Fast Graph Sampling Set Selection Using Gershgorin Disc Alignment Article Swipe
Yuanchao Bai
,
Fen Wang
,
Gene Cheung
,
Yuji Nakatsukasa
,
Wen Gao
·
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.1109/tsp.2020.2981202
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.1109/tsp.2020.2981202
Graph sampling set selection, where a subset of nodes are chosen to collect samples to reconstruct a bandlimited or smooth graph signal, is a fundamental problem in graph signal processing (GSP). Previous works employ an unbiased least square (LS) signal reconstruction scheme and select samples via expensive extreme eigenvector computation. Instead, we assume a biased graph Laplacian regularization (GLR) based scheme that solves a system of linear equations for reconstruction. We then choose samples to minimize the condition number of the coefficient matrix---specifically, maximize the smallest eigenvalue λmin . Circumventing explicit eigenvalue computation, we maximize instead the lower bound of λmin , designated by the smallest left-end of all Gershgorin discs of the matrix. To achieve this efficiently, we first convert the optimization to a dual problem, where we minimize the number of samples needed to align all Gershgorin disc left-ends at a chosen lower-bound target T. Algebraically, the dual problem amounts to optimizing two disc operations: i) shifting of disc centers due to sampling, and ii) scaling of disc radii due to a similarity transformation of the matrix. We further reinterpret the dual to an intuitive disc coverage problem bearing strong resemblance to the famous NP-hard set cover (SC) problem. The reinterpretation enables us to derive a fast approximation algorithm from a known SC error-bounded approximation algorithm. We find the appropriate target T efficiently via binary search. Experiments on real graph data show that our disc-based sampling algorithm runs substantially faster than existing sampling schemes and outperforms other eigen-decomposition-free sampling schemes in reconstruction error.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1109/tsp.2020.2981202
- OA Status
- green
- Cited By
- 51
- References
- 65
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2961495769
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Raw OpenAlex JSON
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https://openalex.org/W2961495769Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1109/tsp.2020.2981202Digital Object Identifier
- Title
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Fast Graph Sampling Set Selection Using Gershgorin Disc AlignmentWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2020Year of publication
- Publication date
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2020-01-01Full publication date if available
- Authors
-
Yuanchao Bai, Fen Wang, Gene Cheung, Yuji Nakatsukasa, Wen GaoList of authors in order
- Landing page
-
https://doi.org/10.1109/tsp.2020.2981202Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/1907.06179Direct OA link when available
- Concepts
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Eigenvalues and eigenvectors, Laplacian matrix, Algorithm, Mathematics, Computation, Combinatorics, Computer science, Graph, Discrete mathematics, Mathematical optimization, Quantum mechanics, PhysicsTop concepts (fields/topics) attached by OpenAlex
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51Total citation count in OpenAlex
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2025: 6, 2024: 11, 2023: 9, 2022: 6, 2021: 8Per-year citation counts (last 5 years)
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65Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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| best_oa_location.pdf_url | https://arxiv.org/pdf/1907.06179 |
