Grassmannian Manifold Optimization Assisted Sparse Spectral Clustering

2017 ◽  
Author(s):  
Qiong Wang ◽  
Junbin Gao ◽  
Hong Li
Keyword(s):  
Spectral Clustering ◽  
Grassmannian Manifold ◽  
Manifold Optimization

scholarly journals Gradient-based Learning Methods Extended to Smooth Manifolds Applied to Automated Clustering

2020 ◽  
Vol 68 ◽  
pp. 777-816
Author(s):  
Alkis Koudounas ◽  
Simone Fiori
Keyword(s):  
Minimization Problem ◽  
Spectral Clustering ◽  
Learning Algorithms ◽  
Optimization Methods ◽  
Smooth Manifolds ◽  
Loss Minimization ◽  
Parameter Spaces ◽  
Manifold Optimization ◽  
Gradient Based ◽  
Smooth Constraints

Grassmann manifold based sparse spectral clustering is a classification technique that  consists in learning a latent representation of data, formed by a subspace basis, which  is sparse. In order to learn a latent representation, spectral clustering is formulated in  terms of a loss minimization problem over a smooth manifold known as Grassmannian.  Such minimization problem cannot be tackled by one of traditional gradient-based learning  algorithms, which are only suitable to perform optimization in absence of constraints among  parameters. It is, therefore, necessary to develop specific optimization/learning algorithms  that are able to look for a local minimum of a loss function under smooth constraints in  an efficient way. Such need calls for manifold optimization methods. In this paper, we  extend classical gradient-based learning algorithms on   at parameter spaces (from classical  gradient descent to adaptive momentum) to curved spaces (smooth manifolds) by means  of tools from manifold calculus. We compare clustering performances of these methods  and known methods from the scientific literature. The obtained results confirm that the  proposed learning algorithms prove lighter in computational complexity than existing ones  without detriment in clustering efficacy.

A Method for Multi-HVDC Grouping Based on Spectral Clustering

2020 ◽  
Author(s):  
Xiaohui Wang ◽  
Yu Bai ◽  
Yadong Gao ◽  
Dong Liu ◽  
Yan Zhang ◽  
...  
Keyword(s):  
Spectral Clustering

scholarly journals Alignment and integration of complex networks by hypergraph-based spectral clustering

2012 ◽  
Vol 86 (5) ◽  
Author(s):  
Tom Michoel ◽  
Bruno Nachtergaele
Keyword(s):  
Complex Networks ◽  
Spectral Clustering

scholarly journals A Novel Unsupervised Classification Method for Sandy Land Using Fully Polarimetric SAR Data

2021 ◽  
Vol 13 (3) ◽  
pp. 355
Author(s):  
Weixian Tan ◽  
Borong Sun ◽  
Chenyu Xiao ◽  
Pingping Huang ◽  
Wei Xu ◽  
...  
Keyword(s):  
Spectral Clustering ◽  
Large Scale ◽  
Clustering Algorithm ◽  
Feature Vector ◽  
Unsupervised Classification ◽  
Classification Method ◽  
Sandy Land ◽  
Classification Methods ◽  
The Many ◽  
Representative Points

Classification based on polarimetric synthetic aperture radar (PolSAR) images is an emerging technology, and recent years have seen the introduction of various classification methods that have been proven to be effective to identify typical features of many terrain types. Among the many regions of the study, the Hunshandake Sandy Land in Inner Mongolia, China stands out for its vast area of sandy land, variety of ground objects, and intricate structure, with more irregular characteristics than conventional land cover. Accounting for the particular surface features of the Hunshandake Sandy Land, an unsupervised classification method based on new decomposition and large-scale spectral clustering with superpixels (ND-LSC) is proposed in this study. Firstly, the polarization scattering parameters are extracted through a new decomposition, rather than other decomposition approaches, which gives rise to more accurate feature vector estimate. Secondly, a large-scale spectral clustering is applied as appropriate to meet the massive land and complex terrain. More specifically, this involves a beginning sub-step of superpixels generation via the Adaptive Simple Linear Iterative Clustering (ASLIC) algorithm when the feature vector combined with the spatial coordinate information are employed as input, and subsequently a sub-step of representative points selection as well as bipartite graph formation, followed by the spectral clustering algorithm to complete the classification task. Finally, testing and analysis are conducted on the RADARSAT-2 fully PolSAR dataset acquired over the Hunshandake Sandy Land in 2016. Both qualitative and quantitative experiments compared with several classification methods are conducted to show that proposed method can significantly improve performance on classification.

scholarly journals Spectral Clustering Reveals Different Profiles of Central Sensitization in Women with Carpal Tunnel Syndrome

