CUR Decompositions, Similarity Matrices, and Subspace Clustering

Aldroubi, Akram; Hamm, Keaton; Koku, Ahmet Buğra; Sekmen, Ali

doi:10.3389/fams.2018.00065

Cited by 30 publications

(37 citation statements)

References 66 publications

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“…The CUR decomposition technique has more and more applications in other fields: CUR decomposition for web image classification (Liu & Shao, ); the analysis of the antibacterial activity of cephalosporin (Rodríguez, Ones, García, & Velar, ); machine learning applications (S. Wang & Zhang, ); CUR decomposition for compression and compressed sensing of large‐scale traffic data (Mitrovic, Asif, Rasheed, Dauwels, & Jaillet, ); identifying important ions and positions in mass spectrometry imaging data (Yang, Rubel, Mahoney, & Bowen, ); unsupervised learning for simultaneous selection of samples and characteristics (Li et al, ); pedagogical statistical models (Villegas Barahona, ) and 3‐D massive antenna systems (Zhao et al, ), among others (Aldroubi, Hamm, Koku, & Sekmen, ; Anderson et al, ; Boutsidis & Woodruff, ). It is a technique with a wide range when working with data from different fields, it obtains very good results in genomics and it is increasingly being used.…”

Section: Methodsmentioning

confidence: 99%

Bias in composite indexes of CSR practice: An analysis of CUR matrix decomposition

Amor‐Esteban

Galindo‐Villardón

García‐Sánchez

2020

Corp Soc Responsibility Env

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The main objective of this research is to propose the best aggregate index of corporate social responsibility practice at the organisational level. To achieve this, we analyse the consistency of the different aggregated measures that researchers use in their analyses through a robust statistical technique, the CUR matrix, framed in the big data environment for selecting individuals. Accordingly, we use an international sample of 2,675 large listed companies. The results show that the CUR leverage identifies greater consistency of the different aggregate measures of CSR, confirming its coherence with a correlation analysis. In this sense, it is possible to affirm that the composite indexes used in academia do not introduce any bias into the analysis of CSR practices. In addition, we demonstrate the utility of this technique to identify the most powerful companies, analysing their CSR commitment at the country and industry levels, namely, Norsk Hydro in the metal and mining industry in Norway, Stora Enso in forestry and paper in Finland, Akzo Nobel in chemical products in the Netherlands, BMW in automobiles and parts in Germany, Generali in finance in Italy, Novartis in pharmaceuticals in Switzerland, the BT Group in telecommunications in the United Kingdom and Inditex in textiles in Spain. Moreover, the results of the CUR study confirm that companies adapt to the demands or pressures from the stakeholders in different areas of interest, which are specific to each country and industry. The availability of these data allows the identification of the structural drivers of their growth and the establishment of priorities that allow the design of more effective sustainable development momentum policies.

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Section: Methodsmentioning

confidence: 99%

Bias in composite indexes of CSR practice: An analysis of CUR matrix decomposition

Amor‐Esteban

Galindo‐Villardón

García‐Sánchez

2020

Corp Soc Responsibility Env

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“…More recent works [31], [32], [33] use a different subset selection method for subspace clustering. In particular, the method named Scalable and Robust SSC (SR-SSC) [33] selects a few sets of anchor points using a randomized hierarchical clustering method.…”

Section: A Fast and Scalable Subspace Clustering Methodsmentioning

confidence: 99%

A fast and accurate similarity-constrained subspace clustering algorithm for land cover segmentation

Hinojosa¹,

Vera²,

Argüello³

2021

Preprint

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Accurate land cover segmentation of spectral images is challenging and has drawn widespread attention in remote sensing due to its inherent complexity. Although significant efforts have been made for developing a variety of methods, most of them rely on supervised strategies. Subspace clustering methods, such as Sparse Subspace Clustering (SSC), have become a popular tool for unsupervised learning due to their high performance. However, the computational complexity of SSC methods prevents their use on large spectral remotely sensed datasets. Furthermore, since SSC ignores the spatial information in the spectral images, its discrimination capability is limited, hampering the clustering results' spatial homogeneity. To address these two relevant issues, in this paper, we propose a fast algorithm that obtains a sparse representation coefficient matrix by first selecting a small set of pixels that best represent their neighborhood. Then, it performs spatial filtering to enforce the connectivity of neighboring pixels and uses fast spectral clustering to get the final segmentation. Extensive simulations with our method demonstrate its effectiveness in land cover segmentation, obtaining remarkable high clustering performance compared with state-of-the-art SSC-based algorithms and even novel unsupervised-deep-learning-based methods. Besides, the proposed method is up to three orders of magnitude faster than SSC when clustering more than 2x10<sup>4</sup> spectral pixels.

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“…Matrix factorization methods have been used to good effect in solving the Subspace Clustering Problem [1,2,7] as have associated low-rank based optimization methods [13,22]. In particular, it is known that under certain subspace configurations, the truncated SVD, any basis factorization with basis vectors coming from the subspaces S i , and CUR decompositions can all be used to give a valid clustering of the data.…”

Section: 3mentioning

confidence: 99%

“…In particular, it is known that under certain subspace configurations, the truncated SVD, any basis factorization with basis vectors coming from the subspaces S i , and CUR decompositions can all be used to give a valid clustering of the data. For a longer discussion, the reader may consult [1]. Here we illustrate how random sampling may be used to guarantee a CUR-based solution to the subspace clustering problem.…”

Section: 3mentioning

confidence: 99%

Stability of sampling for CUR decompositions

Hamm¹,

Huang²

2020

Foundations of Data Science

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This article studies how to form CUR decompositions of low-rank matrices via primarily random sampling, though deterministic methods due to previous works are illustrated as well. The primary problem is to determine when a column submatrix of a rank k matrix also has rank k. For random column sampling schemes, there is typically a tradeoff between the number of columns needed to be chosen and the complexity of determining the sampling probabilities. We discuss several sampling methods and their complexities as well as stability of the method under perturbations of both the probabilities and the underlying matrix. As an application, we give a high probability guarantee of the exact solution of the Subspace Clustering Problem via CUR decompositions when columns are sampled according to their Euclidean lengths.

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CUR Decompositions, Similarity Matrices, and Subspace Clustering

Cited by 30 publications

References 66 publications

Bias in composite indexes of CSR practice: An analysis of CUR matrix decomposition

Bias in composite indexes of CSR practice: An analysis of CUR matrix decomposition

A fast and accurate similarity-constrained subspace clustering algorithm for land cover segmentation

Stability of sampling for CUR decompositions

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