arXiv research

Proposes MvLPE for better multi-view representation learning.

During the last decades, we have witnessed a surge of interests of learning a low-dimensional space with discriminative information from one single view. Even though most of them can achieve satisfactory performance in some certain situations, they fail to fully consider the information from multiple views which are hi…

CDF uses centroids to split features for high-dimensional classification.

The study characterizes quadrics among affine hyperspheres based on centroid collinearity of sections.

A new classification method using disjoint centroids and normalized distance.

Ball k-means reduces point-centroid distance computations for faster k-means clustering.

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…

During the last decades, learning a low-dimensional space with discriminative information for dimension reduction (DR) has gained a surge of interest. However, it's not accessible for these DR methods to achieve satisfactory performance when facing the features from multiple views. In multi-view learning problems, one …

Centroid Transformers reduce memory and computation by summarizing inputs into centroids.

EKM addresses imbalanced data clustering by repelling centroids in large clusters.

Empty core found in max-loss non-centroid clustering.

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.

Centroids Matching tackles catastrophic forgetting by matching feature vectors to class centroids.

Optimizes a small set of centroid points to approximate bootstrap distribution.

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.

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…

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…

The paper generalizes the second Pappus-Guldin theorem for calculating volumes of bodies.

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…

CCC clusters with controlled spread, outperforming standard methods.

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).

Visualizing high-dimensional data is an essential task in Data Science and Machine Learning. The Centroid-Encoder (CE) method is similar to the autoencoder but incorporates label information to keep objects of a class close together in the reduced visualization space. CE exploits nonlinearity and labels to encode high …

Method counters noisy labels by discounting distant samples.

New meta-learning method improves domain generalization by balancing parameters closer to domain centroids.

New clustering method reduces data redundancy for better summaries.

SIVF k-means algorithm speeds up sparse data clustering.

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…

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 study evaluates cluster search algorithms using Gaussian mixture models.

Paper presents robust clustering methods for general mixture models.

The paper explores centroids and static equilibrium points in non-Euclidean geometries.

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…

A new method clusters complex networks using topological and geometric structure.

Proposes a robust clustering method using the Median-of-Means estimator.

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.

HD-BWDM improves clustering validation in high-dimensional data.

CoHiRF extends clustering methods to handle high-dimensional data efficiently.

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 article examines different thresholding methods for improving PAM algorithm in cancer classification.

New method improves fairness of facial recognition systems.

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…

The paper proposes a method to assess when automated predictions are reliable.