New method improves text classification using KL divergence.
problem Multinomial text classification problem
method Centroid estimation based on symmetric KL divergence
result Substantial improvements over traditional classifiers
In addition to finding meaningful clusters, centroid-based clustering algorithms such as K-means or mean-shift should ideally find centroids that are valid patterns in the input space, representative of data in their cluster. This is challenging with data having a nonconvex or manifold structure, as with images or text…
Optimizes a small set of centroid points to approximate bootstrap distribution.
problem Computational inefficiency of standard bootstrap methods in large-scale machine learning.
method Explicitly optimizes a small set of high quality centroid points to approximate the ideal bootstrap distribution.
result Accurately estimates uncertainty with a small number of bootstrap centroids, outperforming i.i.d. sampling.
Multilayer bootstrap network builds a gradually narrowed multilayer nonlinear network from bottom up for unsupervised nonlinear dimensionality reduction. Each layer of the network is a nonparametric density estimator. It consists of a group of k-centroids clusterings. Each clustering randomly selects data points with r…
Modified Epanechnikov Mean Shift converges to cluster centroids.
problem Lack of theoretical support for convergence of Epanechnikov Mean Shift due to non-smooth kernel density functions.
method Proposed a simple remedy to fix convergence issues, ensuring termination at a local maximum of the estimated density.
result Modified Epanechnikov Mean Shift guarantees convergence to a cluster centroid within a finite number of iterations.
Proposes a robust clustering method using the Median-of-Means estimator.
problem Noise and outliers in data affect clustering quality and require specifying the number of clusters.
method Integrates model-based and centroid-based clustering methods using the Median-of-Means estimator.
result Mitigates noise effects and estimates the number of clusters automatically.
New meta-learning method improves domain generalization by balancing parameters closer to domain centroids.
problem Improving domain generalization by reducing overfitting to specific domains.
method Arithmetic meta-learning with arithmetic-weighted gradients to balance parameters closer to domain centroids.
result Experimental validation of improved domain generalization performance.
Paper proposes a neural network for sparse recovery using Laplace techniques.
problem Sparse recovery from compressed measurements.
method Designing a neural network to compute the centroid of a polytope.
result Analytical computation of volume and centroid enables efficient sparse recovery.
CDF uses centroids to split features for high-dimensional classification.
problem High-dimensional classification problems with complex class structures.
method CDF introduces a centroid-driven splitting strategy in decision trees.
result CDF outperforms conventional methods in high-dimensional classification.
The study characterizes quadrics among affine hyperspheres based on centroid collinearity of sections.
problem Characterizing quadrics among affine hyperspheres based on section centroid collinearity.
method Extending Meyer and Reisner's theorem to unbounded convex sets and identifying additional assumptions.
result Ellipsoids, paraboloids, and one sheet of a two-sheeted hyperboloid are the only quadrics satisfying the centroid collinearity condition.
Paper presents robust clustering methods for general mixture models.
problem Clustering with sub-Gaussian error assumptions often invalid in practice.
method Hybrid clustering with robust centroid estimate and data-driven initialization.
result Provably near-optimal mislabeling guarantees for general error distributions.
New method uses geometric properties for better density estimation.
problem Uncertainty quantification in ambiguous tasks.
method Winner-takes-all training with centroidal Voronoi tessellations.
result Improved quantization and density estimation.
A new classification method using disjoint centroids and normalized distance.
problem Improving classification accuracy and feature selection.
method Nearest disjoint centroid classifier with normalized distance.
result Our method outperforms other classifiers in terms of misclassification rates and feature usage.
Sparse nearest-centroid classifiers detect relevant features for classification.
problem Classifying data with low computational cost and feature selection.
method Proposes ℓ1 and ℓ2 sparse variants of nearest-centroid classifiers. result Training sparse classifiers can be done exactly and at quasi-linear cost.
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.
Improved image classification using centroids and stochastic sampling.
problem Limited accuracy of nearest-neighbor classification.
method Coarse-graining (replacing images by centroids) and stochastic sampling of centroids.
result Stochastic sampling of centroids improves classification accuracy.
