Related papers: A Robust Spectral Clustering Algorithm for Sub-Gau…

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…

This paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower-dimensional planes. As is common in computer vision or unsupervised learning applications, we do not know in advance…

One of the fundamental problems in network analysis is detecting community structure in multi-layer networks, of which each layer represents one type of edge information among the nodes. We propose integrative spectral clustering approaches…

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…

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…

This paper presents a batch-wise density-based clustering approach for local outlier detection in massive-scale datasets. Unlike the well-known traditional algorithms, which assume that all the data is memory-resident, our proposed method…

We introduce and study the $k$-center clustering problem with set outliers, a natural and practical generalization of the classical $k$-center clustering with outliers. Instead of removing individual data points, our model allows discarding…

In many situations where the interest lies in identifying clusters one might expect that not all available variables carry information about these groups. Furthermore, data quality (e.g. outliers or missing entries) might present a serious…

Clustering with outliers is one of the most fundamental problems in Computer Science. Given a set $X$ of $n$ points and two integers $k$ and $m$, the clustering with outliers aims to exclude $m$ points from $X$ and partition the remaining…

Clustering large, mixed data is a central problem in data mining. Many approaches adopt the idea of k-means, and hence are sensitive to initialisation, detect only spherical clusters, and require a priori the unknown number of clusters. We…

Under the framework of spectral clustering, the key of subspace clustering is building a similarity graph which describes the neighborhood relations among data points. Some recent works build the graph using sparse, low-rank, and…

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…

In this paper, we study the problem of {\em $k$-center clustering with outliers}. The problem has many important applications in real world, but the presence of outliers can significantly increase the computational complexity. Though a…

Outlier detection and cluster number estimation is an important issue for clustering real data. This paper focuses on spectral clustering, a time-tested clustering method, and reveals its important properties related to outliers. The…

Spectral clustering has found extensive use in many areas. Most traditional spectral clustering algorithms work in three separate steps: similarity graph construction; continuous labels learning; discretizing the learned labels by k-means…

Spectral clustering is one of the most popular algorithms to group high dimensional data. It is easy to implement and computationally efficient. Despite its popularity and successful applications, its theoretical properties have not been…

Individual fairness guarantees are often desirable properties to have, but they become hard to formalize when the dataset contains outliers. Here, we investigate the problem of developing an individually fair $k$-means clustering algorithm…

Cluster analysis and outlier detection are strongly coupled tasks in data mining area. Cluster structure can be easily destroyed by few outliers; on the contrary, outliers are defined by the concept of cluster, which are recognized as the…

Clustering analysis is one of the critical tasks in machine learning. Traditionally, clustering has been an independent task, separate from outlier detection. Due to the fact that the performance of clustering can be significantly eroded by…

Clustering has many important applications in computer science, but real-world datasets often contain outliers. Moreover, the presence of outliers can make the clustering problems to be much more challenging. To reduce the complexities,…