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Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. Non-standard multilayer graph clustering methods are needed for assigning clusters to a common…

We present a scheme to improve the noise threshold for the fault-tolerant topological one-way computation with a constant overhead. Certain cluster states of finite size, say star clusters, are constructed with logical qubits through an…

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…

Current graph clustering methods emphasize individual node and edge con nections, while ignoring higher-order organization at the level of motif. Re cently, higher-order graph clustering approaches have been designed by motif based…

Machine learning and in particular deep learning algorithms are the emerging approaches to data analysis. These techniques have transformed traditional data mining-based analysis radically into a learning-based model in which existing data…

The proliferation of models for networks raises challenging problems of model selection: the data are sparse and globally dependent, and models are typically high-dimensional and have large numbers of latent variables. Together, these…

Medical data often exhibit characteristics that make cluster analysis particularly challenging, such as missing values, outliers, and cluster features like skewness. Typically, such data would need to be preprocessed -- by cleaning outliers…

Machine Learning approaches like clustering methods deal with massive datasets that present an increasing challenge. We devise parallel algorithms to compute the Multi-Slice Clustering (MSC) for 3rd-order tensors. The MSC method is based on…

Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…

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…

Clustering is one of the most crucial problems in unsupervised learning, and the well-known $k$-means clustering algorithm has been shown to be implementable on a quantum computer with a significant speedup. However, many clustering…

This paper considers a canonical clustering problem where one receives unlabeled samples drawn from a balanced mixture of two elliptical distributions and aims for a classifier to estimate the labels. Many popular methods including PCA and…

We propose a Bayesian approach for model-based clustering of multivariate categorical data where variables are allowed to be associated within clusters and the number of clusters is unknown. The approach uses a two-layer mixture of finite…

Graph clustering is a central topic in unsupervised learning with a multitude of practical applications. In recent years, multi-view graph clustering has gained a lot of attention for its applicability to real-world instances where one has…

We present a new algorithm for spectral clustering based on a column-pivoted QR factorization that may be directly used for cluster assignment or to provide an initial guess for k-means. Our algorithm is simple to implement, direct, and…

In this paper, we propose an efficient clustering technique to solve the problem of clustering in the presence of obstacles. The proposed algorithm divides the spatial area into rectangular cells. Each cell is associated with statistical…

The graph partitioning problem has many applications in scientific computing such as computer aided design, data mining, image compression and other applications with sparse-matrix vector multiplications as a kernel operation. In many cases…

The problem of Hybrid Linear Modeling (HLM) is to model and segment data using a mixture of affine subspaces. Different strategies have been proposed to solve this problem, however, rigorous analysis justifying their performance is missing.…

The burgeoning growth of public domain data and the increasing complexity of deep learning model architectures have underscored the need for more efficient data representation and analysis techniques. This paper is motivated by the work of…

Tensor networks, which have been traditionally used to simulate many-body physics, have recently gained significant attention in the field of machine learning due to their powerful representation capabilities. In this work, we propose a…