Related papers: Improved Analysis of Spectral Algorithm for Cluste…
Clustering is an effective tool for astronomical spectral analysis, to mine clustering patterns among data. With the implementation of large sky surveys, many clustering methods have been applied to tackle spectroscopic and photometric data…
We propose a spectral clustering method based on local principal components analysis (PCA). After performing local PCA in selected neighborhoods, the algorithm builds a nearest neighbor graph weighted according to a discrepancy between the…
In this work, a graph partitioning problem in a fixed number of connected components is considered. Given an undirected graph with costs on the edges, the problem consists of partitioning the set of nodes into a fixed number of subsets with…
Spectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to reuse information of past cluster assignments to expedite computation. Our approach…
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…
Spectral clustering is a widely used algorithm to find clusters in networks. Several researchers have studied the stability of spectral clustering under local differential privacy with the additional assumption that the underlying networks…
Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take…
Spectral clustering methods have gained widespread recognition for their effectiveness in clustering high-dimensional data. Among these techniques, constrained spectral clustering has emerged as a prominent approach, demonstrating enhanced…
Spectral Embedding (SE) has often been used to map data points from non-linear manifolds to linear subspaces for the purpose of classification and clustering. Despite significant advantages, the subspace structure of data in the original…
Graph clustering is a fundamental technique in data analysis with applications in many different fields. While there is a large body of work on clustering undirected graphs, the problem of clustering directed graphs is much less understood.…
In the context of clustering, we assume a generative model where each cluster is the result of sampling points in the neighborhood of an embedded smooth surface; the sample may be contaminated with outliers, which are modeled as points…
Our problem of interest is to cluster vertices of a graph by identifying underlying community structure. Among various vertex clustering approaches, spectral clustering is one of the most popular methods because it is easy to implement…
Spectral clustering is a novel clustering method which can detect complex shapes of data clusters. However, it requires the eigen decomposition of the graph Laplacian matrix, which is proportion to $O(n^3)$ and thus is not suitable for…
Spectral clustering methodologies, when extended to accommodate signed graphs, have encountered notable limitations in effectively encapsulating inherent grouping relationships. Recent findings underscore a substantial deterioration in the…
Spectral clustering is popular among practitioners and theoreticians alike. While performance guarantees for spectral clustering are well understood, recent studies have focused on enforcing ``fairness'' in clusters, requiring them to be…
In an illiquid stock, traders can collude and place orders on a predetermined price and quantity at a fixed schedule. This is usually done to manipulate the price of the stock or to create artificial liquidity in the stock, which may…
This paper studies clustering algorithms for dynamically evolving graphs $\{G_t\}$, in which new edges (and potential new vertices) are added into a graph, and the underlying cluster structure of the graph can gradually change. The paper…
Consistency is a key property of all statistical procedures analyzing randomly sampled data. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of…
Many algorithms to detect communities in networks typically work without any information on the cluster structure to be found, as one has no a priori knowledge of it, in general. Not surprisingly, knowing some features of the unknown…
The extraction of clusters from a dataset which includes multiple clusters and a significant background component is a non-trivial task of practical importance. In image analysis this manifests for example in anomaly detection and target…