| best_oa_location.version | submittedVersion |
| best_oa_location.raw_type | text |
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| best_oa_location.is_accepted | False |
| best_oa_location.is_published | False |
| best_oa_location.raw_source_name | |
| best_oa_location.landing_page_url | http://arxiv.org/abs/1907.06179 |
| primary_location.id | doi:10.1109/tsp.2020.2981202 |
| primary_location.is_oa | False |
| primary_location.source.id | https://openalex.org/S168680287 |
| primary_location.source.issn | 1053-587X, 1941-0476 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | False |
| primary_location.source.issn_l | 1053-587X |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | IEEE Transactions on Signal Processing |
| primary_location.source.host_organization | https://openalex.org/P4310319808 |
| primary_location.source.host_organization_name | Institute of Electrical and Electronics Engineers |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310319808 |
| primary_location.source.host_organization_lineage_names | Institute of Electrical and Electronics Engineers |
| primary_location.license | |
| primary_location.pdf_url | |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | IEEE Transactions on Signal Processing |
| primary_location.landing_page_url | https://doi.org/10.1109/tsp.2020.2981202 |
| publication_date | 2020-01-01 |
| publication_year | 2020 |
| referenced_works | https://openalex.org/W4230938240, https://openalex.org/W2508691887, https://openalex.org/W2963059693, https://openalex.org/W2402638897, https://openalex.org/W6688349277, https://openalex.org/W6719831127, https://openalex.org/W2030319053, https://openalex.org/W2796431263, https://openalex.org/W2101491865, https://openalex.org/W2179147795, https://openalex.org/W2900169675, https://openalex.org/W2963629755, https://openalex.org/W2797386627, https://openalex.org/W1690143098, https://openalex.org/W2790590247, https://openalex.org/W2972918686, https://openalex.org/W2606654184, https://openalex.org/W2215668387, https://openalex.org/W2158787690, https://openalex.org/W2161763921, https://openalex.org/W4250589301, https://openalex.org/W6629852587, https://openalex.org/W2962817598, https://openalex.org/W2115789358, https://openalex.org/W2788790154, https://openalex.org/W2810526380, https://openalex.org/W2571662414, https://openalex.org/W1511572470, https://openalex.org/W2195972617, https://openalex.org/W2620264943, https://openalex.org/W1555827348, https://openalex.org/W1537592944, https://openalex.org/W2412442671, https://openalex.org/W2964201712, https://openalex.org/W2024457004, https://openalex.org/W2718610763, https://openalex.org/W2963521934, https://openalex.org/W2051142108, https://openalex.org/W2890403598, https://openalex.org/W2316564661, https://openalex.org/W2964292630, https://openalex.org/W2059586807, https://openalex.org/W2621679680, https://openalex.org/W3003775208, https://openalex.org/W2894310056, https://openalex.org/W1491300635, https://openalex.org/W6693397905, https://openalex.org/W1497214886, https://openalex.org/W2904160178, https://openalex.org/W4246219036, https://openalex.org/W2964228184, https://openalex.org/W3105775869, https://openalex.org/W2469963130, https://openalex.org/W3145128584, https://openalex.org/W2073625612, https://openalex.org/W3106333616, https://openalex.org/W3100267724, https://openalex.org/W3106135392, https://openalex.org/W2963984243, https://openalex.org/W3102208898, https://openalex.org/W2210832646, https://openalex.org/W3105198140, https://openalex.org/W2267893120, https://openalex.org/W4299133008, https://openalex.org/W2156195892 |
| referenced_works_count | 65 |
| abstract_inverted_index., | 101 |
