Comparison of Biological Graph Alignment Algorithms With Hyperbolic Heterophilic Deep Graph Learning-Based Approach

This work proposes codebook encodings for graph networks that operate on hyperbolic manifolds. Where graph networks commonly learn node representations in Euclidean space, recent work has provided a generalization to Riemannian manifolds, with a particular focus on the hyperbolic space. Expressive node representations are obtained by repeatedly performing a logarithmic map, followed by message passing in the tangent space and an exponential map back to the manifold at hand. Where current hyperbolic graph approaches predominantly focus on node representation, we propose a way to aggregate over nodes for graph-level inference. We introduce Hyperbolic Graph Codebooks, a family of graph encodings where a shared codebook is learned and used to aggregate over nodes. The resulting representations are permutation invariant and fixed-size, yet expressive. We show how to obtain zeroth-order codebook encodings through soft assignments over hyperbolic distances, first-order encodings with anchored logarithmic mappings, and second-order encodings by computing variance information in the tangent space. Empirically, we highlight the effectiveness of our approach, especially when few examples and embedding dimensions are available.

Hyperbolic spaces offer a rich setup to learn embeddings with superior properties that have been leveraged in areas such as computer vision, natural language processing and computational biology. Recently, several hyperbolic approaches have been proposed to learn robust representations for users and items in the recommendation setting. However, these approaches don’t capture the higher order relationships that typically exist in the recommendation domain. Graph convolutional neural networks (GCNs) on the other hand excel at capturing higher order information by applying multiple levels of aggregation to local representations. In this paper we combine these frameworks in a novel way, by proposing a hyperbolic GCN model for collaborative filtering. We demonstrate that our model can be effectively learned with a margin ranking loss, and show that hyperbolic space has desirable properties under the rank margin setting. At test time, inference in our model is done using the hyperbolic distance which preserves the structure of the learned space. We conduct extensive empirical analysis on three public benchmarks and compare against a large set of baselines. Our approach achieves highly competitive results and outperforms leading baselines including the Euclidean GCN counterpart. We further study the properties of the learned hyperbolic embeddings and show that they offer meaningful insights into the data. Full code for this work is available here: https://github.com/layer6ai-labs/HGCF.

The problem of graph alignment is to find corresponding nodes between a pair of graphs. Past work has treated the problem in a monolithic fashion, with the graph as input and the alignment as output, offering limited opportunities to adapt the algorithm to task requirements or input graph characteristics. Recently, node embedding techniques are utilized for graph alignment. In this paper, we study two state-of-the-art graph alignment algorithms utilizing node representations, CONE-Align and GRASP, and describe them in terms of an overarching modular framework. In a targeted experimental study, we exploit this modularity to develop enhanced algorithm variants that are more effective in the alignment task.

This paper estimates a non-parametric production frontier for a population of 117 corn/livestock farms in the Corn Belt region in 1987, employing a hyperbolic graph efficiency approach. There are 7 outputs, 39 variable inputs, 4 fixed inputs, and one “bad” input (residual nitrogen). Three graph efficiency models are estimated. A profit maximization model is specified to estimate a production frontier constrained only by the fixed factors. Two other models involving tax constraints are also estimated. One involves a tax directly on nitrogen and the other involves a tax directly on residual nitrogen, making the disposal of residual nitrogen costly. The nitrogen tax constraint is more effective in reducing residual nitrogen loadings and causes a larger reduction in income than the residual tax constraint.

The effects of privatization on return to the dollar: A case study on technical efficiency, and price distortions of Taiwan’s intercity bus services

A new memetic algorithm for multiple graph alignment

Recently the study of the complex system of connections in neural systems, i.e. the connectome, has gained a central role in neurosciences. The modeling and analysis of connectomes is therefore a growing area. Here we focus on the representation of connectomes by using graph theory formalisms. Macroscopic human brain connectomes are usually derived from neuroimages, the analyzed brains are co-registered in the image domain and brought to a common anatomical space. An atlas is then applied in order to define anatomically meaningful regions that will serve as the nodes of the network and this process is referred to as parcellation. The atlas-based parcellations present some known limitations in cases of early brain development and abnormal anatomy. Consequently, it has been recently proposed to perform atlas-free random brain parcellation into nodes and align brains in the network space instead of the anatomical image space, as a way to deal with the unknown correspondences of the parcels. Such process requires modeling of the brain using graph theory and the subsequent comparison of the structure of graphs. The latter step may be modeled as a graph alignment (GA) problem. In this work, we first define the problem formally, then we test some existing state of the art aligners on diffusion MRI-derived brain networks, and we compare the performances. The results confirm that GA algorithms may be applied in cases of atlas-free parcellation for a fully network-driven comparison of connectomes.

