A faster Wasserstein k-means algorithm for histogram data reduces computation and maintains clustering quality.
problem Efficiently clustering histogram data with reduced computation time.
method Sparse simplex projection to reduce data samples, centroids, and ground cost matrix, dynamically removing lower-valued samples.
result Significant reduction in computational complexity without compromising clustering quality.
Simple, scalable sparse k-means for high-dimensional data.
problem Clustering in high-dimensional feature spaces with few relevant features.
method Feature ranking-based sparse k-means algorithm.
result Consistent and convergent sparse k-means clustering.
Proposes ARSK for robust and sparse clustering.
problem Outliers and high-dimensional noisy variables in K-means clustering.
method Introduces redundant error component and group sparse penalty for robustness, and weights and sparsity control penalty for noisy variables.
result Superior performance in identifying clusters without outliers and informative variables.
We propose the Lasso Weighted k-means (LW-k-means) algorithm as a simple yet efficient sparse clustering procedure for high-dimensional data where the number of features (p) can be much larger compared to the number of observations (n). In the LW-k-means algorithm, we introduce a lasso-based penalty term,…
Sparse clustering, which aims to find a proper partition of an extremely high-dimensional data set with redundant noise features, has been attracted more and more interests in recent years. The existing studies commonly solve the problem in a framework of maximizing the weighted feature contributions subject to a $\ell…
In many situations where the interest lies in identifying clusters one might expect that not all available variables carry information about these groups. Furthermore, data quality (e.g. outliers or missing entries) might present a serious and sometimes hard-to-assess problem for large and complex datasets. In this pap…
Proposes a semi-supervised K-Means algorithm for better feature selection.
problem Data clustering with unknown feature quality and limited labelled data.
method Combines unsupervised sparse clustering and semi-supervised learning with labelled data.
result The algorithm identifies informative features and maintains high performance.
SIVF k-means algorithm speeds up sparse data clustering.
problem Efficiently clustering large-scale high-dimensional sparse data.
method Inverted-file structure for centroids, filter-based similarity reduction.
result SIVF achieves higher speed and lower memory consumption.
IVF k-means algorithm improves performance on large sparse data sets.
problem Efficiently clustering large-scale sparse data sets with numerous classes.
method Sparse data representation and inverted-file structure for high-speed and low-memory clustering.
result IVF achieves better performance than other algorithms on real document data sets.
A new framework improves fairness in clustering and Wasserstein Barycenter problems.
problem Fair clustering in datasets with multiple groups.
method Relax and Merge framework for (1+4ρ+O(ε))-approximate solutions. result Improved approximation guarantees for fairness constraints.
Consider the problem of sparse clustering, where it is assumed that only a subset of the features are useful for clustering purposes. In the framework of the COSA method of Friedman and Meulman, subsequently improved in the form of the Sparse K-means method of Witten and Tibshirani, a natural and simpler hill-climbing …
Paper accelerates K-means clustering for large sparse document data.
problem Efficiently clustering large-scale sparse document data.
method Designs an AFM algorithm leveraging UCs and inverted-index structure.
result Significantly improves clustering speed for large-scale documents.
This paper deals with unsupervised clustering with feature selection. The problem is to estimate both labels and a sparse projection matrix of weights. To address this combinatorial non-convex problem maintaining a strict control on the sparsity of the matrix of weights, we propose an alternating minimization of the Fr…
Proposes a new clustering algorithm for high-dimensional data.
problem Challenges of feature selection in high-dimensional clustering.
method An EM algorithm with lasso-type constraints on cluster pairs.
result Identifies informative features and cluster separability.
New method for community detection in sparse directed SBMs with exact recovery guarantees.
problem Exact recovery in sparse directed SBMs, especially with growing communities.
method Two-stage procedure: neighborhood-smoothing followed by K-means clustering. result Exact recovery of all community labels with probability tending to one under mild sparsity and separation conditions.
Paper identifies sparse structures and communities in heterogeneous graphical models.
problem Detecting community structures in graphical models.
method Novel decomposition into sparse and low-rank parts, three-stage estimation procedure.
result Consistent model selection for adaptive ℓ1 penalized estimator. 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.