| abstract_inverted_index.. | 88 |
| abstract_inverted_index.T | 223 |
| abstract_inverted_index.a | 5, 16, 23, 53, 63, 124, 142, 173, 207, 212 |
| abstract_inverted_index.SC | 214 |
| abstract_inverted_index.T. | 146 |
| abstract_inverted_index.To | 114 |
| abstract_inverted_index.We | 70, 179, 218 |
| abstract_inverted_index.an | 34, 185 |
| abstract_inverted_index.at | 141 |
| abstract_inverted_index.by | 103 |
| abstract_inverted_index.i) | 157 |
| abstract_inverted_index.in | 26, 252 |
| abstract_inverted_index.is | 22 |
| abstract_inverted_index.of | 7, 65, 79, 99, 107, 111, 132, 159, 168, 176 |
| abstract_inverted_index.on | 229 |
| abstract_inverted_index.or | 18 |
| abstract_inverted_index.to | 11, 14, 74, 123, 135, 152, 163, 172, 184, 193, 205 |
| abstract_inverted_index.us | 204 |
| abstract_inverted_index.we | 51, 93, 118, 128 |
| abstract_inverted_index.The | 201 |
| abstract_inverted_index.all | 108, 137 |
| abstract_inverted_index.and | 42, 165, 246 |
| abstract_inverted_index.are | 9 |
| abstract_inverted_index.due | 162, 171 |
| abstract_inverted_index.for | 68 |
| abstract_inverted_index.ii) | 166 |
| abstract_inverted_index.our | 235 |
| abstract_inverted_index.set | 2, 197 |
| abstract_inverted_index.the | 76, 80, 84, 96, 104, 112, 121, 130, 148, 177, 182, 194, 220 |
| abstract_inverted_index.two | 154 |
| abstract_inverted_index.via | 45, 225 |
| abstract_inverted_index.(LS) | 38 |
| abstract_inverted_index.(SC) | 199 |
| abstract_inverted_index.data | 232 |
| abstract_inverted_index.disc | 139, 155, 160, 169, 187 |
| abstract_inverted_index.dual | 125, 149, 183 |
| abstract_inverted_index.fast | 208 |
| abstract_inverted_index.find | 219 |
| abstract_inverted_index.from | 211 |
| abstract_inverted_index.real | 230 |
| abstract_inverted_index.runs | 239 |
| abstract_inverted_index.show | 233 |
| abstract_inverted_index.than | 242 |
| abstract_inverted_index.that | 61, 234 |
| abstract_inverted_index.then | 71 |
| abstract_inverted_index.this | 116 |
| abstract_inverted_index.(GLR) | 58 |
| abstract_inverted_index.Graph | 0 |
| abstract_inverted_index.align | 136 |
| abstract_inverted_index.based | 59 |
| abstract_inverted_index.bound | 98 |
| abstract_inverted_index.cover | 198 |
| abstract_inverted_index.discs | 110 |
| abstract_inverted_index.first | 119 |
| abstract_inverted_index.graph | 20, 27, 55, 231 |
| abstract_inverted_index.known | 213 |
| abstract_inverted_index.least | 36 |
| abstract_inverted_index.lower | 97 |
| abstract_inverted_index.nodes | 8 |
| abstract_inverted_index.other | 248 |
| abstract_inverted_index.radii | 170 |
| abstract_inverted_index.where | 4, 127 |
| abstract_inverted_index.works | 32 |
| abstract_inverted_index.λmin | 87, 100 |
| abstract_inverted_index.(GSP). | 30 |
| abstract_inverted_index.assume | 52 |
| abstract_inverted_index.biased | 54 |
| abstract_inverted_index.binary | 226 |
| abstract_inverted_index.choose | 72 |
| abstract_inverted_index.chosen | 10, 143 |
| abstract_inverted_index.derive | 206 |
| abstract_inverted_index.employ | 33 |
| abstract_inverted_index.error. | 254 |
| abstract_inverted_index.famous | 195 |
| abstract_inverted_index.faster | 241 |
| abstract_inverted_index.linear | 66 |
| abstract_inverted_index.needed | 134 |
| abstract_inverted_index.number | 78, 131 |
| abstract_inverted_index.scheme | 41, 60 |
| abstract_inverted_index.select | 43 |
| abstract_inverted_index.signal | 28, 39 |
| abstract_inverted_index.smooth | 19 |
| abstract_inverted_index.solves | 62 |
| abstract_inverted_index.square | 37 |
| abstract_inverted_index.strong | 191 |
| abstract_inverted_index.subset | 6 |
| abstract_inverted_index.system | 64 |
| abstract_inverted_index.target | 145, 222 |
| abstract_inverted_index.NP-hard | 196 |
