Related papers: Subspace Clustering by Block Diagonal Representati…

Subspace clustering refers to the problem of clustering high-dimensional data points into a union of low-dimensional linear subspaces, where the number of subspaces, their dimensions and orientations are all unknown. In this paper, we…

Spectral clustering is one of the most popular clustering methods. However, the high computational cost due to the involved eigen-decomposition procedure can immediately hinder its applications in large-scale tasks. In this paper we use…

Recent years have witnessed a growing academic interest in multi-view subspace clustering. In this paper, we propose a novel Double Graphs Regularized Multi-view Subspace Clustering (DGRMSC) method, which aims to harness both global and…

Subspace clustering refers to the problem of segmenting data drawn from a union of subspaces. State-of-the-art approaches for solving this problem follow a two-stage approach. In the first step, an affinity matrix is learned from the data…

The problem of diagonalizing a class of complicated matrices, to be called ultrametric matrices, is investigated. These matrices appear at various stages in the description of disordered systems with many equilibrium phases by the technique…

Block diagonalization (BD) is a practical linear precoding technique that eliminates the inter-user interference in downlink multiuser multiple-input multiple-output (MIMO) systems. In this paper, we apply BD to the downlink transmission in…

We consider the multidimensional space-fractional diffusion equations with spatially varying diffusivity and fractional order. Significant computational challenges are encountered when solving these equations due both to the kernel…

Modern inference and learning often hinge on identifying low-dimensional structures that approximate large scale data. Subspace clustering achieves this through a union of linear subspaces. However, in contemporary applications data is…

Clustering methods with dimension reduction have been receiving considerable wide interest in statistics lately and a lot of methods to simultaneously perform clustering and dimension reduction have been proposed. This work presents a novel…

Spectral clustering is a fundamental technique in the field of data mining and information processing. Most existing spectral clustering algorithms integrate dimensionality reduction into the clustering process assisted by manifold learning…

The problem of fitting a union of subspaces to a collection of data points drawn from multiple subspaces is considered in this paper. In the traditional low rank representation model, the dictionary used to represent the data points is…

Spectral clustering and its extensions usually consist of two steps: (1) constructing a graph and computing the relaxed solution; (2) discretizing relaxed solutions. Although the former has been extensively investigated, the discretization…

The clustering methods have recently absorbed even-increasing attention in learning and vision. Deep clustering combines embedding and clustering together to obtain optimal embedding subspace for clustering, which can be more effective…

Discovering and clustering subspaces in high-dimensional data is a fundamental problem of machine learning with a wide range of applications in data mining, computer vision, and pattern recognition. Earlier methods divided the problem into…

Most learning approaches treat dimensionality reduction (DR) and clustering separately (i.e., sequentially), but recent research has shown that optimizing the two tasks jointly can substantially improve the performance of both. The premise…

Clustering, as an unsupervised technique, plays a pivotal role in various data analysis applications. Among clustering algorithms, Spectral Clustering on Euclidean Spaces has been extensively studied. However, with the rapid evolution of…

Tensor clustering has become an important topic, specifically in spatio-temporal modeling, due to its ability to cluster spatial modes (e.g., stations or road segments) and temporal modes (e.g., time of the day or day of the week). Our…

State-of-the-art algorithms for sparse subspace clustering perform spectral clustering on a similarity matrix typically obtained by representing each data point as a sparse combination of other points using either basis pursuit (BP) or…

Superpixel segmentation aims at dividing the input image into some representative regions containing pixels with similar and consistent intrinsic properties, without any prior knowledge about the shape and size of each superpixel. In this…

Matrix rank minimizing subject to affine constraints arises in many application areas, ranging from signal processing to machine learning. Nuclear norm is a convex relaxation for this problem which can recover the rank exactly under some…