Sparse Convex Clustering improves clustering performance in high-dimensional data.
problem Distortion in convex clustering performance with uninformative features.
method Introduces Sparse Convex Clustering with an adaptive group-lasso penalty and a tuning criterion based on clustering stability.
result Demonstrates improved clustering performance through feature selection.
Bayesian method clusters data and selects variables with shrinkage priors.
problem Sparse convex clustering with limited data accuracy issues.
method Bayesian approach using global-local shrinkage priors and Gibbs sampling.
result Improved estimation accuracy in sparse convex clustering.
Unified method for simultaneous denoising and clustering.
problem Clustering noisy signals.
method Sparse convex wavelet clustering with fusion and group-sparse penalties.
result Unified approach that denoises and clusters simultaneously.
Unified framework for clustering with sparse convex combinations.
problem Challenges in subspace clustering with limited labelled data.
method Spectral-based sparse subspace representation with extensions to constrained and active learning.
result Effective and competitive clustering results on simulated and real data.
This paper converts ADMM to proximal gradient for efficient sparse estimation.
problem Sparse estimation problems like fused lasso and convex clustering.
method General method converting ADMM to proximal gradient, assuming Lipschitz continuity of derivative.
result Significant improvement in efficiency for sparse estimation problems.
The paper proposes a new method for clustering high-dimensional data.
problem Clustering high-dimensional data with separation of clustered and noise variables.
method Discriminative clustering with sparse regularizers, convex relaxations, and efficient iterative algorithm.
result The proposed method achieves scalings of d = O ( n ) d=O(\sqrt{n}) d = O ( n ) for the affine invariant case and d = O ( n ) d=O(n) d = O ( n ) for the sparse case. New method fits sparse Markov models to categorical time series using convex clustering.
problem Exponentially growing parameters in higher-order Markov chains.
method Convex clustering and regularization for parsimonious modeling.
result Theoretical consistency and finite sample performance demonstrated.
Inspired by recent work on convex formulations of clustering (Lashkari & Golland, 2008; Nowozin & Bakir, 2008) we investigate a new formulation of the Sparse Coding Problem (Olshausen & Field, 1997). In sparse coding we attempt to simultaneously represent a sequence of data-vectors sparsely (i.e. sparse approximation (…
Sparse Convex Biclustering improves accuracy and robustness in high-dimensional datasets.
problem Challenges in clustering rows and columns of large-scale datasets due to noise and computational complexity.
method Sparse Convex Biclustering (SpaCoBi) using convex optimization and stability-based tuning.
result Significantly outperforms state-of-the-art methods in accuracy for high-dimensional datasets.
Paper proposes an efficient algorithm for clustering with sparse feature selection.
problem Estimating labels and sparse weights in unsupervised clustering.
method Alternating minimization of Frobenius norm criterion with K-sparse algorithm.
result Significantly improves clustering results on single-cell RNA sequencing datasets.
Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of nonzero elements of the factors is assumed fixed and known. The formulation counts sparse PCA with multiple factors, subspace clustering and low-rank sparse bilinear regression as potential ap…
Paper proposes a new method for sparse spectral clustering on Stiefel manifold.
problem Sparse spectral clustering on Stiefel manifold with nonsmooth and nonconvex objective.
method Proposes a manifold proximal linear method (ManPL) to solve the original SSC formulation.
result Demonstrates the advantage of ManPL over existing methods on single-cell RNA sequencing data.
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…
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…
In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures corresponding to several classes or categories the data belongs to. In this paper, we…
Paper improves community detection in sparse networks with node covariates.
problem Community detection in sparse networks with node covariates.
method Proposes a simple optimization framework for sparse networks with node covariates.
result Proposed method outperforms other existing methodologies in various simulated and real data examples.
MTLRRC improves MTL by robustly clustering tasks and detecting outliers.
problem Improving MTL by handling outlier tasks and sharing common information.
method Robust regularized clustering with non-convex group penalties.
result MTLRRC effectively detects and clusters tasks, improving overall performance.
