相关论文: Adapting $k$-means algorithms for outliers

Center-based clustering is a fundamental primitive for data analysis and becomes very challenging for large datasets. In this paper, we focus on the popular $k$-center variant which, given a set $S$ of points from some metric space and a…

We initiate the study of metric embeddings with \emph{outliers}. Given some metric space $(X,\rho)$ we wish to find a small set of outlier points $K \subset X$ and either an isometric or a low-distortion embedding of $(X\setminus K,\rho)$…

Recently, due to an increasing interest for transparency in artificial intelligence, several methods of explainable machine learning have been developed with the simultaneous goal of accuracy and interpretability by humans. In this paper,…

We present a simple analysis of k-means|| (Bahmani et al., PVLDB 2012) -- a distributed variant of the k-means++ algorithm (Arthur and Vassilvitskii, SODA 2007). Moreover, the bound on the number of rounds is improved from $O(\log n)$ to…

The subspace approximation problem with outliers, for given $n$ points in $d$ dimensions $x_{1},\ldots, x_{n} \in R^{d}$, an integer $1 \leq k \leq d$, and an outlier parameter $0 \leq \alpha \leq 1$, is to find a $k$-dimensional linear…

Many real-world problems can be formulated as geometric optimization problems in high dimensions, especially in the fields of machine learning and data mining. Moreover, we often need to take into account of outliers when optimizing the…

Outliers are the points which are different from or inconsistent with the rest of the data. They can be novel, new, abnormal, unusual or noisy information. Outliers are sometimes more interesting than the majority of the data. The main…

We design a new algorithm for the Euclidean $k$-means problem that operates in the local model of differential privacy. Unlike in the non-private literature, differentially private algorithms for the $k$-means objective incur both additive…

The $k$-means algorithm (Lloyd's algorithm) is a widely used method for clustering unlabeled data. A key bottleneck of the $k$-means algorithm is that each iteration requires time linear in the number of data points, which can be expensive…

Classical clustering problems such as \emph{Facility Location} and \emph{$k$-Median} aim to efficiently serve a set of clients from a subset of facilities -- minimizing the total cost of facility openings and client assignments in Facility…

The development of effective knowledge discovery techniques has become in the recent few years a very active research area due to the important impact it has in several relevant application areas. One interesting task thereof is that of…

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…

This paper presents fast, distributed, $O(1)$-approximation algorithms for metric facility location problems with outliers in the Congested Clique model, Massively Parallel Computation (MPC) model, and in the $k$-machine model. The paper…

Notwithstanding the popularity of conventional clustering algorithms such as K-means and probabilistic clustering, their clustering results are sensitive to the presence of outliers in the data. Even a few outliers can compromise the…

The $k$-means problem is a classic objective for modeling clustering in a metric space. Given a set of points in a metric space, the goal is to find $k$ representative points so as to minimize the sum of the squared distances from each…

Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…

We consider the Euclidean $k$-means clustering problem in a dynamic setting, where we have to explicitly maintain a solution (a set of $k$ centers) $S \subseteq \mathbb{R}^d$ subject to point insertions/deletions in $\mathbb{R}^d$. We…

We revisit the problem of estimating the mean of a high-dimensional distribution in the presence of an $\varepsilon$-fraction of adversarial outliers. When $\varepsilon$ is at most some sufficiently small constant, previous works can…

Over half a century old and showing no signs of aging, k-means remains one of the most popular data processing algorithms. As is well-known, a proper initialization of k-means is crucial for obtaining a good final solution. The recently…

In this paper we initiate a systematic study of exact algorithms for well-known clustering problems, namely $k$-Median and $k$-Means. In $k$-Median, the input consists of a set $X$ of $n$ points belonging to a metric space, and the task is…