Graph alignment refers to the problem of finding a bijective mapping across vertices of two graphs such that, if two nodes are connected in the first graph, their images are connected in the second graph. This problem arises in many fields, such as computational biology, social sciences, and computer vision and is often cast as a quadratic assignment problem (QAP). Most standard graph alignment methods consider an optimization that maximizes the number of matches between the two graphs, ignoring the effect of mismatches. We propose a generalized graph alignment formulation that considers both matches and mismatches in a standard QAP formulation. This modification can have a major impact in aligning graphs with different sizes and heterogeneous edge densities. Moreover, we propose two methods for solving the generalized graph alignment problem based on spectral decomposition of matrices. We compare the performance of proposed methods with some existing graph alignment algorithms including Natalie2, GHOST, IsoRank, NetAlign, Klau's approach as well as a semidefinite programming-based method over various synthetic and real graph models. Our proposed method based on simultaneous alignment of multiple eigenvectors leads to consistently good performance in different graph models. In particular, in the alignment of regular graph structures, which is one of the most difficult graph alignment cases, our proposed method significantly outperforms other methods.

A key issue in software evolution analysis is being able to compute evolutionary change accurately and with rich semantics. This dissertation describes a mathematical framework for enabling accurate computation of semantic evolutionary change. It is based on graphs for representing software semantics, graph transformations for modeling evolution, and effects of graph transformations for capturing evolutionary change. We formulate the notions of evolution sets and the evolution distance to measure evolutionary change. Then, we define an appropriate notion of optimal graph alignment to compute evolutionary change accurately. Establishing a rigorous foundation for computing evolutionary change is important for developing powerful automated tools for software evolution analysis. Cost estimation, software merging, reliability analysis, clone detection, incremental testing, validation and other software applications can benefit from precise computation of evolutionary change. A rigorous foundation also allows leveraging the extensive research on graph alignments to advance software engineering. We have created a framework for experimental evaluation of graph alignment algorithms. The framework includes a graph testbed, an accuracy metric, and a graph alignment visualization (GAV) mechanism. The framework is targeted at applications where a precise computation of evolutionary change from one system to the next is needed to reveal valuable knowledge about the system and its evolution. The accuracy metric is based on a new measure for graph difference and a new notion of optimality of graph alignment. The metric is designed to measure the degree to which an alignment is inaccurate, that is the degree to which it reports spurious differences. Such a metric is meaningful for estimating the efficiency of and resources necessary for many software evolution analyses.

What is the best way to match the nodes of two graphs? This graph alignment problem generalizes graph isomorphism and arises in applications from social network analysis to bioinformatics. Some solutions assume that auxiliary information on known matches or node or edge attributes is available, or utilize arbitrary graph features. Such methods fare poorly in the pure form of the problem, in which only graph structures are given. Other proposals translate the problem to one of aligning node embeddings, yet, by doing so, provide only a single-scale view of the graph. In this article, we transfer the shape-analysis concept of functional maps from the continuous to the discrete case, and treat the graph alignment problem as a special case of the problem of finding a mapping between functions on graphs. We present GRASP, a method that first establishes a correspondence between functions derived from Laplacian matrix eigenvectors, which capture multiscale structural characteristics, and then exploits this correspondence to align nodes. We enhance the basic form of GRASP by altering two of its components, namely the embedding method and the assignment procedure it employs, leveraging its modular, hence adaptable design. Our experimental study, featuring noise levels higher than anything used in previous studies, shows that the enhanced form of GRASP outperforms scalable state-of-the-art methods for graph alignment across noise levels and graph types, and performs competitively with respect to the best non-scalable ones. We include in our study another modular graph alignment algorithm, CONE, which is also adaptable thanks to its modular nature, and show it can manage graphs with skewed power-law degree distributions.

