As an indicator of the stability spectral clustering undirected weighted graph into k clusters, th gap Laplacian is often considered. The characterized in this paper as unstructured distance to ambiguity, namely minimal arbitrary symmetric matrices with vanishing gap. a conceptually more appropriate measure stability, structured ambiguity -clustering introduced Laplacians graphs same vertices a...

Spectral methods offer a tractable, global framework for clustering in graphs via eigenvector computations on graph matrices. Hypergraph data, which entities interact edges of arbitrary size, poses challenges matrix representations and therefore spectral clustering. We study nonuniform hypergraphs based the hypergraph nonbacktracking operator. After reviewing definition this operator its basic ...

This work focuses on the active selection of pairwise constraints for spectral clustering. We develop and analyze a technique for Active Constrained Clustering by Examining Spectral eigenvectorS (ACCESS) derived from a similarity matrix. The ACCESS method uses an analysis based on the theoretical properties of spectral decomposition to identify data items that are likely to be located on the bo...

In this study we apply hierarchical spectral partitioning of bipartite graphs to a Dutch dialect dataset to cluster dialect varieties and determine the concomitant sound correspondences. An important advantage of this clustering method over other dialectometric methods is that the linguistic basis is simultaneously determined, bridging the gap between traditional and quantitative dialectology. ...

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 clustering algorithms such as the k-means algorithm. On the first glance spectral clustering appears slightly mysterious, and it is not obvious to see why it works at...

Compressive spectral clustering combines the distance preserving measurements of compressed sensing with the power of spectral clustering. Our analysis provides rigorous bounds on how small errors in the affinity matrix can affect the spectral coordinates and clusterability. This work generalizes the current perturbation results of two-class spectral clustering to incorporate multiclass cluster...

In this paper I’ll speak about non-spectral clustering techniques and see how a node ordering based on centrality measures can improve the quality of communities detected. I’ll also discuss an improvement to existing techniques, which further improves modularity.