相关论文: Outlier-Robust Clustering of Non-Spherical Mixture…

We investigate a clustering problem with data from a mixture of Gaussians that share a common but unknown, and potentially ill-conditioned, covariance matrix. We start by considering Gaussian mixtures with two equally-sized components and…

Though very popular, it is well known that the EM for GMM algorithm suffers from non-Gaussian distribution shapes, outliers and high-dimensionality. In this paper, we design a new robust clustering algorithm that can efficiently deal with…

Learning a Gaussian mixture model (GMM) is a fundamental problem in machine learning, learning theory, and statistics. One notion of learning a GMM is proper learning: here, the goal is to find a mixture of $k$ Gaussians $\mathcal{M}$ that…

Clustering problems (such as $k$-means and $k$-median) are fundamental unsupervised machine learning primitives, and streaming clustering algorithms have been extensively studied in the past. However, since data privacy becomes a central…

We study the problem of list-decodable mean estimation, where an adversary can corrupt a majority of the dataset. Specifically, we are given a set $T$ of $n$ points in $\mathbb{R}^d$ and a parameter $0< \alpha <\frac 1 2$ such that an…

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…

Outlier detection in data streams has gained wide importance presently due to the increasing cases of fraud in various applications of data streams. The techniques for outlier detection have been divided into either statistics based,…

The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples…

Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data…

There has been much progress on efficient algorithms for clustering data points generated by a mixture of $k$ probability distributions under the assumption that the means of the distributions are well-separated, i.e., the distance between…

We give a new algorithm for learning mixtures of $k$ Gaussians (with identity covariance in $\mathbb{R}^n$) to TV error $\varepsilon$, with quasi-polynomial ($O(n^{\text{poly\,log}\left(\frac{n+k}{\varepsilon}\right)})$) time and sample…

Metric $k$-center clustering is a fundamental unsupervised learning primitive. Although widely used, this primitive is heavily affected by noise in the data, so that a more sensible variant seeks for the best solution that disregards a…

We develop novel clustering algorithms for functional data when the number of clusters $K$ is unknown and also when it is prefixed. These algorithms are developed based on the Maximum Mean Discrepancy (MMD) measure between two sets of…

Centroid based clustering methods such as k-means, k-medoids and k-centers are heavily applied as a go-to tool in exploratory data analysis. In many cases, those methods are used to obtain representative centroids of the data manifold for…

In this work, we give a ${\rm poly}(d,k)$ time and sample algorithm for efficiently learning the parameters of a mixture of $k$ spherical distributions in $d$ dimensions. Unlike all previous methods, our techniques apply to heavy-tailed…

We give a polynomial-time algorithm for the problem of robustly estimating a mixture of $k$ arbitrary Gaussians in $\mathbb{R}^d$, for any fixed $k$, in the presence of a constant fraction of arbitrary corruptions. This resolves the main…

We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…

Statistical and machine-learning algorithms are frequently applied to high-dimensional data. In many of these applications data is scarce, and often much more costly than computation time. We provide the first sample-efficient…

We consider the problem of clustering with $K$-means and Gaussian mixture models with a constraint on the separation between the centers in the context of real-valued data. We first propose a dynamic programming approach to solving the…

We address general-shaped clustering problems under very weak parametric assumptions with a two-step hybrid robust clustering algorithm based on trimmed k-means and hierarchical agglomeration. The algorithm has low computational complexity…