We analyze a compression scheme for large data sets that randomly keeps a small percentage of the components of each data sample. The benefit is that the output is a sparse matrix and therefore subsequent processing, such as PCA or K-means, is significantly faster, especially in a distributed-data setting. Furthermore,…
Improves classification of microbiome data using mixture distributions.
problem Challenges in classifying sparse and heterogeneous microbiome count data.
method Distance-based classification using mixture distributions.
result The method outperforms existing distance-based classifiers and machine learning approaches.
This paper tackles spatio-temporal information preservation in machine learning.
problem Conventional machine learning assumes orthogonal data attributes, disrupting spatio-temporal information.
method Shift-invariant k-means, convolutional dictionary learning, and spatio-temporal hypercomplex encoding schemes are proposed.
result Gabor feature extraction outperforms convolutional dictionary learning in spatio-temporal information preservation.
Performing signal processing tasks on compressive measurements of data has received great attention in recent years. In this paper, we extend previous work on compressive dictionary learning by showing that more general random projections may be used, including sparse ones. More precisely, we examine compressive K-mean…
Breathing k-means outperforms greedy k-means++ in clustering.
problem Improving k-means clustering solutions.
method Dynamic adjustment of centroids through breathing technique.
result Breathing k-means outperforms other k-means techniques, especially greedy k-means++.
K-means -- and the celebrated Lloyd algorithm -- is more than the clustering method it was originally designed to be. It has indeed proven pivotal to help increase the speed of many machine learning and data analysis techniques such as indexing, nearest-neighbor search and prediction, data compression; its beneficial u…
Improved K-Means++ and K-Means∥ with faster run-time.
problem Efficiently selecting initial seeds for K-means clustering.
method Triangle inequality pruning and dynamic priority queue.
result Up to 17x speedup for K-Means++ and 551x for K-Means$\$.
We propose a simple and efficient time-series clustering framework particularly suited for low Signal-to-Noise Ratio (SNR), by simultaneous smoothing and dimensionality reduction aimed at preserving clustering information. We extend the sparse K-means algorithm by incorporating structured sparsity, and use it to exploi…
A new K-means method HT K-means uses ℓ0 penalty for sparsity.
problem Cluster center regularization for improved clustering performance.
method HT K-means with ℓ0 penalty for sparsity. result HT K-means outperforms other regularized K-means methods in simulations and real data. Deep k-means learns clustering and features from unlabeled data.
problem Clustering and feature learning from unlabeled data.
method Gradient-estimator for non-differentiable k-means objective via Gumbel-Softmax reparameterisation.
result Concrete k-means model optimised for canonical k-means objective, end-to-end trainable.
Modified K-means ensures local optimality with same complexity.
problem Lack of rigorous analysis on local optimality guarantees of K-means.
method Proposed modifications to K-means ensuring local optimality.
result Proposed methods provide improved locally optimal solutions.
k-means algorithm is one of the most classical clustering methods, which has been widely and successfully used in signal processing. However, due to the thin-tailed property of the Gaussian distribution, k-means algorithm suffers from relatively poor performance on the dataset containing heavy-tailed data or outlie…
Clustering is a separation of data into groups of similar objects. Every group called cluster consists of objects that are similar to one another and dissimilar to objects of other groups. In this paper, the K-Means algorithm is implemented by three distance functions and to identify the optimal distance function for c…
Paper improves clustering risk bounds for kernel k-means.
problem Improving clustering risk bounds for kernel k-means.
method Analyzes kernel k-means and Nyström approximation.
result Achieves nearly optimal excess clustering risk bound.
Ball k-means reduces point-centroid distance computations for faster k-means clustering.
problem Efficiently finding k-means clusters in large datasets.
method Uses a ball to describe clusters, dividing them into stable and active areas, and adjusting points within annulus areas.
result Significantly reduces point-centroid distance computations, making k-means faster and more efficient.
