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.
The nearest-centroid classifier is a simple linear-time classifier based on computing the centroids of the data classes in the training phase, and then assigning a new datum to the class corresponding to its nearest centroid. Thanks to its very low computational cost, the nearest-centroid classifier is still widely use…
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.
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.
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…
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.
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.
HIV RNA viral load (VL) is an important outcome variable in studies of HIV infected persons. There exists only a handful of methods which classify patients by viral load patterns. Most methods place limits on the use of viral load measurements, are often specific to a particular study design, and do not account for com…
This paper introduces Laplace techniques for designing a neural network, with the goal of estimating simplex-constraint sparse vectors from compressed measurements. To this end, we recast the problem of MMSE estimation (w.r.t. a pre-defined uniform input distribution) as the problem of computing the centroid of some po…
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.
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.
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.
A new geometric method for clustering SPD data improves upon Euclidean and Riemannian approaches.
problem Skewed interpretations of SPD data in Euclidean analysis and computational inefficiency of Riemannian methods.
method Proposes a geometric method based on the Thompson metric for unsupervised clustering of SPD data.
result Demonstrates improved clustering results using inductive midrange centroid computation.
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.
We define a new method to estimate centroid for text classification based on the symmetric KL-divergence between the distribution of words in training documents and their class centroids. Experiments on several standard data sets indicate that the new method achieves substantial improvements over the traditional classi…
It is well known that multiplication operations in convolutional layers of common CNNs consume a lot of time during inference stage. In this article we present a flexible method to decrease both computational complexity of convolutional layers in inference as well as amount of space to store them. The method is based o…
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.
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.
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.
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.
This paper proposes the use of an optimization algorithm, namely PSO to decide the initial centroids in K-means, to eventually get better accuracy. The vectorized notation of the optimal centroids can be thought of as entities in an optimization space, where the accuracy of K-means over a random subset of the data coul…
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.
We formally prove the connection between k-means clustering and the predictions of neural networks based on the softmax activation layer. In existing work, this connection has been analyzed empirically, but it has never before been mathematically derived. The softmax function partitions the transformed input space into…
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.
A conceptually simple way to classify images is to directly compare test-set data and training-set data. The accuracy of this approach is limited by the method of comparison used, and by the extent to which the training-set data cover configuration space. Here we show that this coverage can be substantially increased u…
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…
A simpler edge-based discretization method without dual volumes.
problem Efficiently computing edge-based discretization vectors without forming dual volumes.
method Directly compute edge-midpoint vectors and reduce dual volume formation.
result Significant reduction in computing time for tetrahedral grids.
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.
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.
New method improves fairness of facial recognition systems.
problem Facial recognition systems exhibit bias across different demographic groups.
method Optimizes centroid-based scores to reduce bias in pre-trained models.
result Demonstrates significant improvement in fairness with minimal loss in accuracy.
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).
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.
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.
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.
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…
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.
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.
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…
Computational approaches to transcription factor binding site identification have been actively researched for the past decade. Negative examples have long been utilized in de novo motif discovery and have been shown useful in transcription factor binding site search as well. However, understanding of the roles of nega…
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.
Pedal curves derived from ellipses are invariant in area.
problem Finding invariant areas of pedal curves derived from ellipses.
method Analytical proof and explicit area expressions.
result Pedal curves derived from ellipses are invariant in area.
Archimedes showed that the area between a parabola and any chord AB on the parabola is four thirds of the area of triangle ΔABP, where P is the point on the parabola at which the tangent is parallel to the chord AB. Recently, this property of parabolas was proved to be a characteristic property of parabolas. With…
Optimal inequality on sphere for convex bodies.
problem Bounding the spherical measure of a convex body's intersection with a plane orthogonal to its centroid.
method Proving an inequality on the sphere using convex geometry.
result The inequality is optimal with a constant of \((1-1/n)^{n-1}\).
HD-BWDM improves clustering validation in high-dimensional data.
problem Determining the right number of clusters in high-dimensional data.
method HD-BWDM integrates random projection, PCA, trimmed clustering, and medoid-based distances.
result HD-BWDM remains stable and interpretable under high-dimensional projections and contamination.
Centroid-based methods including k-means and fuzzy c-means are known as effective and easy-to-implement approaches to clustering purposes in many applications. However, these algorithms cannot be directly applied to supervised tasks. This paper thus presents a generative model extending the centroid-based clustering ap…
A fast algorithm for K-means clustering using subsampled SDP.
problem Efficiently solving large-scale K-means clustering problems. method Sketch-and-Lift (SL) approach for approximating SDP relaxed K-means. result SL method achieves similar exact recovery threshold as full SDP on full dataset.