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Random Projections of Sparse Adjacency Matrices

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Frank Qiu

Data Structures and Algorithms · Submitted 4 Sep 2023

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

The authors' main claim We conclude by characterizing our random projection as a distance-preserving map of adjacency matrices analogous to the usual Johnson-Lindenstrauss map.

how it is stated · asserted 1.00 read the record →

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arXiv ID2309.01360 (version 1)
Pith ID6GJJFI7L, Pith's permanent record of this paper and its review
CitationFrank Qiu. "Random Projections of Sparse Adjacency Matrices." arXiv:2309.01360 (2023). https://pith.science/paper/6GJJFI7L
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,256 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.20 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.02 · states quantitative result 0.71 · compares with prior results 0.28 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We analyze a random projection method for adjacency matrices, studying its utility in representing sparse graphs. We show that these random projections retain the functionality of their underlying adjacency matrices while having extra properties that make them attractive as dynamic graph representations. In particular, they can represent graphs of different sizes and vertex sets in the same space, allowing for the aggregation and manipulation of graphs in a unified manner. We also provide results on how the size of the projections need to scale in order to preserve accurate graph operations, showing that the size of the projections can scale linearly with the number of vertices while accurately retaining first-order graph information. We conclude by characterizing our random projection as a distance-preserving map of adjacency matrices analogous to the usual Johnson-Lindenstrauss map.

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 We analyze a random projection method for adjacency matrices, studying its utility in representing sparse graphs. contribution 0.98 0.90 0.05 asserted 0.65
s1 We show that these random projections retain the functionality of their underlying adjacency matrices while having extra properties that make them attractive as dynamic graph representations. result 0.88 0.93 0.41 asserted 1.00
s2 In particular, they can represent graphs of different sizes and vertex sets in the same space, allowing for the aggregation and manipulation of graphs in a unified manner. result 0.55 0.68 0.14 asserted 0.88
s3 We also provide results on how the size of the projections need to scale in order to preserve accurate graph operations, showing that the size of the projections can scale linearly with the number of vertices while accurately retaining first-order graph information. result 0.99 0.94 0.19 asserted 1.00
s4 We conclude by characterizing our random projection as a distance-preserving map of adjacency matrices analogous to the usual Johnson-Lindenstrauss map. interpretation 0.84 0.89 0.67 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.78 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

We analyze a random projection method for adjacency matrices, studying its utility in representing sparse graphs. We show that these random projections retain the functionality of their underlying adjacency matrices while having extra properties that make them attractive as dynamic graph representations. In particular, they can represent graphs of different sizes and vertex sets in the same space, allowing for the aggregation and manipulation of graphs in a unified manner. We also provide results on how the size of the projections need to scale in order to preserve accurate graph operations, showing that the size of the projections can scale linearly with the number of vertices while accurately retaining first-order graph information. We conclude by characterizing our random projection as a distance-preserving map of adjacency matrices analogous to the usual Johnson-Lindenstrauss map.

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