相关论文: Kernel k-Means, By All Means: Algorithms and Stron…

Quantum kernel methods promise enhanced expressivity for learning structured data, but their usefulness has been limited by kernel concentration and barren plateaus. Both effects are mathematically equivalent and suppress trainability. We…

K-means clustering is a workhorse of unsupervised learning, but it is notoriously brittle to outliers, distribution shifts, and limited sample sizes. Viewing k-means as Lloyd--Max quantization of the empirical distribution, we develop a…

We study feature selection for $k$-means clustering. Although the literature contains many methods with good empirical performance, algorithms with provable theoretical behavior have only recently been developed. Unfortunately, these…

This paper introduces a novel K-means clustering algorithm, an advancement on the conventional Big-means methodology. The proposed method efficiently integrates parallel processing, stochastic sampling, and competitive optimization to…

Multiple kernel methods less consider the intrinsic manifold structure of multiple kernel data and estimate the consensus kernel matrix with quadratic number of variables, which makes it vulnerable to the noise and outliers within multiple…

Kernel segmentation aims at partitioning a data sequence into several non-overlapping segments that may have nonlinear and complex structures. In general, it is formulated as a discrete optimization problem with combinatorial constraints. A…

K-Means clustering still plays an important role in many computer vision problems. While the conventional Lloyd method, which alternates between centroid update and cluster assignment, is primarily used in practice, it may converge to a…

The kernel least-mean-square (KLMS) algorithm is an appealing tool for online identification of nonlinear systems due to its simplicity and robustness. In addition to choosing a reproducing kernel and setting filter parameters, designing a…

Recent advances in operator learning theory have improved our knowledge about learning maps between infinite dimensional spaces. However, for large-scale engineering problems such as concurrent multiscale simulation for mechanical…

Many similarity-based clustering methods work in two separate steps including similarity matrix computation and subsequent spectral clustering. However, similarity measurement is challenging because it is usually impacted by many factors,…

In order to fully utilize "big data", it is often required to use "big models". Such models tend to grow with the complexity and size of the training data, and do not make strong parametric assumptions upfront on the nature of the…

K-means is a popular clustering algorithm with significant applications in numerous scientific and engineering areas. One drawback of K-means is its inability to identify non-linearly separable clusters, which may lead to inaccurate…

In this paper, the decades-old clustering method k-means is revisited. The original distortion minimization model of k-means is addressed by a pure stochastic minimization procedure. In each step of the iteration, one sample is tentatively…

Clustering is a cornerstone of data analysis that is particularly suited to identifying coherent subgroups or substructures in unlabeled data, as are generated continuously in large amounts these days. However, in many cases traditional…

Data mining focuses on discovering interesting, non-trivial and meaningful information from large datasets. Data clustering is one of the unsupervised and descriptive data mining task which group data based on similarity features and…

Traditional k-means clustering underperforms on non-convex shapes and requires the number of clusters k to be specified in advance. We propose a simple geometric enhancement: after standard k-means, each cluster center is assigned a radius…

Clustering is a usual unsupervised machine learning technique for grouping the data points into groups based upon similar features. We focus here on unsupervised clustering for contaminated data, i.e in the case where K-medians should be…

$k$-means++ \cite{arthur2007k} is a widely used clustering algorithm that is easy to implement, has nice theoretical guarantees and strong empirical performance. Despite its wide adoption, $k$-means++ sometimes suffers from being slow on…

We present an approach to clustering time series data using a model-based generalization of the K-Means algorithm which we call K-Models. We prove the convergence of this general algorithm and relate it to the hard-EM algorithm for mixture…

Being robust to the presence of outliers is crucial for applying clustering algorithms in practice. In the $\textit{robust $k$-Means}$ problem (i.e., $k$-Means with outliers), the goal is to remove $z$ outliers and minimize the $k$-Means…