Related papers: Compressive Spectral Clustering
We build upon recent advances in graph signal processing to propose a faster spectral clustering algorithm. Indeed, classical spectral clustering is based on the computation of the first k eigenvectors of the similarity matrix' Laplacian,…
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…
In this paper we study variants of the widely used spectral clustering that partitions a graph into k clusters by (1) embedding the vertices of a graph into a low-dimensional space using the bottom eigenvectors of the Laplacian matrix, and…
Spectral clustering is a popular and effective algorithm designed to find $k$ clusters in a graph $G$. In the classical spectral clustering algorithm, the vertices of $G$ are embedded into $\mathbb{R}^k$ using $k$ eigenvectors of the graph…
Spectral clustering is a powerful unsupervised machine learning algorithm for clustering data with non convex or nested structures. With roots in graph theory, it uses the spectral properties of the Laplacian matrix to project the data in a…
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 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 is a popular algorithm that clusters points using the eigenvalues and eigenvectors of Laplacian matrices derived from the data. For years, spectral clustering has been working mysteriously. This paper explains spectral…
Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…
In recent years, spectral clustering has become one of the most popular modern clustering algorithms. It is simple to implement, can be solved efficiently by standard linear algebra software, and very often outperforms traditional…
In this paper, we introduce an algorithm for performing spectral clustering efficiently. Spectral clustering is a powerful clustering algorithm that suffers from high computational complexity, due to eigen decomposition. In this work, we…
Our previous experiments demonstrated that subsets collections of (short) documents (with several hundred entries) share a common normalized in some way eigenvalue spectrum of combinatorial Laplacian. Based on this insight, we propose a…
The recently emerged spectral clustering surpasses conventional clustering methods by detecting clusters of any shape without the convexity assumption. Unfortunately, with a computational complexity of $O(n^3)$, it was infeasible for…
Spectral clustering is one of the most important algorithms in data mining and machine intelligence; however, its computational complexity limits its application to truly large scale data analysis. The computational bottleneck in spectral…
This work studies the classical spectral clustering algorithm which embeds the vertices of some graph $G=(V_G, E_G)$ into $\mathbb{R}^k$ using $k$ eigenvectors of some matrix of $G$, and applies $k$-means to partition $V_G$ into $k$…
Spectral clustering has become one of the most widely used clustering techniques when the structure of the individual clusters is non-convex or highly anisotropic. Yet, despite its immense popularity, there exists fairly little theory about…
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…
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…
Clustering is a common technique for statistical data analysis, Clustering is the process of grouping the data into classes or clusters so that objects within a cluster have high similarity in comparison to one another, but are very…
We present a simple spectral approach to the well-studied constrained clustering problem. It captures constrained clustering as a generalized eigenvalue problem with graph Laplacians. The algorithm works in nearly-linear time and provides…