Related papers: Multi Layer Peeling for Linear Arrangement and Hie…

In the paper a piecewise constant image approximations of sequential number of pixel clusters or segments are treated. A majorizing of optimal approximation sequence by hierarchical sequence of image approximations is studied. Transition…

Clustering aims to group unlabelled samples based on their similarities. It has become a significant tool for the analysis of high-dimensional data. However, most of the clustering methods merely generate pseudo labels and thus are unable…

Co-clustering simultaneously clusters rows and columns, revealing more fine-grained groups. However, existing co-clustering methods suffer from poor scalability and cannot handle large-scale data. This paper presents a novel and scalable…

Multi-manifold modeling is increasingly used in segmentation and data representation tasks in computer vision and related fields. While the general problem, modeling data by mixtures of manifolds, is very challenging, several approaches…

Matrices are two-dimensional data structures allowing one to conceptually organize information. For example, adjacency matrices are useful to store the links of a network; correlation matrices are simple ways to arrange gene co-expression…

In subspace clustering, a group of data points belonging to a union of subspaces are assigned membership to their respective subspaces. This paper presents a new approach dubbed Innovation Pursuit (iPursuit) to the problem of subspace…

The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…

Superpixel segmentation can be used as an intermediary step in many applications, often to improve object delineation and reduce computer workload. However, classical methods do not incorporate information about the desired object.…

Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. "Structure" can be understood as symmetry and a range of symmetries are expressed by hierarchy. Such symmetries directly…

This paper proposes a Mixed-Integer Linear Programming approach for the Soft Graph Clustering Problem. This is the first method that simultaneously allocates membership proportion for vertices that lie in multiple clusters, and that…

Clustering high-dimensional datasets is hard because interpoint distances become less informative in high-dimensional spaces. We present a clustering algorithm that performs nonlinear dimensionality reduction and clustering jointly. The…

Large-scale multi-layer networks with large numbers of nodes, edges, and layers arise across various domains, which poses a great computational challenge for the downstream analysis. In this paper, we develop an efficient randomized…

In this paper, we first propose a new iterative algorithm, called the K-sets+ algorithm for clustering data points in a semi-metric space, where the distance measure does not necessarily satisfy the triangular inequality. We show that the…

Comparing and aligning large datasets is a pervasive problem occurring across many different knowledge domains. We introduce and study MREC, a recursive decomposition algorithm for computing matchings between data sets. The basic idea is to…

Recently, Hierarchical Clustering (HC) has been considered through the lens of optimization. In particular, two maximization objectives have been defined. Moseley and Wang defined the \emph{Revenue} objective to handle similarity…

Clustering is often used for discovering structure in data. Clustering systems differ in the objective function used to evaluate clustering quality and the control strategy used to search the space of clusterings. Ideally, the search…

In spectral clustering, one defines a similarity matrix for a collection of data points, transforms the matrix to get the Laplacian matrix, finds the eigenvectors of the Laplacian matrix, and obtains a partition of the data using the…

Hierarchical Clustering (HC) is a widely studied problem in exploratory data analysis, usually tackled by simple agglomerative procedures like average-linkage, single-linkage or complete-linkage. In this paper we focus on two objectives,…

We examine the efficiency of clustering a set of points, when the encompassing metric space may be preprocessed in advance. In computational problems of this genre, there is a first stage of preprocessing, whose input is a collection of…

Spectral clustering is one of the most prominent clustering approaches. The distance-based similarity is the most widely used method for spectral clustering. However, people have already noticed that this is not suitable for multi-scale…