Related papers: Spectral Clustering using Eigenspectrum Shape Base…
The topological patterns exhibited by many real-world networks motivate the development of topology-based methods for assessing the similarity of networks. However, extracting topological structure is difficult, especially for large and…
We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity…
Based on a Gaussian mixture type model , we derive an eigen selection procedure that improves the usual spectral clustering in high-dimensional settings. Concretely, we derive the asymptotic expansion of the spiked eigenvalues under…
Spectral clustering is one of the most popular methods for community detection in graphs. A key step in spectral clustering algorithms is the eigen decomposition of the $n{\times}n$ graph Laplacian matrix to extract its $k$ leading…
We study a relaxed version of the column-sampling problem for the Nystr\"om approximation of kernel matrices, where approximations are defined from multisets of landmark points in the ambient space; such multisets are referred to as…
Spectral clustering is one of the most popular unsupervised machine learning methods. Constructing similarity matrix is crucial to this type of method. In most existing works, the similarity matrix is computed once for all or is updated…
We study the problem of applying spectral clustering to cluster multi-scale data, which is data whose clusters are of various sizes and densities. Traditional spectral clustering techniques discover clusters by processing a similarity…
The discrete distribution is often used to describe complex instances in machine learning, such as images, sequences, and documents. Traditionally, clustering of discrete distributions (D2C) has been approached using Wasserstein barycenter…
A least squares semi-supervised local clustering algorithm based on the idea of compressed sensing is proposed to extract clusters from a graph with known adjacency matrix. The algorithm is based on a two-stage approach similar to the one…
Clustering is a fundamental task in data mining and machine learning, particularly for analyzing large-scale data. In this paper, we introduce Clust-Splitter, an efficient algorithm based on nonsmooth optimization, designed to solve the…
In this paper we propose a unified framework to simultaneously discover the number of clusters and group the data points into them using subspace clustering. Real data distributed in a high-dimensional space can be disentangled into a union…
In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the low-dimensional structure often prevalent in high-dimensional data. Here we provide an introduction to spectral…
High-throughput spectrometers are capable of producing data sets containing thousands of spectra for a single biological sample. These data sets contain a substantial amount of redundancy from peptides that may get selected multiple times…
We introduce a novel criterion in clustering that seeks clusters with limited range of values associated with each cluster's elements. In clustering or classification the objective is to partition a set of objects into subsets, called…
In this paper, we propose a unified framework for sampling, clustering and embedding data points in semi-metric spaces. For a set of data points $\Omega=\{x_1, x_2, \ldots, x_n\}$ in a semi-metric space, we consider a complete graph with…
Spectral-based subspace clustering methods have proved successful in many challenging applications such as gene sequencing, image recognition, and motion segmentation. In this work, we first propose a novel spectral-based subspace…
One of the main challenges for hierarchical clustering is how to appropriately identify the representative points in the lower level of the cluster tree, which are going to be utilized as the roots in the higher level of the cluster tree…
We analyze the Nystr\"om approximation of a positive definite kernel associated with a probability measure. We first prove an improved error bound for the conventional Nystr\"om approximation with i.i.d. sampling and singular-value…
Partitioning a graph into groups of vertices such that those within each group are more densely connected than vertices assigned to different groups, known as graph clustering, is often used to gain insight into the organisation of large…
Clustering is a fundamental task in data analysis, and spectral clustering has been recognized as a promising approach to it. Given a graph describing the relationship between data, spectral clustering explores the underlying cluster…