Related papers: Quantum Spectral Clustering
When it comes to clustering nonconvex shapes, two paradigms are used to find the most suitable clustering: minimum cut and maximum density. The most popular algorithms incorporating these paradigms are Spectral Clustering and DBSCAN. Both…
Spectral clustering is one of the most popular clustering methods. However, how to balance the efficiency and effectiveness of the large-scale spectral clustering with limited computing resources has not been properly solved for a long…
This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. Under a generalised random dot product graph, the embedding provides uniformly…
Cluster structure detection is a fundamental task for the analysis of graphs, in order to understand and to visualize their functional characteristics. Among the different cluster structure detection methods, spectral clustering is…
Clustering is an unsupervised machine learning methodology where unlabeled elements/objects are grouped together aiming to the construction of well-established clusters that their elements are classified according to their similarity. The…
Kernel spectral clustering corresponds to a weighted kernel principal component analysis problem in a constrained optimization framework. The primal formulation leads to an eigen-decomposition of a centered Laplacian matrix at the dual…
Spectral clustering has become one of the most popular algorithms in data clustering and community detection. We study the performance of classical two-step spectral clustering via the graph Laplacian to learn the stochastic block model.…
Spectral clustering is known as a powerful technique in unsupervised data analysis. The vast majority of approaches to spectral clustering are driven by a single modality, leaving the rich information in multi-modal representations…
As an indicator of the stability of spectral clustering of an undirected weighted graph into $k$ clusters, the $k$th spectral gap of the graph Laplacian is often considered. The $k$th spectral gap is characterized in this paper as an…
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…
Clustering algorithms are one of the main analytical methods to detect patterns in unlabeled data. Existing clustering methods typically treat samples in a dataset as points in a metric space and compute distances to group together similar…
Quantum machine learning is one of the most promising applications of a full-scale quantum computer. Over the past few years, many quantum machine learning algorithms have been proposed that can potentially offer considerable speedups over…
The objective functions used in spectral clustering are usually composed of two terms: i) a term that minimizes the local quadratic variation of the cluster assignments on the graph and; ii) a term that balances the clustering partition and…
The quantum convolutional neural network (QCNN) is a promising quantum machine learning (QML) model that is expected to achieve quantum advantages in classically intractable problems. However, the QCNN requires a large number of…
Kernel-based clustering algorithms have the ability to capture the non-linear structure in real world data. Among various kernel-based clustering algorithms, kernel k-means has gained popularity due to its simple iterative nature and ease…
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…
The last decades have seen a surge of interests in distributed computing thanks to advances in clustered computing and big data technology. Existing distributed algorithms typically assume {\it all the data are already in one place}, and…
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…
The smallest eigenvalues and the associated eigenvectors (i.e., eigenpairs) of a graph Laplacian matrix have been widely used for spectral clustering and community detection. However, in real-life applications the number of clusters or…
Correlation clustering is a central topic in unsupervised learning, with many applications in ML and data mining. In correlation clustering, one receives as input a signed graph and the goal is to partition it to minimize the number of…