluster queries for arbitrary ellipsoidal clusters.
problem Recovering clusters from same-cluster queries in arbitrary ellipsoidal clusters.
method Relaxing spherical -means assumption to arbitrary ellipsoidal clusters, designing an algorithm with logarithmic query complexity.
result Exact recovery of clusters using queries and time.
This paper provides new algorithms for distributed clustering for two popular center-based objectives, k-median and k-means. These algorithms have provable guarantees and improve communication complexity over existing approaches. Following a classic approach in clustering by \cite{har2004coresets}, we reduce the proble…
Discrete random variables are natural components of probabilistic clustering models. A number of VAE variants with discrete latent variables have been developed. Training such methods requires marginalizing over the discrete latent variables, causing training time complexity to be linear in the number clusters. By appl…
We propose a method to compute complex volume of 2-bridge link complements. Our construction sheds light on a relationship between cluster variables with coefficients and canonical decompositions of link complements.
Probabilistically Sampled and Spectrally Clustered Plant Genotypes using Phenotypic Characteristicscs.LG
New algorithm improves plant breeding by clustering soybean genotypes more accurately and efficiently.
problem Low accuracy and high computational complexity in clustering plant genotypes.
method Spectral Clustering with Pivotal Sampling for phenotypic data.
result Our algorithm achieves substantially more accuracy than existing methods.
Proposes new random models for fuzzy clustering similarity measures.
problem Challenges in choosing a random model for fuzzy clustering similarity measures.
method Introduces three intuitive and explainable random models for fuzzy clusterings.
result Each random model has distinct behavior, emphasizing the importance of accurate model selection.
We propose a novel method to quantify the clustering behavior in a complex time series and apply it to a high-frequency data of the financial markets. We find that regardless of used data sets, all data exhibits the volatility clustering properties, whereas those which filtered the volatility clustering effect by using…
Proposes ConiVAT for better cluster assessment and clustering with background knowledge.
problem Challenges in cluster assessment and clustering with noise and bridge points.
method Uses background constraints to improve VAT/iVAT for complex datasets.
result Improves clustering accuracy and resolves issues with noise and bridge points.
Suppose, we are given a set of elements to be clustered into (unknown) clusters, and an oracle/expert labeler that can interactively answer pair-wise queries of the form, "do two elements and belong to the same cluster?". The goal is to recover the optimum clustering by asking the minimum number of quer…
Clustering ensemble, or consensus clustering, has emerged as a powerful tool for improving both the robustness and the stability of results from individual clustering methods. Weighted clustering ensemble arises naturally from clustering ensemble. One of the arguments for weighted clustering ensemble is that elements (…
New matrix reveals cluster info in sparse directed graphs.
problem Analyzing cluster information in directed graphs.
method Proposed complex non-backtracking matrix integrating Hermitian adjacency matrix and non-backtracking matrix properties.
result The complex non-backtracking matrix holds cluster information, especially for sparse directed graphs.
PEA improves PCA and k-means for non-linear data and complex clusters.
problem Non-linear dimensionality reduction and clustering challenges.
method Principal Elliptical Analysis (PEA) for efficient non-linear approximation.
result PEA outperforms k-means in complex data clustering.
In this paper we target the class of modal clustering methods where clusters are defined in terms of the local modes of the probability density function which generates the data. The most well-known modal clustering method is the k-means clustering. Mean Shift clustering is a generalization of the k-means clustering wh…
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.
Can clustering scale sublinearly with its clusters? A variational EM acceleration of GMMs and -meansstat.ML
One iteration of standard -means (i.e., Lloyd's algorithm) or standard EM for Gaussian mixture models (GMMs) scales linearly with the number of clusters , data points , and data dimensionality . In this study, we explore whether one iteration of -means or EM for GMMs can scale sublinearly with at run…
SNG-DBSCAN clusters data faster with subsampled similarity queries.
problem Efficiently clustering large datasets with DBSCAN's high complexity.
method Subsampled -neighborhood graph for similarity queries.
result Subsampling of the graph leads to 200x speedup and 250x RAM reduction.
We propose infinite mixture prototypes to adaptively represent both simple and complex data distributions for few-shot learning. Our infinite mixture prototypes represent each class by a set of clusters, unlike existing prototypical methods that represent each class by a single cluster. By inferring the number of clust…
A scalable Gaussian process clustering method for large datasets.
problem Infeasibility of Gaussian process clustering on large grids.
method Embedding Vecchia approximation in EM algorithm for scalability.
result Efficient Gaussian process clustering for large environmental applications.