| abstract_inverted_index.achieve | 115 |
| abstract_inverted_index.amounts | 151 |
| abstract_inverted_index.bearing | 190 |
| abstract_inverted_index.centers | 161 |
| abstract_inverted_index.collect | 12 |
| abstract_inverted_index.convert | 120 |
| abstract_inverted_index.enables | 203 |
| abstract_inverted_index.extreme | 47 |
| abstract_inverted_index.further | 180 |
| abstract_inverted_index.instead | 95 |
| abstract_inverted_index.matrix. | 113, 178 |
| abstract_inverted_index.problem | 25, 150, 189 |
| abstract_inverted_index.samples | 13, 44, 73, 133 |
| abstract_inverted_index.scaling | 167 |
| abstract_inverted_index.schemes | 245, 251 |
| abstract_inverted_index.search. | 227 |
| abstract_inverted_index.signal, | 21 |
| abstract_inverted_index.Instead, | 50 |
| abstract_inverted_index.Previous | 31 |
| abstract_inverted_index.coverage | 188 |
| abstract_inverted_index.existing | 243 |
| abstract_inverted_index.explicit | 90 |
| abstract_inverted_index.left-end | 106 |
| abstract_inverted_index.maximize | 83, 94 |
| abstract_inverted_index.minimize | 75, 129 |
| abstract_inverted_index.problem, | 126 |
| abstract_inverted_index.problem. | 200 |
| abstract_inverted_index.sampling | 1, 237, 244, 250 |
| abstract_inverted_index.shifting | 158 |
| abstract_inverted_index.smallest | 85, 105 |
| abstract_inverted_index.unbiased | 35 |
| abstract_inverted_index.Laplacian | 56 |
| abstract_inverted_index.algorithm | 210, 238 |
| abstract_inverted_index.condition | 77 |
| abstract_inverted_index.equations | 67 |
| abstract_inverted_index.expensive | 46 |
| abstract_inverted_index.intuitive | 186 |
| abstract_inverted_index.left-ends | 140 |
| abstract_inverted_index.sampling, | 164 |
| abstract_inverted_index.Gershgorin | 109, 138 |
| abstract_inverted_index.algorithm. | 217 |
| abstract_inverted_index.designated | 102 |
| abstract_inverted_index.disc-based | 236 |
| abstract_inverted_index.eigenvalue | 86, 91 |
| abstract_inverted_index.optimizing | 153 |
| abstract_inverted_index.processing | 29 |
| abstract_inverted_index.selection, | 3 |
| abstract_inverted_index.similarity | 174 |
| abstract_inverted_index.Experiments | 228 |
| abstract_inverted_index.appropriate | 221 |
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| abstract_inverted_index.coefficient | 81 |
| abstract_inverted_index.efficiently | 224 |
| abstract_inverted_index.eigenvector | 48 |
| abstract_inverted_index.fundamental | 24 |
| abstract_inverted_index.lower-bound | 144 |
| abstract_inverted_index.operations: | 156 |
| abstract_inverted_index.outperforms | 247 |
| abstract_inverted_index.reconstruct | 15 |
| abstract_inverted_index.reinterpret | 181 |
| abstract_inverted_index.resemblance | 192 |
| abstract_inverted_index.computation, | 92 |
| abstract_inverted_index.computation. | 49 |
| abstract_inverted_index.efficiently, | 117 |
| abstract_inverted_index.optimization | 122 |
| abstract_inverted_index.Circumventing | 89 |
| abstract_inverted_index.approximation | 209, 216 |
| abstract_inverted_index.error-bounded | 215 |
| abstract_inverted_index.substantially | 240 |
| abstract_inverted_index.Algebraically, | 147 |
| abstract_inverted_index.reconstruction | 40, 253 |
| abstract_inverted_index.regularization | 57 |
| abstract_inverted_index.transformation | 175 |
| abstract_inverted_index.reconstruction. | 69 |
| abstract_inverted_index.reinterpretation | 202 |
| abstract_inverted_index.matrix---specifically, | 82 |
| abstract_inverted_index.eigen-decomposition-free | 249 |
| cited_by_percentile_year.max | 99 |
| cited_by_percentile_year.min | 98 |
| countries_distinct_count | 4 |
| institutions_distinct_count | 5 |
| citation_normalized_percentile.value | 0.95588183 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |