Related papers: Incremental Method for Spectral Clustering of Incr…
Graph clustering under the framework of differential privacy, which aims to process graph-structured data while protecting individual privacy, has been receiving increasing attention. Despite significant achievements in current research,…
Incremental versions of batch algorithms are often desired, for increased time efficiency in the streaming data setting, or increased memory efficiency in general. In this paper we present a novel algorithm for incremental kernel PCA, based…
While spectral clustering algorithms for undirected graphs are well established and have been successfully applied to unsupervised machine learning problems ranging from image segmentation and genome sequencing to signal processing and…
Local clustering aims to identify specific substructures within a large graph without any additional structural information of the graph. These substructures are typically small compared to the overall graph, enabling the problem to be…
We consider the problem of estimating the number of clusters (k) in a dataset. We propose a non-parametric approach to the problem that utilizes similarity graphs to construct a robust statistic that effectively captures similarity…
Spectral clustering became a popular choice for data clustering for its ability of uncovering clusters of different shapes. However, it is not always preferable over other clustering methods due to its computational demands. One of the…
We consider the problem of estimating a consensus community structure by combining information from multiple layers of a multi-layer network using methods based on the spectral clustering or a low-rank matrix factorization. As a general…
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 spectral clustering algorithm is often used as a binary clustering method for unclassified data by applying the principal component analysis. To study theoretical properties of the algorithm, the assumption of conditional…
Multilayer graphs encode different kind of interactions between the same set of entities. When one wants to cluster such a multilayer graph, the natural question arises how one should merge the information different layers. We introduce in…
We propose two related unsupervised clustering algorithms which, for input, take data assumed to be sampled from a uniform distribution supported on a metric space $X$, and output a clustering of the data based on the selection of a…
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…
Graph clustering is a fundamental task in unsupervised learning with broad real-world applications. While spectral clustering methods for undirected graphs are well-established and guided by a minimum cut optimization consensus, their…
With the development of quantum algorithms, high-cost computations are being scrutinized in the hope of a quantum advantage. While graphs offer a convenient framework for multiple real-world problems, their analytics still comes with high…
Finding the number of meaningful clusters in an unlabeled dataset is important in many applications. Regularized k-means algorithm is a possible approach frequently used to find the correct number of distinct clusters in datasets. The most…
In this paper, we investigate the learning-augmented $k$-median clustering problem, which aims to improve the performance of traditional clustering algorithms by preprocessing the point set with a predictor of error rate $\alpha \in [0,1)$.…
This study presents a novel approach utilizing cluster means to address the non-differentiability issue arising from multiple eigenvalues in eigenfrequency and bandgap optimization. By constructing symmetric functions of repeated…
The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…
We consider three distinct and well studied problems concerning network structure: community detection by modularity maximization, community detection by statistical inference, and normalized-cut graph partitioning. Each of these problems…
We study random graphs with possibly different edge probabilities in the challenging sparse regime of bounded expected degrees. Unlike in the dense case, neither the graph adjacency matrix nor its Laplacian concentrate around their…