Natalie 2.0: Sparse Global Network Alignment as a Special Case of Quadratic Assignment

Abstract

Data on molecular interactions is increasing at a tremendous pace, while the development of solid methods for analyzing this network data is still lagging behind. This holds in particular for the field of comparative network analysis, where one wants to identify commonalities between biological networks. Since biological functionality primarily operates at the network level, there is a clear need for topology-aware comparison methods. We present a method for global network alignment that is fast and robust and can flexibly deal with various scoring schemes taking both node-to-node correspondences as well as network topologies into account. We exploit that network alignment is a special case of the well-studied quadratic assignment problem (QAP). We focus on sparse network alignment, where each node can be mapped only to a typically small subset of nodes in the other network. This corresponds to a QAP instance with a symmetric and sparse weight matrix. We obtain strong upper and lower bounds for the problem by improving a Lagrangian relaxation approach and introduce the open source software tool Natalie 2.0, a publicly Algorithms 2015, 8 1036 available implementation of our method. In an extensive computational study on protein interaction networks for six different species, we find that our new method outperforms alternative established and recent state-of-the-art methods.

A family of tractable graph metrics

“…We briefly review here additional impementation details about the algorithms summarized in Table 2. • NetAlignBP, IsoRank, SparseIsoRank and NetAlignMR are described by (Bayati et al 2009). Natalie is described in (El-Kebir et al 2015). All five algorithms output P ∈ P n .…”

“…However, finding an optimal permutation P is notoriously hard; graph isomorphism, which is equivalent to deciding if there exists a permutation P such that AP = PB (for both adjacency and path matrices), is famously a problem that is neither known to be in P nor shown to be NP-hard (Babai 2016). There is a large and expanding literature on scalable heuristics to estimate the optimal permutation P (Klau 2009;Bayati et al 2009;Lyzinski et al 2016;El-Kebir et al 2015). Despite their computational advantages, unfortunately, using them to approximate d P n (A, B) breaks the metric property.…”

Active Network Alignment

“…Numerous methods have been developed for the non-active networkalignment problem. e problem has drawn particular a ention in the bioinformatics domain [12,15,17,21,24,27,37], due to the interest in the the task of matching protein-protein interaction networks; a recent survey in the area is provided by Elmsallati et al [13]. Non-active network alignment methods are classi ed according to how the matching cost is de ned and how they algorithmically proceed to nding a solution.…”

“…Finding an alignment is o en reduced into the problem of nding a matching on a weighted bipartite graph H = (V s , V t , E h ), where the weights incorporate both a ribute and structural similarities. Examples of such methods include L G [27], N [12,17], N A MP++ [3], and I R [37]. In this paper we propose a new approach for active network alignment, which can be employed on top of any matching-based (non-active) network-alignment method.…”

Network Alignment by Discrete Ollivier-Ricci Flow

“…Here similarity can be either attribute similarity or structural similarity (quantifying their positions in the network). The two graphs are aligned by taking a matching of high similarity in graph H. Many algorithms use this approach and they differ by how to define node similarity: L-Graal [46], Natalie [14], NetAl-ignMP++ [6], NSD [35], and IsoRank [59]. In this paper, our main contribution is to provide a new method to compute node structural similarity using the idea of graph curvature and curvature flow.…”