Related papers: Quantized Compressive K-Means
In sensor networks, it is not always practical to set up a fusion center. Therefore, there is need for fully decentralized clustering algorithms. Decentralized clustering algorithms should minimize the amount of data exchanged between…
We study how to learn multiple dictionaries from a dataset, and approximate any data point by the sum of the codewords each chosen from the corresponding dictionary. Although theoretically low approximation errors can be achieved by the…
Training of a Machine Learning model requires sufficient data. The sufficiency of the data is not always about the quantity, but about the relevancy and reduced redundancy. Data-generating processes create massive amounts of data. When used…
This paper presents an algorithm to solve the Soft k-Means problem globally. Unlike Fuzzy c-Means, Soft k-Means (SkM) has a matrix factorization-type objective and has been shown to have a close relation with the popular probability…
We study federated clustering, where interconnected devices collaboratively cluster the data points of private local datasets. Focusing on hard clustering via the k-means principle, we formulate federated k-means as an instance of…
In this paper we show that the computational complexity of the Iterative Thresholding and K-residual-Means (ITKrM) algorithm for dictionary learning can be significantly reduced by using dimensionality-reduction techniques based on the…
We provide the first analysis of a non-trivial quantization scheme for compressed sensing measurements arising from structured measurements. Specifically, our analysis studies compressed sensing matrices consisting of rows selected at…
Large-sample data became prevalent as data acquisition became cheaper and easier. While a large sample size has theoretical advantages for many statistical methods, it presents computational challenges. Sketching, or compression, is a…
We investigate the efficiency of k-means in terms of both statistical and computational requirements. More precisely, we study a Nystr\"om approach to kernel k-means. We analyze the statistical properties of the proposed method and show…
In compressive learning, a mixture model (a set of centroids or a Gaussian mixture) is learned from a sketch vector, that serves as a highly compressed representation of the dataset. This requires solving a non-convex optimization problem,…
As datasets continue to grow in size and complexity, finding succinct yet accurate data summaries poses a key challenge. Centroid-based clustering, a widely adopted approach to address this challenge, finds informative summaries of datasets…
We introduce a sketch-and-solve approach to speed up the Peng-Wei semidefinite relaxation of k-means clustering. When the data is appropriately separated we identify the k-means optimal clustering. Otherwise, our approach provides a…
$k$-Clustering in $\mathbb{R}^d$ (e.g., $k$-median and $k$-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality $n$, it remains…
Hidden Markov models (HMM) are commonly used in generation tasks and have demonstrated strong capabilities in neuro-symbolic applications for the Markov property. These applications leverage the strengths of neural networks and symbolic…
Convex clustering is a modern method with both hierarchical and $k$-means clustering characteristics. Although convex clustering can capture complex clustering structures hidden in data, the existing convex clustering algorithms are not…
The paper is focused on the forecasting method for time series groups with the use of algorithms for cluster analysis. $K$-means algorithm is suggested to be a basic one for clustering. The coordinates of the centers of clusters have been…
We give a quantum approximation scheme (i.e., $(1 + \varepsilon)$-approximation for every $\varepsilon > 0$) for the classical $k$-means clustering problem in the QRAM model with a running time that has only polylogarithmic dependence on…
Fuzzy K-Means clustering is a critical technique in unsupervised data analysis. Unlike traditional hard clustering algorithms such as K-Means, it allows data points to belong to multiple clusters with varying degrees of membership,…
This paper presents an accelerated spherical K-means clustering algorithm for large-scale and high-dimensional sparse document data sets. We design an algorithm working in an architecture-friendly manner (AFM), which is a procedure of…
The immense amount of daily generated and communicated data presents unique challenges in their processing. Clustering, the grouping of data without the presence of ground-truth labels, is an important tool for drawing inferences from data.…