Protein–protein interaction creates a complex relation among molecular organs. The pivotal functionalities among cells depend on these interactions. In the light of computational biology (CB), it is possible to retrieve the exact information regarding these relationships. The global alignments among proteins are more important. Toward the development of the PPI network analysis, various methods such as heuristics, evolutionary, probabilistic, semi-probabilistic, spectral graph analysis and mapping methods have been developed and this is an ongoing process of progress. Some remarkable contributions to the PPI global network alignments are Common neighbors-based global GRAph (C-GRAAL), GRAph ALigner (GRAAL), Hungarian algorithm-based GRAAL (H-GRAAL), Matching-based GRAph aligner (M-GRAAL), IsoRankN, IsoRank, Scalable Global alignment algorithm, SMETENA, (software package) and GraphCrunch 2 (software package). All the mentioned algorithms and software package mentioned above have tried to address the best illustration and mapping between protein networks for global protein network alignment. For simplicity we avoid local sequence alignment methods and algorithms. For experimental data analysis, five eukaryotic species such as C. elegans (CE), D. melanogaster (DM), S. cerevisiae (SC), H. sapiens (HS) and M. musculus (MM) have been considered.

Chapter 2 - Multi-case-based reasoning by syntactic-semantic alignment and discourse analysis

Scene Graph Generation (SGG) aims to extract entities, predicates and their semantic structure from images, enabling deep understanding of visual content, with many applications such as visual reasoning and image retrieval. Nevertheless, existing SGG methods require millions of manually annotated bounding boxes for training, and are computationally inefficient, as they exhaustively process all pairs of object proposals to detect predicates. In this paper, we address those two limitations by first proposing a generalized formulation of SGG, namely Visual Semantic Parsing, which disentangles entity and predicate recognition, and enables sub-quadratic performance. Then we propose the Visual Semantic Parsing Network, VSPNet, based on a dynamic, attention-based, bipartite message passing framework that jointly infers graph nodes and edges through an iterative process. Additionally, we propose the first graph-based weakly supervised learning framework, based on a novel graph alignment algorithm, which enables training without bounding box annotations. Through extensive experiments, we show that VSPNet outperforms weakly supervised baselines significantly and approaches fully supervised performance, while being several times faster. We publicly release the source code of our method.

Network alignment, the process of finding correspondences between nodes in different graphs, has many scientific and industrial applications. Existing unsupervised network alignment methods find suboptimal alignments that break up node neighborhoods, i.e. do not preserve matched neighborhood consistency. To improve this, we propose CONE-Align, which models intra-network proximity with node embeddings and uses them to match nodes across networks after aligning the embedding subspaces. Experiments on diverse, challenging datasets show that CONE-Align is robust and obtains 19.25% greater accuracy on average than the best-performing state-of-the-art graph alignment algorithm in highly noisy settings.

Complex proteoforms contain various primary structural alterations resulting from variations in genes, RNA, and proteins. Top-down mass spectrometry is commonly used for analyzing complex proteoforms because it provides whole sequence information of the proteoforms. Proteoform identification by top-down mass spectral database search is a challenging computational problem because the types and/or locations of some alterations in target proteoforms are in general unknown. Although spectral alignment and mass graph alignment algorithms have been proposed for identifying proteoforms with unknown alterations, they are extremely slow to align millions of spectra against tens of thousands of protein sequences in high throughput proteome level analyses. Many software tools in this area combine efficient protein sequence filtering algorithms and spectral alignment algorithms to speed up database search. As a result, the performance of these tools heavily relies on the sensitivity and efficiency of their filtering algorithms. Here, we propose two efficient approximate spectrum-based filtering algorithms for proteoform identification. We evaluated the performances of the proposed algorithms and four existing ones on simulated and real top-down mass spectrometry data sets. Experiments showed that the proposed algorithms outperformed the existing ones for complex proteoform identification. In addition, combining the proposed filtering algorithms and mass graph alignment algorithms identified many proteoforms missed by ProSightPC in proteome-level proteoform analyses.