Centroid Transformers reduce memory and computation by summarizing inputs into centroids.
problem Efficiently summarize inputs with reduced memory and computation.
method Generalizes self-attention to map N inputs to M centroids (M ≤ N), reducing complexity.
result Centroid Transformers reduce memory and computation while preserving key information.
The article examines different thresholding methods for improving PAM algorithm in cancer classification.
problem High-dimensional classification with too many features selected by PAM.
method Extends PAM with hard and order thresholding methods and a deep search algorithm.
result Improved cancer status prediction accuracy and smaller number of features.
EKM addresses imbalanced data clustering by repelling centroids in large clusters.
problem Imbalanced data leads to biased clustering of large clusters.
method EKM introduces a novel centroid repulsion mechanism based on the Boltzmann operator.
result EKM outperforms benchmark algorithms on imbalanced data.
Centroid-Encoder reduces high-dimensional data for better visualization.
problem Visualizing high-dimensional data efficiently and accurately.
method Centroid-Encoder integrates label information to keep similar objects close in reduced space.
result Centroid-Encoder outperforms other techniques in visualizing high-dimensional data.
Empty core found in max-loss non-centroid clustering.
problem Core stability in non-centroid clustering under max-loss objective.
method Proof for all k≥3 and n≥9 agents, computer-aided proof for 2D Euclidean points.
result Core can be empty in non-centroid clustering under max-loss objective.
Confirmation bias leads to biased estimates in noisy data analysis.
problem Confirmation bias affects scientific conclusions in noisy data environments.
method Investigation of confirmation bias in Gaussian mixture models using K-means and EM algorithms.
result Estimates from algorithms are biased and resemble initial hypotheses, not the noise.
Softmax and k-means clustering are mathematically linked, improving neural network robustness.
problem Improving neural network robustness against adversarial attacks.
method Formally proving the connection between softmax and k-means, proposing Centroid Based Tailoring.
result The proposed Gauss network is less susceptible to one-pixel attacks.
Due to the success of the bag-of-word modeling paradigm, clustering histograms has become an important ingredient of modern information processing. Clustering histograms can be performed using the celebrated k-means centroid-based algorithm. From the viewpoint of applications, it is usually required to deal with symm…
The paper proves a theorem linking convex body centroids and category theory.
problem Understanding centroids of sections of convex bodies.
method Lusternik-Schnirelmann category theory.
result At least n hyperplanes exist such that the center of mass of their intersection with a convex body lies on the boundary of the convex body.
Centroids Matching tackles catastrophic forgetting by matching feature vectors to class centroids.
problem Catastrophic forgetting in neural networks when learning new tasks.
method Centroids Matching operates in the embedding space of neural network features, matching these vectors to class centroids.
result Centroids Matching achieves high accuracy on all tasks without using external memory, even in realistic scenarios.
Text clustering method replaces centroids with summaries for interpretability and scalability.
problem Efficiently clustering text data while maintaining interpretability and scalability.
method k-NLPmeans and k-LLMmeans, which periodically replace numeric centroids with textual summaries.
result Consistently outperforms classical baselines and recent LLM-based clustering methods.
The paper generalizes the second Pappus-Guldin theorem for calculating volumes of bodies.
problem Calculating the volume of a body cut into perpendicular slices.
method Using a generalized formula and properties of centroids and floating bodies.
result A curve with centroid property exists for convex bodies, leading to simpler volume calculations.
Sharp Lp affine isoperimetric inequalities are established for the entire class of Lp projection bodies and the entire class of Lp centroid bodies. These new inequalities strengthen the Lp Petty projection and the Lp Busemann--Petty centroid inequality.
Many clustering algorithms exist that estimate a cluster centroid, such as K-means, K-medoids or mean-shift, but no algorithm seems to exist that clusters data by returning exactly K meaningful modes. We propose a natural definition of a K-modes objective function by combining the notions of density and cluster assignm…
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.
Optimizes K-means clustering with PSO for better accuracy.
problem Improving the accuracy of K-means clustering.
method Uses Particle Swarm Optimization (PSO) to find optimal initial centroids for K-means.
result Optimal centroids found using PSO lead to better clustering accuracy.
CCC clusters with controlled spread, outperforming standard methods.
problem Compact and structured clustering with spread control.
method Constrained Centroid Clustering using Lagrangian formulation.
result CCC achieves more compact clusters with reduced radial spread.
