# Metric Distribution to Vector: Constructing Data Representation via Broad-Scale Discrepancies

arXiv: https://arxiv.org/abs/2210.00415 · HTML: https://mlsanity.com/paper/2210.00415/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 61 references that are in the map.
- First posted on arXiv 2 Oct 2022.

## Builds on (most cited first, 27 of 27)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [graph2vec: Learning Distributed Representations of Graphs](https://mlsanity.com/paper/1707.05005/) (2017)
- [No Fuss Distance Metric Learning using Proxies](https://mlsanity.com/paper/1703.07464/) (2017)
- [SoftTriple Loss: Deep Metric Learning Without Triplet Sampling](https://mlsanity.com/paper/1909.05235/) (2019)
- [A Survey on Graph Kernels](https://mlsanity.com/paper/1903.11835/) (2019)
- [Wasserstein Weisfeiler-Lehman Graph Kernels](https://mlsanity.com/paper/1906.01277/) (2019)
- [Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties](https://mlsanity.com/paper/1811.02834/) (2018)
- [AutoGCL: Automated Graph Contrastive Learning via Learnable View Generators](https://mlsanity.com/paper/2109.10259/) (2021)
- [Hypergraph Contrastive Collaborative Filtering](https://mlsanity.com/paper/2204.12200/) (2022)
- [Learning metrics for persistence-based summaries and applications for graph classification](https://mlsanity.com/paper/1904.12189/) (2019)
- [Anonymous Walk Embeddings](https://mlsanity.com/paper/1805.11921/) (2018)
- [Few-Shot Learning with Global Class Representations](https://mlsanity.com/paper/1908.05257/) (2019)
- [An Optimal Transport approach for the Schr"odinger bridge problem and convergence of Sinkhorn algorithm](https://mlsanity.com/paper/1911.06850/) (2019)
- [Fewer is More: A Deep Graph Metric Learning Perspective Using Fewer Proxies](https://mlsanity.com/paper/2010.13636/) (2020)
- [Persistence Fisher Kernel: A Riemannian Manifold Kernel for Persistence Diagrams](https://mlsanity.com/paper/1802.03569/) (2018)
- [Faster Kernels for Graphs with Continuous Attributes via Hashing](https://mlsanity.com/paper/1610.00064/) (2016)
- [A gradient descent perspective on Sinkhorn](https://mlsanity.com/paper/2002.03758/) (2020)
- [Learning to Compare Relation: Semantic Alignment for Few-Shot Learning](https://mlsanity.com/paper/2003.00210/) (2020)
- [Learning subtree pattern importance for Weisfeiler-Lehmanbased graph kernels](https://mlsanity.com/paper/2106.04739/) (2021)
- [Distance Metric Learning for Graph Structured Data](https://mlsanity.com/paper/2002.00727/) (2020)
- [Trading Hard Negatives and True Negatives: A Debiased Contrastive Collaborative Filtering Approach](https://mlsanity.com/paper/2204.11752/) (2022)

## Abstract (arXiv)

Graph embedding provides a feasible methodology to conduct pattern classification for graph-structured data by mapping each data into the vectorial space. Various pioneering works are essentially coding method that concentrates on a vectorial representation about the inner properties of a graph in terms of the topological constitution, node attributions, link relations, etc. However, the classification for each targeted data is a qualitative issue based on understanding the overall discrepancies within the dataset scale. From the statistical point of view, these discrepancies manifest a metric distribution over the dataset scale if the distance metric is adopted to measure the pairwise similarity or dissimilarity. Therefore, we present a novel embedding strategy named MetricDistribution2vec to extract such distribution characteristics into the vectorial representation for each data. We demonstrate the application and effectiveness of our representation method in the supervised prediction tasks on extensive real-world structural graph datasets. The results have gained some unexpected increases compared with a surge of baselines on all the datasets, even if we take the lightweight models as classifiers. Moreover, the proposed methods also conducted experiments in Few-Shot classification scenarios, and the results still show attractive discrimination in rare training samples based inference.