Efficient Approximation of Gromov-Wasserstein Distance Using Importance Sparsification
As a valid metric of metric-measure spaces, Gromov-Wasserstein (GW) distance has shown the potential for matching problems of structured data like point clouds and graphs. However, its application in practice is limited due to the high computational complexity. To overcome this challenge, we propose...
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| Vydáno v: | Journal of computational and graphical statistics Ročník 32; číslo 4; s. 1512 - 1523 |
|---|---|
| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Alexandria
Taylor & Francis
02.10.2023
Taylor & Francis Ltd |
| Témata: | |
| ISSN: | 1061-8600, 1537-2715 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | As a valid metric of metric-measure spaces, Gromov-Wasserstein (GW) distance has shown the potential for matching problems of structured data like point clouds and graphs. However, its application in practice is limited due to the high computational complexity. To overcome this challenge, we propose a novel importance sparsification method, called Spar-GW, to approximate GW distance efficiently. In particular, instead of considering a dense coupling matrix, our method leverages a simple but effective sampling strategy to construct a sparse coupling matrix and update it with few computations. The proposed Spar-GW method is applicable to the GW distance with arbitrary ground cost, and it reduces the complexity from
O
(
n
4
)
to
O
(
n
2
+
δ
)
for an arbitrary small
δ
>
0
. Theoretically, the convergence and consistency of the proposed estimation for GW distance are established under mild regularity conditions. In addition, this method can be extended to approximate the variants of GW distance, including the entropic GW distance, the fused GW distance, and the unbalanced GW distance. Experiments show the superiority of our Spar-GW to state-of-the-art methods in both synthetic and real-world tasks.
Supplementary materials
for this article are available online. |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1061-8600 1537-2715 |
| DOI: | 10.1080/10618600.2023.2165500 |