Learning representations of nodes in a low dimensional space is a crucial task with many interesting applications in network analysis, including link prediction and node classification. Two popular approaches for this problem include matrix factorization and random walk-based models. In this paper, we aim to bring together the best of both worlds, towards learning latent node representations. In particular, we propose a weighted matrix factorization model which encodes random walk-based information about the nodes of the graph. The main benefit of this formulation is that it allows to utilize kernel functions on the computation of the embeddings. We perform an empirical evaluation on real-world networks, showing that the proposed model outperforms baseline node embedding algorithms in two downstream machine learning tasks.
Network embedding has proved extremely useful in a variety of network analysis tasks such as node classification, link prediction, and network visualization. Almost all the existing network embedding methods learn to map the node IDs to their corresponding node embeddings. This design principle, however, hinders the existing methods from being applied in real cases. Node ID is not generalizable and, thus, the existing methods have to pay great effort in cold-start problem. The heterogeneous network usually requires extra work to encode node types, as node type is not able to be identified by n…
Rutgers University(罗格斯大学);University of Delaware(特拉华大学)
Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is still ill-posed and the state-of-the-art methods are heavily based on heuristics. Here, we present a novel theoretical kernel-based framework for node classification that can bridge the gap between these two representation learning problems on graphs. Our approach is motivated by graph kernel methodology but extended to learn the node representations capturin…
Soochow University(苏州大学);Georgia Institute of Technology(佐治亚理工学院);State Key Laboratory of Mathematical Engineering and Advanced Computing(数学工程与先进计算国家重点实验室)
Network representation learning (NRL) advances the conventional graph mining of social networks, knowledge graphs, and complex biomedical and physics information networks. Over dozens of network representation learning algorithms have been reported in the literature. Most of them focus on learning node embeddings for homogeneous networks, but they differ in the specific encoding schemes and specific types of node semantics captured and used for learning node embedding. This survey paper reviews the design principles and the different node embedding techniques for network representation learnin…
With the increasing popularity of graph-based methods for dimensionality reduction and representation learning, node embedding functions have become important objects of study in the literature. In this paper, we take an axiomatic approach to understanding node embedding methods, first stating three properties for embedding dissimilarity networks, then proving that all three cannot be satisfied simultaneously by any node embedding method. Similar to existing results on the impossibility of clustering under certain axiomatic assumptions, this points to fundamental difficulties inherent to node …
Node embedding is the task of extracting informative and descriptive features over the nodes of a graph. The importance of node embeddings for graph analytics, as well as learning tasks such as node classification, link prediction and community detection, has led to increased interest on the problem leading to a number of recent advances. Much like PCA in the feature domain, node embedding is an inherently \emph{unsupervised} task; in lack of metadata used for validation, practical methods may require standardization and limiting the use of tunable hyperparameters. Finally, node embedding meth…
Ghent University(根特大学);Technical University of Munich(慕尼黑工业大学)
Node embedding methods map network nodes to low dimensional vectors that can be subsequently used in a variety of downstream prediction tasks. The popularity of these methods has grown significantly in recent years, yet, their robustness to perturbations of the input data is still poorly understood. In this paper, we assess the empirical robustness of node embedding models to random and adversarial poisoning attacks. Our systematic evaluation covers representative embedding methods based on Skip-Gram, matrix factorization, and deep neural networks. We compare edge addition, deletion and rewiri…
IBM Research(IBM研究院);Indian Institute of Science(印度科学学院)
Network representation learning has traditionally been used to find lower dimensional vector representations of the nodes in a network. However, there are very important edge driven mining tasks of interest to the classical network analysis community, which have mostly been unexplored in the network embedding space. For applications such as link prediction in homogeneous networks, vector representation (i.e., embedding) of an edge is derived heuristically just by using simple aggregations of the embeddings of the end vertices of the edge. Clearly, this method of deriving edge embedding is subo…
In this work, we introduce a hypergraph representation learning framework called Hypergraph Neural Networks (HNN) that jointly learns hyperedge embeddings along with a set of hyperedge-dependent embeddings for each node in the hypergraph. HNN derives multiple embeddings per node in the hypergraph where each embedding for a node is dependent on a specific hyperedge of that node. Notably, HNN is accurate, data-efficient, flexible with many interchangeable components, and useful for a wide range of hypergraph learning tasks. We evaluate the effectiveness of the HNN framework for hyperedge predict…
The fundamental goal of self-supervised learning (SSL) is to produce useful representations of data without access to any labels for classifying the data. Modern methods in SSL, which form representations based on known or constructed relationships between samples, have been particularly effective at this task. Here, we aim to extend this framework to incorporate algorithms based on kernel methods where embeddings are constructed by linear maps acting on the feature space of a kernel. In this kernel regime, we derive methods to find the optimal form of the output representations for contrastiv…
Technical University of Munich(慕尼黑工业大学);Mercateo AG(Mercateo股份公司)
In this paper, we study how to simultaneously learn two highly correlated tasks of graph analysis, i.e., community detection and node representation learning. We propose an efficient generative model called VECoDeR for jointly learning Variational Embeddings for Community Detection and node Representation. VECoDeR assumes that every node can be a member of one or more communities. The node embeddings are learned in such a way that connected nodes are not only "closer" to each other but also share similar community assignments. A joint learning framework leverages community-aware node embedding…
Local graph neighborhood sampling is a fundamental computational problem that is at the heart of algorithms for node representation learning. Several works have presented algorithms for learning discrete node embeddings where graph nodes are represented by discrete features such as attributes of neighborhood nodes. Discrete embeddings offer several advantages compared to continuous word2vec-like node embeddings: ease of computation, scalability, and interpretability. We present LoNe Sampler, a suite of algorithms for generating discrete node embeddings by Local Neighborhood Sampling, and addre…
Graph neural networks (GNNs) are deep learning models designed specifically for graph data, and they typically rely on node features as the input to the first layer. When applying such a type of network on the graph without node features, one can extract simple graph-based node features (e.g., number of degrees) or learn the input node representations (i.e., embeddings) when training the network. While the latter approach, which trains node embeddings, more likely leads to better performance, the number of parameters associated with the embeddings grows linearly with the number of nodes. It is…
Quantum kernel methods, i.e., kernel methods with quantum kernels, offer distinct advantages as a hybrid quantum-classical approach to quantum machine learning (QML), including applicability to Noisy Intermediate-Scale Quantum (NISQ) devices and usage for solving all types of machine learning problems. Kernel methods rely on the notion of similarity between points in a higher (possibly infinite) dimensional feature space. For machine learning, the notion of similarity assumes that points close in the feature space should be close in the machine learning task space. In this paper, we discuss th…
ZBW-Leibniz Information Centre for Economics(莱布尼茨经济信息中心);Indian Institute of Technology Patna(印度理工学院巴特那分校)
Traditional Collaborative Filtering (CF) based methods are applied to understand the personal preferences of users/customers for items or products from the rating matrix. Usually, the rating matrix is sparse in nature. So there are some improved variants of the CF method that apply the increasing amount of side information to handle the sparsity problem. Only linear kernel or only non-linear kernel is applied in most of the available recommendation-related work to understand user-item latent feature embeddings from data. Only linear kernel or only non-linear kernel is not sufficient to learn c…
University of Tsukuba(筑波大学);National Institute of Advanced Industrial Science and Technology (AIST)(产业技术综合研究所)
Embedding graph nodes into a vector space can allow the use of machine learning to e.g. predict node classes, but the study of node embedding algorithms is immature compared to the natural language processing field because of a diverse nature of graphs. We examine the performance of node embedding algorithms with respect to graph centrality measures that characterize diverse graphs, through systematic experiments with four node embedding algorithms, four or five graph centralities, and six datasets. Experimental results give insights into the properties of node embedding algorithms, which can …
Technion, Israel Institute of Technology(以色列理工学院);eBay Research(易贝研究院)
In this work, we present a method for node embedding in temporal graphs. We propose an algorithm that learns the evolution of a temporal graph's nodes and edges over time and incorporates this dynamics in a temporal node embedding framework for different graph prediction tasks. We present a joint loss function that creates a temporal embedding of a node by learning to combine its historical temporal embeddings, such that it optimizes per given task (e.g., link prediction). The algorithm is initialized using static node embeddings, which are then aligned over the representations of a node at di…
Huawei(华为);École Polytechnique(巴黎综合理工学院);Institute Polytechnique de Paris(巴黎理工学院);AUEB(雅典经济与商业大学)
The robustness of the much-used Graph Convolutional Networks (GCNs) to perturbations of their input is becoming a topic of increasing importance. In this paper, the random GCN is introduced for which a random matrix theory analysis is possible. This analysis suggests that if the graph is sufficiently perturbed, or in the extreme case random, then the GCN fails to benefit from the node features. It is furthermore observed that enhancing the message passing step in GCNs by adding the node feature kernel to the adjacency matrix of the graph structure solves this problem. An empirical study of a G…
Skolkovo Institute of Science and Technology (Skoltech)(斯科尔科沃科学技术研究所(斯科尔科沃理工学院));Moscow Institute of Physics and Technology(莫斯科物理技术学院);Institute for Information Transmission Problems of RAS(俄罗斯科学院信息传输问题研究所)
The problem of unsupervised learning node embeddings in graphs is one of the important directions in modern network science. In this work we propose a novel framework, which is aimed to find embeddings by \textit{discriminating distributions of similarities (DDoS)} between nodes in the graph. The general idea is implemented by maximizing the \textit{earth mover distance} between distributions of decoded similarities of similar and dissimilar nodes. The resulting algorithm generates embeddings which give a state-of-the-art performance in the problem of link prediction in real-world graphs.
University of Michigan(密歇根大学);Lawrence Livermore National Laboratory(劳伦斯利弗莫尔国家实验室)
While most network embedding techniques model the relative positions of nodes in a network, recently there has been significant interest in structural embeddings that model node role equivalences, irrespective of their distances to any specific nodes. We present PhUSION, a proximity-based unified framework for computing structural and positional node embeddings, which leverages well-established methods for calculating node proximity scores. Clarifying a point of contention in the literature, we show which step of PhUSION produces the different kinds of embeddings and what steps can be used by …
Recent interest in graph embedding methods has focused on learning a single representation for each node in the graph. But can nodes really be best described by a single vector representation? In this work, we propose a method for learning multiple representations of the nodes in a graph (e.g., the users of a social network). Based on a principled decomposition of the ego-network, each representation encodes the role of the node in a different local community in which the nodes participate. These representations allow for improved reconstruction of the nuanced relationships that occur in the g…
Nodes residing in different parts of a graph can have similar structural roles within their local network topology. The identification of such roles provides key insight into the organization of networks and can be used for a variety of machine learning tasks. However, learning structural representations of nodes is a challenging problem, and it has typically involved manually specifying and tailoring topological features for each node. In this paper, we develop GraphWave, a method that represents each node's network neighborhood via a low-dimensional embedding by leveraging heat wavelet diffu…
Institute of Information Systems(信息系统研究所);Leuphana University of Lüneburg(吕讷堡大学)
Node embedding methods find latent lower-dimensional representations which are used as features in machine learning models. In the last few years, these methods have become extremely popular as a replacement for manual feature engineering. Since authors use various approaches for the evaluation of node embedding methods, existing studies can rarely be efficiently and accurately compared. We address this issue by developing a process for a fair and objective evaluation of node embedding procedures w.r.t. node classification. This process supports researchers and practitioners to compare new and…
Despite several signs of progress have been made recently, limited research has been conducted for an inductive setting where embeddings are required for newly unseen nodes -- a setting encountered commonly in practical applications of deep learning for graph networks. This significantly affects the performances of downstream tasks such as node classification, link prediction or community extraction. To this end, we propose SANNE -- a novel unsupervised embedding model -- whose central idea is to employ a transformer self-attention network to iteratively aggregate vector representations of nod…
Unsupervised Framework for Evaluating and Explaining Structural Node Embeddings of Graphs
Toronto Metropolitan University(多伦多都会大学);SGH Warsaw School of Economics(华沙经济学院);Patagona Technologies(帕塔戈纳科技公司);Simons Institute for the Theory of Computing(西蒙斯计算理论研究所)
University of North Carolina at Charlotte(北卡罗来纳大学夏洛特分校);Siemens Corporate Technology(西门子企业技术)
