A high order proximity measure for linear network embedding

Year 2022, Volume: 11 Issue: 3, 477 - 483, 18.07.2022

Mustafa Coskun

https://doi.org/10.28948/ngumuh.957488

Cited By: 2

Abstract

Graph representationion learning (network embedding) is at the heart of network analytics techniques to reveal and examine the complex dependencies among nodes. Owing its importance, many computational methods have been proposed to solve a large volume of learning tasks on graphs, such as node classification, link prediction and clustering. Among various network embedding techniques, linear Matrix Factorization-based (MF) network embedding approaches have demonstrated to be very effective and efficient as they can be stated as singular value decomposition (SVD) problem, which can be efficiently solved by off-the-shelf eigen-solvers, such as Lanczos method. Despite the effectiveness of these linear methods, they rely on high order proximity measures, i.e., random walk restarts (RWR) and/or Katz, which have their own limitations, such as degree biasness, hyper-parameter dependency. In this paper, to alleviate the RWR and Katz depended high proximity usage in the linear embedding methods, we propose an algorithm that uses label propagation and shift-and-invert approach to resort RWR and Katz related problems. Testing our methods on real-networks for link prediction task, we show that our algorithm drastically improves link prediction performance of network embedding comparing against an embedding approach that uses RWR and Katz high order proximity measures.

Keywords

Graph representation learning, Node embedding, Linear embedding

Ağ gömülümü için yüksek boyutlu yakınsaklık ölçüsü

Abstract

Ağ gömülümü öğrenme problemi bir çok ağ analizi gerektiren problemin ifade ve çözümlenmesi için çok büyük önem arz etmektedir. Bu bağlamda, ağ içerisinde bulunan düğümlerin birbirleri ile olan gizli ilişkilerini açığa çıkarmak için, son yıllarda ağ gömülümü öğrenme problemi çokça çalışılmaktadır. Bu gizli ilişkinin açığa çıkarılması, bağlantı tahminleme, öbekleme ve sınıflandırma gibi öğreme problemlerinin daha iyi çözümlenmesinde kullanılmaktadır. Ağ gömülümünü öğrenmek için, farklı yaklaşım ve algoritmalar geliştirilmiş olsada, matris ayrışımı bazlı algoritmalar hızlı olmasından dolayı araştırmacılar tarafından büyük ilgi görmekteler. Matris ayraşım bazlı ağ gömülümü öğrenmede genel anlamı ile yüksek dereceli yakınlık ölçüleri kullanılmaktadır, örneğin random walk with restart (RWR) ve Katz ölçüleri. Ancak, bu ölçülerle yapılan ağ benzerlik ölçüleri matris ayrışımında sıfıra karşılık gelen eigenvectors (özvektörler) üretebilmektedir. Bu ise öğrenilen ağ gömülümün yanlış olmasına sebeb olmaktadır. Bu prolemi aşmak için, bu makalede shift-and-invert (kaydır ve tersini al) yaklaşımına dayanarak bir yaklaşım önerdik. Bağlantı tahimini baz problemi alarak, geliştirdiğimiz algoritmayı üç gerçek veride kullanık ve sonuçların var olan matris ayrışımlı algoritmasını bütün metrik değerlendirmelerinde var olan algoritmanın performansını ciddi miktarda artırdığını gözlemledik.

Keywords

Ağ gömülümü, Düğüm gömülümü, Lineer ağ gömülümü

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