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Spectral clustering is a popular and versatile clustering method based on a relaxation of the normalised graph cut objective. Despite its popularity, however, there is no single agreed upon method for tuning the important scaling parameter,…
Spectral clustering is a broad class of clustering procedures in which an intractable combinatorial optimization formulation of clustering is "relaxed" into a tractable eigenvector problem, and in which the relaxed solution is subsequently…
The bipartite graph structure has shown its promising ability in facilitating the subspace clustering and spectral clustering algorithms for large-scale datasets. To avoid the post-processing via k-means during the bipartite graph…
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…
We revisit the theoretical performances of Spectral Clustering, a classical algorithm for graph partitioning that relies on the eigenvectors of a matrix representation of the graph. Informally, we show that Spectral Clustering works well as…
Spectral Clustering is one of the most traditional methods to solve segmentation problems. Based on Normalized Cuts, it aims at partitioning an image using an objective function defined by a graph. Despite their mathematical attractiveness,…
In the graph clustering problem with a planted solution, the input is a graph on $n$ vertices partitioned into $k$ clusters, and the task is to infer the clusters from graph structure. A standard assumption is that clusters induce…
The minimum sum-of-squares clustering (MSSC), or k-means type clustering, is traditionally considered an unsupervised learning task. In recent years, the use of background knowledge to improve the cluster quality and promote…
Spectral clustering is a popular method for community detection in network graphs: starting from a matrix representation of the graph, the nodes are clustered on a low dimensional projection obtained from a truncated spectral decomposition…
We introduce a sketch-and-solve approach to speed up the Peng-Wei semidefinite relaxation of k-means clustering. When the data is appropriately separated we identify the k-means optimal clustering. Otherwise, our approach provides a…
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…
Graph-Laplacians and their spectral embeddings play an important role in multiple areas of machine learning. This paper is focused on graph-Laplacian dimension reduction for the spectral clustering of data as a primary application. Spectral…
Spectral algorithms are graph partitioning algorithms that partition a node set of a graph into groups by using a spectral embedding map. Clustering techniques based on the algorithms are referred to as spectral clustering and are widely…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…
In [SIAM J. Optim., 2022], the authors introduced a new linear programming (LP) relaxation for K-means clustering. In this paper, we further investigate both theoretical and computational properties of this relaxation. As evident from our…
Spectral clustering is one of the most prominent clustering approaches. The distance-based similarity is the most widely used method for spectral clustering. However, people have already noticed that this is not suitable for multi-scale…
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a…
Spectral clustering is one of the most popular clustering algorithms that has stood the test of time. It is simple to describe, can be implemented using standard linear algebra, and often finds better clusters than traditional clustering…
Spectral clustering, as a popular tool for data clustering, requires an eigen-decomposition step on a given affinity to obtain the spectral embedding. Nevertheless, such a step suffers from the lack of generalizability and scalability.…
This paper proposes a variant of the normalized cut algorithm for spectral clustering. Although the normalized cut algorithm applies the K-means algorithm to the eigenvectors of a normalized graph Laplacian for finding clusters, our…