Recent advances in neural networks have solved common graph problems such as link prediction, node classification, node clustering, node recommendation by developing embeddings of entities and relations into vector spaces. Graph embeddings encode the structural information present in a graph. The encoded embeddings then can be used to predict the missing links in a graph. However, obtaining the optimal embeddings for a graph can be a computationally challenging task specially in an embedded system. Two techniques which we focus on in this work are 1) node embeddings from random walk based meth…
Beijing Institute of Technology(北京理工大学);Huazhong University of Science and Technology(华中科技大学)
Node classification in structural networks has been proven to be useful in many real world applications. With the development of network embedding, the performance of node classification has been greatly improved. However, nearly all the existing network embedding based methods are hard to capture the actual category features of a node because of the linearly inseparable problem in low-dimensional space; meanwhile they cannot incorporate simultaneously network structure information and node label information into network embedding. To address the above problems, in this paper, we propose a nov…
Beihang University(北京航空航天大学);Shen Yuan Honors College, Beihang University(北京航空航天大学沈元荣誉学院);Key Laboratory of Complex System Analysis, Management and Decision (Beihang University), Ministry of Education(教育部复杂系统分析与管理决策重点实验室(北京航空航天大学));Beijing Key Laboratory of Emergence Support Simulation Technologies for City Operations(北京城市运行涌现支持模拟技术重点实验室)
Newly arriving nodes in dynamics networks would gradually make the node embedding space drifted and the retraining of node embedding and downstream models indispensable. An exact threshold size of these new nodes, below which the node embedding space will be predicatively maintained, however, is rarely considered in either theory or experiment. From the view of matrix perturbation theory, a threshold of the maximum number of new nodes that keep the node embedding space approximately equivalent is analytically provided and empirically validated. It is therefore theoretically guaranteed that as …
RWTH Aachen University(亚琛工业大学);VU Amsterdam(阿姆斯特丹自由大学);GESIS - Leibniz Institute for the Social Sciences(GESIS——莱布尼茨社会科学研究所)
Data ownership and data protection are increasingly important topics with ethical and legal implications, e.g., with the right to erasure established in the European General Data Protection Regulation (GDPR). In this light, we investigate network embeddings, i.e., the representation of network nodes as low-dimensional vectors. We consider a typical social network scenario with nodes representing users and edges relationships between them. We assume that a network embedding of the nodes has been trained. After that, a user demands the removal of his data, requiring the full deletion of the corr…
University of Southern California(南加州大学);University of California, Berkeley(加州大学伯克利分校)
A network embedding consists of a vector representation for each node in the network. Its usefulness has been shown in many real-world application domains, such as social networks and web networks. Directed networks with text associated with each node, such as software package dependency networks, are commonplace. However, to the best of our knowledge, their embeddings have hitherto not been specifically studied. In this paper, we propose PCTADW-1 and PCTADW-2, two algorithms based on neural networks that learn embeddings of directed networks with text associated with each node. We create two …
The University of Edinburgh(爱丁堡大学);School of Informatics(信息学院)
We present network embedding algorithms that capture information about a node from the local distribution over node attributes around it, as observed over random walks following an approach similar to Skip-gram. Observations from neighborhoods of different sizes are either pooled (AE) or encoded distinctly in a multi-scale approach (MUSAE). Capturing attribute-neighborhood relationships over multiple scales is useful for a diverse range of applications, including latent feature identification across disconnected networks with similar attributes. We prove theoretically that matrices of node-fea…
The Hong Kong Polytechnic University(香港理工大学);University of Electronic Science and Technology of China(电子科技大学)
In this paper, the task of cross-network node classification, which leverages the abundant labeled nodes from a source network to help classify unlabeled nodes in a target network, is studied. The existing domain adaptation algorithms generally fail to model the network structural information, and the current network embedding models mainly focus on single-network applications. Thus, both of them cannot be directly applied to solve the cross-network node classification problem. This motivates us to propose an adversarial cross-network deep network embedding (ACDNE) model to integrate adversari…
Eindhoven University of Technology(埃因霍温理工大学);National Digital Switching System Engineering Technology R&D Center(国家数字交换系统工程技术研究中心)
Network embedding (NE) is playing a principal role in network mining, due to its ability to map nodes into efficient low-dimensional embedding vectors. However, two major limitations exist in state-of-the-art NE methods: role preservation and uncertainty modeling. Almost all previous methods represent a node into a point in space and focus on local structural information, i.e., neighborhood information. However, neighborhood information does not capture global structural information and point vector representation fails in modeling the uncertainty of node representations. In this paper, we pro…