A new method for subspace clustering that is both efficient and guarantees a subspace-preserving affinity.
problem Efficiently clustering data points from multiple subspaces with theoretical guarantees.
method Orthogonal Matching Pursuit for sparse subspace clustering.
result The method provides a subspace-preserving affinity under broad conditions.
A framework estimates multiple precision matrices with shared structures.
problem Estimating multiple precision matrices with shared structures.
method Penalized likelihood framework with iterative algorithm alternating between convex and clustering problems.
result The method outperforms competitors and performs similarly to methods using prior information.
Adapts PALM to solve NMF with smooth and sparse solutions.
problem Non-negative matrix factorization for dimensionality reduction and source separation.
method Adapted PALM for convex minimization with non-differentiable constraints.
result Solves NMF with smooth and/or sparse solutions.
Traditional nearest points methods use all the samples in an image set to construct a single convex or affine hull model for classification. However, strong artificial features and noisy data may be generated from combinations of training samples when significant intra-class variations and/or noise occur in the image s…
Paper proposes algorithms for sparse signal estimation with nonconvex regularization.
problem Sparse signal estimation with nonconvex regularization.
method Successive convex approximation framework combining majorization-minimization and line search.
result Flexibility, fast convergence, low complexity, guaranteed convergence to stationary point.
Simpler approach for sparse clustering.
problem Sparse clustering with only useful features.
method Hill-climbing approach to Sparse K-means.
result Competitive with COSA and Sparse K-means.
New algorithm finds sparse matrices on Stiefel manifold for optimisation.
problem Finding sparse matrices on Stiefel manifold for optimisation.
method Modified Orthogonal Iteration algorithm for sparse global optimality.
result Proposed method finds globally optimal sparse Stiefel matrices.
New algorithm clusters sparse data effectively.
problem Challenges in clustering sparse data.
method Deterministic Information Bottleneck framework for joint feature weighting and clustering.
result Demonstrated effectiveness on real-world genomics data.
Paper introduces MGLasso for multiscale graph inference in clustering and network analysis.
problem Graphical models in high-dimensional data analysis need to handle clustering and sparsity simultaneously.
method MGLasso combines clustering and graph inference through a convex relaxation of k-means and hierarchical clustering. It uses CONESTA for regularization.
result MGLasso improves network interpretability by estimating graphs at multiple scales.
Convex clustering can only learn convex clusters, with significant gaps between clusters.
problem Understanding the limitations and capabilities of convex clustering.
method Analyzing convex clustering solutions, proving properties, and characterizing clusters.
result Convex clustering can only learn convex clusters with significant gaps between clusters.
Sparse PCA method for clustering Gaussian mixtures.
problem Clustering Gaussian mixture models.
method Sparse Principal Component Analysis (SPCA) for clustering.
result Comparison with IF-PCA method and discussion of non-diagonal covariance matrices.
Paper proposes clustering algorithms for data from Union of Polyhedral Cones model.
problem Clustering data from multiple convex polyhedral cones.
method Sparse Subspace Clustering, Least squares approximation, K-nearest neighbor, Spectral Clustering.
result KNN outperforms NCL and LSA in clustering data from UOPC model.
We apply the OSCAR (octagonal selection and clustering algorithms for regression) in recovering group-sparse matrices (two-dimensional---2D---arrays) from compressive measurements. We propose a 2D version of OSCAR (2OSCAR) consisting of the ℓ 1 \ell_1 ℓ 1 norm and the pair-wise ℓ ∞ \ell_{\infty} ℓ ∞ norm, which is convex but non-d…
This paper improves OMP-based sparse subspace clustering with data-adaptive capability.
problem Existing OMP-based approaches lack data adaptiveness, leading to inaccurate data representation.
method Develops a parameter selection process to adjust OMP parameters based on data distribution and introduces a new SEA ratio metric.
result Proposed approach achieves better clustering accuracy, SEA ratio, and representation quality compared to other OMP-based methods.
Sparse GEMINI selects relevant features for clustering without assumptions.
problem Feature selection in clustering with relevant clusters and variables.
method Discriminative clustering model maximizing GEMINI with l1 penalty.
result Sparse GEMINI selects relevant subsets of variables without prior hypotheses.