New method speeds up k-means clustering using sketch-and-solve.
problem Efficiently solving k-means clustering for large datasets.
method Sketch-and-solve approach with Peng-Wei semidefinite relaxation.
result Provides high-confidence lower bounds on k-means optimal value.
A new k-means variant minimizes pairwise distances within clusters.
problem The need for improved clustering methods.
method A stochastic optimization procedure that minimizes the k-sums target function.
result The new k-sums method outperforms k-means and its variants.
TS-K-means improves financial data clustering with dynamic time warping.
problem Inadequate handling of temporal dependencies in financial time series data.
method Integrates Dynamic Time Warping into Time Series K-means for financial data.
result TS-K-means outperforms traditional K-means in financial data analysis.
Paper proposes a novel unsupervised feature selection method using K-means and ADMM.
problem Finding a subset of features for high-dimensional unsupervised learning problems.
method Developed K-means Derived Unsupervised Feature Selection (K-means UFS) using ADMM to solve NP-hard optimization.
result K-means UFS outperforms baselines in feature selection for clustering.
DISCERN estimates K for K-Means clustering efficiently.
problem Estimating the number of clusters in data.
method A deterministic initialization method for K-Means++.
result Improves both K estimation and clustering performance.
A new k-means method improves clustering accuracy and robustness.
problem Insufficient asymptotic properties in existing k-means methods. method Introducing clustering consistency and proposing a new k-means method. result The new k-means method has lower clustering error rates and is more robust. We show that k-means (Lloyd's algorithm) is obtained as a special case when truncated variational EM approximations are applied to Gaussian Mixture Models (GMM) with isotropic Gaussians. In contrast to the standard way to relate k-means and GMMs, the provided derivation shows that it is not required to consider Gau…
Two algorithms improve K-means clustering speed without sacrificing quality.
problem Improving clustering quality of K-means while speeding up the process.
method Divisive K-means and Parallel Two-Phase K-means.
result Achieved empirically global optimum clustering results with lower complexity.
The study investigates the consistency of k-means clustering under finite expectation assumptions.
problem Consistency of k-means clustering under finite expectation assumptions. method Investigates the conditions under which k-means clustering is consistent, considering finite expectation instead of finite variance. result Inconsistency can arise due to extreme cluster imbalance, leading to some clusters having few points.
The paper assesses conditions for the uniqueness of k-means clustering.
problem Conditions for the uniqueness of k-means clustering.
method Analyzes the choice of k and provides necessary and sufficient conditions for uniqueness.
result Determines the asymptotic distribution of the within cluster sum of squares (WCSS) and provides a bootstrap test for uniqueness.
Finding the optimal k-means clustering is NP-hard in general and many heuristics have been designed for minimizing monotonically the k-means objective. We first show how to extend Lloyd's batched relocation heuristic and Hartigan's single-point relocation heuristic to take into account empty-cluster and single-poin…
This paper presents a general coding method where data in a Hilbert space are represented by finite dimensional coding vectors. The method is based on empirical risk minimization within a certain class of linear operators, which map the set of coding vectors to the Hilbert space. Two results bounding the expected recon…
Data-target association is an important step in multi-target localization for the intelligent operation of un- manned systems in numerous applications such as search and rescue, traffic management and surveillance. The objective of this paper is to present an innovative data association learning approach named multi-la…
K-Means and RBF networks are shown to be equivalent under certain conditions.
problem Discrete clustering vs. continuous optimization in machine learning.
method Established variational and gradient-based equivalence between K-Means and RBF networks.
result Gradient-based updates of RBF centers recover K-Means centroid update rule.
Study reduces dimensions for k-means clustering for better accuracy.
problem Improving accuracy of k-means clustering with high-dimensional data. method Four randomized algorithms: two feature selection and two feature extraction.
result Provably accurate approximations of k-means clustering are obtained. Efficient algorithms for k-means clustering frequently converge to suboptimal partitions, and given a partition, it is difficult to detect k-means optimality. In this paper, we develop an a posteriori certifier of approximate optimality for k-means clustering. The certifier is a sub-linear Monte Carlo algorithm b…