Spectral Clustering of Large-scale Data by Directly Solving Normalized Cut

Chen, Xiaojun; Hong, Weijun; Nie, Feiping; He, Dan; Yang, Min; Huang, Joshua Zhexue

doi:10.1145/3219819.3220039

Cited by 58 publications

(15 citation statements)

References 38 publications

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“…Compared with exhaustive search, the time complexity of the proposed interference-aware graph-based clustering algorithm of is reduced. The proposed user clustering algorithm has a polynomial complexity in O(Q 3 +(Z 2 /2+Z/2+G)+ G 3 ), where the first term corresponds to the complexity of the spectral clustering used for CUE clustering [47], the second term corresponds to the heuristic algorithm used to solve the problem of multi-way MAX K-CUT [45], which is also used for D2D pair clustering, and the third term corresponds to the Hungarian algorithm used for clusters matching [48].…”

Section: Complexity Analysismentioning

confidence: 99%

User Clustering and Optimized Power Allocation for D2D Communications at mmWave Underlaying MIMO-NOMA Cellular Networks

2021

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Fifth-generation (5G) cellular networks are being developed to meet the ever-growing data traffic across mobile devices and their applications. The core of 5G cellular networks is leveraging wider and higher frequencies available at millimeter wave frequency (mmWave) bands, thus providing very high data rates for mobile devices. Multi-input multi-output (MIMO) is an essential technology for overcoming the high propagation loss at mmWave communications. In non-orthogonal multiple access (NOMA), multiple cellular user equipments (CUEs) communicate over the same time-frequency resources using a multiplexed power domain. In device-to-device (D2D) communications, two D2D user equipments (DUEs) communicate without passing through the base station. In the underlaying scenario, DUEs reuse the frequency resources allocated to CUEs for spectrum utilization but DUEs cause interferences for cellular and D2D communications. Integrating D2D communications with other 5G technologies has great potential for spectral efficiency improvement. Unfortunately, interference management and resource allocation are becoming increasingly challenging due to aggressive frequency reuse. In this paper, D2D communications at mmWave underlaying MIMO-NOMA cellular network system model is developed. Consequently, a novel resource allocation for D2D communications underlaying MIMO-NOMA cellular network is proposed. A resource allocation optimization problem is formulated for spectral efficiency maximization. To solve this NP-hard problem, the problem is decomposed into three subproblems: interference-aware graph-based user clustering, MIMO-NOMA beamforming design, and optimized power allocation based on particle swarm optimization. Simulation results demonstrate that the proposed algorithm for D2D communications at mmWave underlaying MIMO-NOMA cellular network delivers a greater spectral efficiency compared to the conventional D2D communications that operate underlay MIMO-orthogonal multiple access cellular networks.

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Section: Complexity Analysismentioning

confidence: 99%

User Clustering and Optimized Power Allocation for D2D Communications at mmWave Underlaying MIMO-NOMA Cellular Networks

2021

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“…Motivated by Chen et al (2018) , objective Eq. (23) can be represented as Since involves all rows of Y , we can sove Y row-wisely; that is, we can update one row of Y by fixing the others as constants.…”

Section: The Proposed Modelmentioning

confidence: 99%

A new Kmeans clustering model and its generalization achieved by joint spectral embedding and rotation

Huang

Peng

et al. 2021

PeerJ Computer Science

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The Kmeans clustering and spectral clustering are two popular clustering methods for grouping similar data points together according to their similarities. However, the performance of Kmeans clustering might be quite unstable due to the random initialization of the cluster centroids. Generally, spectral clustering methods employ a two-step strategy of spectral embedding and discretization postprocessing to obtain the cluster assignment, which easily lead to far deviation from true discrete solution during the postprocessing process. In this paper, based on the connection between the Kmeans clustering and spectral clustering, we propose a new Kmeans formulation by joint spectral embedding and spectral rotation which is an effective postprocessing approach to perform the discretization, termed KMSR. Further, instead of directly using the dot-product data similarity measure, we make generalization on KMSR by incorporating more advanced data similarity measures and call this generalized model as KMSR-G. An efficient optimization method is derived to solve the KMSR (KMSR-G) model objective whose complexity and convergence are provided. We conduct experiments on extensive benchmark datasets to validate the performance of our proposed models and the experimental results demonstrate that our models perform better than the related methods in most cases.

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“…On the other hand, [10,11] employed an iterative optimization algorithm to solve the classical Normalized Cut problem, where the final clustering result can be obtained directly without eigendecomposition. SC can be treated as an approximation of Normalized Cut problem [12].…”

Section: Introductionmentioning

confidence: 99%

A Rank-Constrained Clustering Algorithm with Adaptive Embedding

Pei

Nie

Wang

et al. 2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Most spectral clustering algorithms obtain firstly the embedding based on the similarity matrix of the input data and then discretize the embedding to get the final clustering result. So, their performance is greatly affected by the noise of the similarity matrix, and the two-step strategy may lead to a suboptimal result. In this article, a novel Rank-Constrained clustering algorithm with Adaptive Embedding called RCAE is proposed, where the spectral embedding and the clustering structure are learned simultaneously, so, the influence of noise on performance is greatly reduced. In addition, a rank constraint is adopted in our model, thus, the connectivity matrix with exactly c (the number of clusters to construct) connected components can be learned, therefore, the final clustering result can be obtained according to the connected components. Experiments on several benchmark datasets validate the superiority of the proposed methods, compared to the several state-of-the-art clustering algorithms [GitHub].

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Spectral Clustering of Large-scale Data by Directly Solving Normalized Cut

Cited by 58 publications

References 38 publications

User Clustering and Optimized Power Allocation for D2D Communications at mmWave Underlaying MIMO-NOMA Cellular Networks

User Clustering and Optimized Power Allocation for D2D Communications at mmWave Underlaying MIMO-NOMA Cellular Networks

A new Kmeans clustering model and its generalization achieved by joint spectral embedding and rotation

A Rank-Constrained Clustering Algorithm with Adaptive Embedding

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