CCMM efficiently solves large-scale convex clustering problems.
problem Scalability and hierarchical structure in convex clustering.
method Majorization-minimization algorithm with cluster fusions and efficient updating.
result CCMM achieves efficient solutions for large datasets.
Paper addresses graph connectivity issues in noisy sparse subspace clustering.
problem Graph connectivity problem in noisy sparse subspace clustering.
method Proposes a simple post-processing procedure to ensure graph connectivity.
result Demonstrates consistency of clustering under certain assumptions.
Network Lasso clusters sparse graph clusters efficiently.
problem Local graph clustering of sparse and chain-like clusters.
method Network Lasso minimizes total variation of cluster indicator signals.
result Network Lasso handles sparse clusters difficult for spectral clustering.
New model tackles region-sparse regression with hierarchical Gaussian process.
problem Sparse and dependent parameter vectors in regression settings.
method Hierarchical model with transformed Gaussian process and structured Fourier coefficients.
result Substantial improvements over comparable methods in simulated and real datasets.
Paper optimizes Laplacian regularization for sparse network clustering.
problem Improving spectral clustering in sparse networks.
method Formally determines optimal Laplacian regularization.
result Proper regularization is closely tied to state-of-the-art techniques.
Stochastic Sparse Subspace Clustering improves subspace clustering by reducing over-segmentation through dropout.
problem Over-segmentation in subspace clustering.
method Introducing dropout regularization to enforce denser connections between points from the same subspace.
result Stochastic Sparse Subspace Clustering effectively handles large datasets and reduces over-segmentation.
There has been a surge in the number of large and flat data sets - data sets containing a large number of features and a relatively small number of observations - due to the growing ability to collect and store information in medical research and other fields. Hierarchical clustering is a widely used clustering tool. I…
SparseMix clusters sparse high dimensional binary data efficiently.
problem Clustering sparse high dimensional binary data.
method SparseMix is a mixture model designed for sparse data, using an on-line Hartigan optimization algorithm.
result SparseMix builds partitions with higher compatibility with reference grouping than related methods.
New algorithm clusters sparse, high-dimensional texts efficiently.
problem Clustering very short texts with high dimensions and sparsity.
method Linear algebra-based subspace clustering algorithm.
result Algorithm performs competitively on text categorization tasks.
Paper proposes a new clustering model that preserves cluster recovery with fewer dimensions.
problem Clustering high-dimensional data with limited embedding dimensions.
method Randomly projected convex clustering model with improved embedding dimension.
result Cluster recovery can be preserved with fewer dimensions, independent of data points.
NLSSC improves clustering by enhancing separability in sparse coding.
problem Improving clustering performance in subspace clustering problems.
method Introduces a novel objective term for local separability in non-negative local sparse coding.
result NLSSC outperforms state-of-the-art methods in clustering benchmarks.
Sparse variational posteriors improve clustering and topic modeling speed.
problem Inefficient storage and runtime costs for standard variational posteriors.
method Sparse variational distributions with tunable threshold L L L . result Moderate values of L > 1 L>1 L > 1 provide superior performance in clustering and topic modeling. Improved SSC clustering with reduced computation time and accuracy.
problem Heavy computational burden in Sparse Subspace Clustering.
method RCOMP-SSC algorithm that restricts connections during OMP iterations.
result Improved clustering accuracy with reduced computational time.
A new algorithm speeds up convex clustering.
problem Optimizing clustering with convex optimization and avoiding local minima.
method Smoothing proximal gradient algorithm (Sproga) for convex clustering.
result Sproga is faster and uses less memory than existing methods.
VC-PCR improves prediction by clustering correlated variables.
problem Decreased prediction accuracy due to cluster structure in predictor variables.
method Supervised variable selection and clustering to integrate cluster information into a sparse modeling process.
result VC-PCR achieves better prediction, variable selection, and clustering performance.
Spectral clustering with edge counting detects communities in sparse models.
problem Detecting communities in sparse latent space models.
method Spectral clustering followed by edge counting.
result Algorithm achieves consistency and optimality for a broad class of models.