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Spectral Clustering using Eigenspectrum Shape Based Nystrom Sampling

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Djallel Bouneffouf

Machine Learning · Submitted 21 Jul 2020

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Our heuristic depends on the eigen spectrum shape of the dataset, and yields competitive low-rank approximations in test datasets compared to the other state-of-the-art methods

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arXiv ID2007.11416 (version 1)
Pith IDMCUVB7YH, Pith's permanent record of this paper and its review
CitationDjallel Bouneffouf. "Spectral Clustering using Eigenspectrum Shape Based Nystrom Sampling." arXiv:2007.11416 (2020). https://pith.science/paper/MCUVB7YH
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,861 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.13 · human participants 0.03 · controlled comparison 0.31 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.91 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Spectral clustering has shown a superior performance in analyzing the cluster structure. However, its computational complexity limits its application in analyzing large-scale data. To address this problem, many low-rank matrix approximating algorithms are proposed, including the Nystrom method - an approach with proven approximate error bounds. There are several algorithms that provide recipes to construct Nystrom approximations with variable accuracies and computing times. This paper proposes a scalable Nystrom-based clustering algorithm with a new sampling procedure, Centroid Minimum Sum of Squared Similarities (CMS3), and a heuristic on when to use it. Our heuristic depends on the eigen spectrum shape of the dataset, and yields competitive low-rank approximations in test datasets compared to the other state-of-the-art methods

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Spectral clustering has shown a superior performance in analyzing the cluster structure. background 1.00 0.07 0.03 asserted 0.99
s1 However, its computational complexity limits its application in analyzing large-scale data. background 0.81 0.08 0.02 asserted 1.00
s2 To address this problem, many low-rank matrix approximating algorithms are proposed, including the Nystrom method - an approach with proven approximate error bounds. background 1.00 0.05 0.03 asserted 1.00
s3 There are several algorithms that provide recipes to construct Nystrom approximations with variable accuracies and computing times. background 1.00 0.04 0.03 asserted 1.00
s4 This paper proposes a scalable Nystrom-based clustering algorithm with a new sampling procedure, Centroid Minimum Sum of Squared Similarities (CMS3), and a heuristic on when to use it. contribution 0.99 0.94 0.31 asserted 1.00
s5 Our heuristic depends on the eigen spectrum shape of the dataset, and yields competitive low-rank approximations in test datasets compared to the other state-of-the-art methods result 0.89 0.94 0.74 asserted 0.99

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.90.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Spectral clustering has shown a superior performance in analyzing the cluster structure. However, its computational complexity limits its application in analyzing large-scale data. To address this problem, many low-rank matrix approximating algorithms are proposed, including the Nystrom method - an approach with proven approximate error bounds. There are several algorithms that provide recipes to construct Nystrom approximations with variable accuracies and computing times. This paper proposes a scalable Nystrom-based clustering algorithm with a new sampling procedure, Centroid Minimum Sum of Squared Similarities (CMS3), and a heuristic on when to use it. Our heuristic depends on the eigen spectrum shape of the dataset, and yields competitive low-rank approximations in test datasets compared to the other state-of-the-art methods

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