scholarly journals Scalable Spectral Clustering With Nyström Approximation: Practical and Theoretical Aspects

2020 ◽  
Vol 1 ◽  
pp. 242-256
Author(s):  
Farhad Pourkamali-Anaraki
Author(s):  
Mahesh Mohan ◽  
Claire Monteleoni

In this paper we present a framework for spectral clustering based on the following simple scheme: sample a subset of the input points, compute the clusters for the sampled subset using weighted kernel k-means (Dhillon et al. 2004) and use the resulting centers to compute a clustering for the remaining data points. For the case where the points are sampled uniformly at random without replacement, we show that the number of samples required depends mainly on the number of clusters and the diameter of the set of points in the kernel space. Experiments show that the proposed framework outperforms the approaches based on the Nystrom approximation both in terms of accuracy and computation time.


2019 ◽  
Vol 29 (1) ◽  
pp. 125-137
Author(s):  
Aleksandar Trokicić ◽  
Branimir Todorović

Abstract We present two algorithms in which constrained spectral clustering is implemented as unconstrained spectral clustering on a multi-layer graph where constraints are represented as graph layers. By using the Nystrom approximation in one of the algorithms, we obtain time and memory complexities which are linear in the number of data points regardless of the number of constraints. Our algorithms achieve superior or comparative accuracy on real world data sets, compared with the existing state-of-the-art solutions. However, the complexity of these algorithms is squared with the number of vertices, while our technique, based on the Nyström approximation method, has linear time complexity. The proposed algorithms efficiently use both soft and hard constraints since the time complexity of the algorithms does not depend on the size of the set of constraints.


Author(s):  
Xiaohui Wang ◽  
Yu Bai ◽  
Yadong Gao ◽  
Dong Liu ◽  
Yan Zhang ◽  
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2021 ◽  
Vol 13 (3) ◽  
pp. 355
Author(s):  
Weixian Tan ◽  
Borong Sun ◽  
Chenyu Xiao ◽  
Pingping Huang ◽  
Wei Xu ◽  
...  

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.


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