New method speeds up CNN inference by storing centroids instead of full filters.
problem Reduction of time and space complexity in CNN inference.
method Centroid filter quantization for convolutional layers.
result 2.9 times better computational gain on ImageNet benchmark.
We study a notion of a Lipschitz, permutation-invariant "centroid" for triples of points in mapping class groups MCG(S), which satisfies a certain polynomial growth bound. A consequence (via work of Drutu-Sapir or Chatterji-Ruane) is the Rapid Decay Property for MCG(S).
In [Centro-affine invariants for smooth convex bodies, Int. Math. Res. Notices. doi: 10.1093/imrn/rnr110, 2011] Stancu introduced a family of centro-affine normal flows, p-flow, for 1≤p<∞. Here we investigate the asymptotic behavior of the planar p-flow for p=∞ in the class of smooth, origin-symme…
Proposes an MTL method with clustering to improve regression accuracy.
problem Improving regression accuracy by sharing information among related tasks.
method Centroid parameter for clustering tasks, separating regression and clustering parameters.
result Improves estimation and prediction accuracy for regression coefficient vectors.
Method counters noisy labels by discounting distant samples.
problem Training models with noisy labels in medical and autonomous domains.
method Discounting distant samples from class centroids in latent space.
result Significant improvements in classification accuracy.
This paper introduces a novel clustering algorithm for heteroscedastic Gaussian data without needing to know the number of clusters.
problem Clustering heteroscedastic Gaussian data without prior knowledge of the number of clusters.
method Introduces a novel cost function and fixed-point analysis to estimate centroids, introduces Wald kernel for measurement plausibility, and derives CENTRE-X algorithm.
result CENTRE-X algorithm can estimate centroids without prior knowledge of the number of clusters and performs comparably to standard algorithms K-means and Mean-Shift.
New clustering method reduces data redundancy for better summaries.
problem Redundancies in data summaries limit their effectiveness in large datasets.
method Khatri-Rao clustering extends centroid-based clustering to produce more succinct summaries.
result Khatri-Rao k-Means and deep clustering frameworks produce more succinct summaries with similar accuracy.
A new algorithm is proposed which accelerates the mini-batch k-means algorithm of Sculley (2010) by using the distance bounding approach of Elkan (2003). We argue that, when incorporating distance bounds into a mini-batch algorithm, already used data should preferentially be reused. To this end we propose using nested …
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.
We introduce a new volume definition on normed vector spaces. We show that the induced k-area functionals are convex for all k. In the particular case k=2, our theorem implies that Busemann's 2-volume density is convex, which was recently shown by Burago-Ivanov. We also show how the new volume definition is relat…
A semi-supervised learning method using predefined class centroids for image classification.
problem Reducing the need for labeled data in deep learning.
method Use a small number of labeled samples and data augmentation on unlabeled samples. Constrain all samples to predefined evenly-distributed class centroids (PEDCC) using loss functions.
result Achieves state-of-the-art results with minimal labeled data.
Proportional centroid clustering aims to fairly group points without prior protected subsets.
problem Fairly group points without prior protected subsets.
method Define fairness as proportionality, present algorithms for efficient computation and optimization.
result Proportional solutions trade off with the k-means objective.
This study evaluates cluster search algorithms using Gaussian mixture models.
problem Determining the optimal number of clusters in data sets generated by Gaussian mixture models.
method Examined centroid- and model-based cluster search algorithms in various cases.
result Model-based algorithms are more robust to cluster overlap and covariance type than centroid-based methods.
Novel method classifies HIV patients based on viral load patterns.
problem Limited methods classify patients by viral load patterns, often specific to study design.
method Four features, centroid-based classification algorithm, radial normalization classification.
result Classifies 1,576 HIV positive clinic patients into five viral load patterns.
The paper explores centroids and static equilibrium points in non-Euclidean geometries.
problem Investigating centroids and static equilibrium points in spherical, hyperbolic, and normed spaces.
method Extending Gal'perin's work, the paper examines convex bodies in these spaces and analyzes the minimum number of equilibrium points.
result Every plane convex body in any of these spaces has at least four equilibrium points, and there are mono-monostatic convex bodies in 3D spherical, hyperbolic, and certain normed spaces.