Related papers: Coresets for Clustering Under Stochastic Noise
$(j,k)$-projective clustering is the natural generalization of the family of $k$-clustering and $j$-subspace clustering problems. Given a set of points $P$ in $\mathbb{R}^d$, the goal is to find $k$ flats of dimension $j$, i.e., affine…
Due to rapid advancements in technology, datasets are available from various domains. In order to carry out more relevant and appropriate analysis, it is often necessary to project the dataset into a higher or lower dimensional space based…
The clustering of a data set is one of the core tasks in data analytics. Many clustering algorithms exhibit a strong contrast between a favorable performance in practice and bad theoretical worst-cases. Prime examples are least-squares…
Comparison of three kind of the clustering and find cost function and loss function and calculate them. Error rate of the clustering methods and how to calculate the error percentage always be one on the important factor for evaluating the…
The coresets approach, also called subsampling or subset selection, aims to select a subsample as a surrogate for the observed sample and has found extensive applications in large-scale data analysis. Existing coresets methods construct the…
Performance of clustering algorithms is evaluated with the help of accuracy metrics. There is a great diversity of clustering algorithms, which are key components of many data analysis and exploration systems. However, there exist only few…
Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…
This paper considers $k$-means clustering in the presence of noise. It is known that $k$-means clustering is highly sensitive to noise, and thus noise should be removed to obtain a quality solution. A popular formulation of this problem is…
Accurate modeling of noise in realistic quantum processors is critical for constructing fault-tolerant quantum computers. While a full simulation of actual noisy quantum circuits provides information about correlated noise among all qubits…
We develop new algorithmic methods with provable guarantees for feature selection in regard to categorical data clustering. While feature selection is one of the most common approaches to reduce dimensionality in practice, most of the known…
Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…
In many machine learning tasks, a common approach for dealing with large-scale data is to build a small summary, {\em e.g.,} coreset, that can efficiently represent the original input. However, real-world datasets usually contain outliers…
The fuzzy $K$-means problem is a popular generalization of the well-known $K$-means problem to soft clusterings. We present the first coresets for fuzzy $K$-means with size linear in the dimension, polynomial in the number of clusters, and…
We present methods for k-means clustering on a stream with a focus on providing fast responses to clustering queries. Compared to the current state-of-the-art, our methods provide substantial improvement in the query time for cluster…
Model compression is crucial for deployment of neural networks on devices with limited computational and memory resources. Many different methods show comparable accuracy of the compressed model and similar compression rates. However, the…
This paper considers coresets for the robust $k$-medians problem with $m$ outliers, and new constructions in various metric spaces are obtained. Specifically, for metric spaces with a bounded VC or doubling dimension $d$, the coreset size…
We introduce the aggregated clustering problem, where one is given $T$ instances of a center-based clustering task over the same $n$ points, but under different metrics. The goal is to open $k$ centers to minimize an aggregate of the…
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…
In this paper, we test whether two datasets share a common clustering structure. As a leading example, we focus on comparing clustering structures in two independent random samples from two mixtures of multivariate normal distributions.…
In this paper, we initiate a rigorous theoretical study of clustering with noisy queries (or a faulty oracle). Given a set of $n$ elements, our goal is to recover the true clustering by asking minimum number of pairwise queries to an…