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1042
Author(s):  
Oscar J. Pellicer-Valero ◽  
José D. Martín-Guerrero ◽  
César Fernández-de-las-Peñas ◽  
Ana I. De-la-Llave-Rincón ◽  
Jorge Rodríguez-Jiménez ◽  
...  
Keyword(s):  
Carpal Tunnel Syndrome ◽  
Clinical Features ◽  
Carpal Tunnel ◽  
Spectral Clustering ◽  
Grip Force ◽  
The Other ◽  
Pressure Pain ◽  
Thermal Pain ◽  
Pressure Pain Thresholds ◽  
Tunnel Syndrome

Identification of subgroups of patients with chronic pain provides meaningful insights into the characteristics of a specific population, helping to identify individuals at risk of chronification and to determine appropriate therapeutic strategies. This paper proposes the use of spectral clustering (SC) to distinguish subgroups (clusters) of individuals with carpal tunnel syndrome (CTS), making use of the obtained patient profiling to argue about potential management implications. SC is a powerful algorithm that builds a similarity graph among the data points (the patients), and tries to find the subsets of points that are strongly connected among themselves, but weakly connected to others. It was chosen due to its advantages with respect to other simpler clustering techniques, such as k-means, and the fact that it has been successfully applied to similar problems. Clinical (age, duration of symptoms, pain intensity, function, and symptom severity), psycho-physical (pressure pain thresholds—PPTs—over the three main nerve trunks of the upper extremity, cervical spine, carpal tunnel, and tibialis anterior), psychological (depressive levels), and motor (pinch tip grip force) variables were collected in 208 women with clinical/electromyographic diagnosis of CTS, whose symptoms usually started unilaterally but eventually evolved into bilateral symmetry. SC was used to identify clusters of patients without any previous assumptions, yielding three clusters. Patients in cluster 1 exhibited worse clinical features, higher widespread pressure pain hyperalgesia, higher depressive levels, and lower pinch tip grip force than the other two. Patients in cluster 2 showed higher generalized thermal pain hyperalgesia than the other two. Cluster 0 showed less hypersensitivity to pressure and thermal pain, less severe clinical features, and more normal motor output (tip grip force). The presence of subgroups of individuals with different altered nociceptive processing (one group being more sensitive to pressure pain and another group more sensitive to thermal pain) could lead to different therapeutic programs.

Group-wise Hub Identification by Learning Common Graph Embeddings on Grassmannian Manifold

2021 ◽  
pp. 1-1
Author(s):  
Defu Yang ◽  
Jiazhou Chen ◽  
Chenggang Yan ◽  
Minjeong Kim ◽  
Paul J. Laurienti ◽  
...  
Keyword(s):  
Graph Embeddings ◽  
Grassmannian Manifold

scholarly journals Identifying cell types from single-cell data based on similarities and dissimilarities between cells

2021 ◽  
Vol 22 (S3) ◽  
Author(s):  
Yuanyuan Li ◽  
Ping Luo ◽  
Yi Lu ◽  
Fang-Xiang Wu
Keyword(s):  
Gene Expression ◽  
Single Cell ◽  
Spectral Clustering ◽  
Incidence Matrix ◽  
Expression Patterns ◽  
Cell Types ◽  
Clustering Method ◽  
Different Types ◽  
Cell Data ◽  
Spectral Clustering Method

Abstract Background With the development of the technology of single-cell sequence, revealing homogeneity and heterogeneity between cells has become a new area of computational systems biology research. However, the clustering of cell types becomes more complex with the mutual penetration between different types of cells and the instability of gene expression. One way of overcoming this problem is to group similar, related single cells together by the means of various clustering analysis methods. Although some methods such as spectral clustering can do well in the identification of cell types, they only consider the similarities between cells and ignore the influence of dissimilarities on clustering results. This methodology may limit the performance of most of the conventional clustering algorithms for the identification of clusters, it needs to develop special methods for high-dimensional sparse categorical data. Results Inspired by the phenomenon that same type cells have similar gene expression patterns, but different types of cells evoke dissimilar gene expression patterns, we improve the existing spectral clustering method for clustering single-cell data that is based on both similarities and dissimilarities between cells. The method first measures the similarity/dissimilarity among cells, then constructs the incidence matrix by fusing similarity matrix with dissimilarity matrix, and, finally, uses the eigenvalues of the incidence matrix to perform dimensionality reduction and employs the K-means algorithm in the low dimensional space to achieve clustering. The proposed improved spectral clustering method is compared with the conventional spectral clustering method in recognizing cell types on several real single-cell RNA-seq datasets. Conclusions In summary, we show that adding intercellular dissimilarity can effectively improve accuracy and achieve robustness and that improved spectral clustering method outperforms the traditional spectral clustering method in grouping cells.

Spectral Clustering Based Millimeter-Wave Beam Management in V2I Networks

2020 ◽  
Author(s):  
ZhaoZhen Lin ◽  
YiFeng Zhao ◽  
LianFen Huang ◽  
ZhiYuan Shi
Keyword(s):  
Millimeter Wave ◽  
Spectral Clustering ◽  
Wave Beam
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