We consider the question of embedding nodes with similar local neighborhoods together in embedding space, commonly referred to as "role embeddings." We propose RAE, an unsupervised framework that learns role embeddings. It combines a within-node loss function and a graph neural network (GNN) architecture to place nodes with similar local neighborhoods close in embedding space. We also propose a faster way of generating negative examples called neighbor shuffling, which quickly creates negative examples directly within batches. These techniques can be easily combined with existing GNN methods t…
University of Technology Sydney(悉尼科技大学);The University of Sydney(悉尼大学);Florida Atlantic University(佛罗里达大西洋大学)
Network embedding aims to learn a latent, low-dimensional vector representations of network nodes, effective in supporting various network analytic tasks. While prior arts on network embedding focus primarily on preserving network topology structure to learn node representations, recently proposed attributed network embedding algorithms attempt to integrate rich node content information with network topological structure for enhancing the quality of network embedding. In reality, networks often have sparse content, incomplete node attributes, as well as the discrepancy between node attribute f…
KTH Royal Institute of Technology(瑞典皇家理工学院);SEB Group(SEB集团)
Structural node embeddings, vectors capturing local connectivity information for each node in a graph, have many applications in data mining and machine learning, e.g., network alignment and node classification, clustering and anomaly detection. For the analysis of directed graphs, e.g., transactions graphs, communication networks and social networks, the capability to capture directional information in the structural node embeddings is highly desirable, as is scalability of the embedding extraction method. Most existing methods are nevertheless only designed for undirected graph. Therefore, w…
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…
Proximity preserving and structural role-based node embeddings have become a prime workhorse of applied graph mining. Novel node embedding techniques are often tested on a restricted set of benchmark datasets. In this paper, we propose a new diverse social network dataset called Twitch Gamers with multiple potential target attributes. Our analysis of the social network and node classification experiments illustrate that Twitch Gamers is suitable for assessing the predictive performance of novel proximity preserving and structural role-based node embedding algorithms.
We develop a fused matrix multiplication kernel that unifies sampled dense-dense matrix multiplication and sparse-dense matrix multiplication under a single operation called FusedMM. By using user-defined functions, FusedMM can capture almost all computational patterns needed by popular graph embedding and GNN approaches. FusedMM is an order of magnitude faster than its equivalent kernels in Deep Graph Library. The superior performance of FusedMM comes from the low-level vectorized kernels, a suitable load balancing scheme and an efficient utilization of the memory bandwidth. FusedMM can tune …
Dartmouth College(达特茅斯学院);Stony Brook University(石溪大学);Jefferies Financial Group LLC(杰富瑞金融集团有限责任公司)
Recently, there has been an interest in embedding networks in hyperbolic space, since hyperbolic space has been shown to work well in capturing graph/network structure as it can naturally reflect some properties of complex networks. However, the work on network embedding in hyperbolic space has been focused on microscopic node embedding. In this work, we are the first to present a framework to embed the structural roles of nodes into hyperbolic space. Our framework extends struct2vec, a well-known structural role preserving embedding method, by moving it to a hyperboloid model. We evaluated ou…
South China University of Technology(华南理工大学);University of California, Irvine(加州大学欧文分校)
Complex networks represented as node adjacency matrices constrains the application of machine learning and parallel algorithms. To address this limitation, network embedding (i.e., graph representation) has been intensively studied to learn a fixed-length vector for each node in an embedding space, where the node properties in the original graph are preserved. Existing methods mainly focus on learning embedding vectors to preserve nodes proximity, i.e., nodes next to each other in the graph space should also be closed in the embedding space, but do not enforce algebraic statistical properties …
Network embeddings learn to represent nodes as low-dimensional vectors to preserve the proximity between nodes and communities of the network for network analysis. The temporal edges (e.g., relationships, contacts, and emails) in dynamic networks are important for network evolution analysis, but few existing methods in network embeddings can capture the dynamic information from temporal edges. In this paper, we propose a novel dynamic network embedding method to analyze evolution patterns of dynamic networks effectively. Our method uses random walk to keep the proximity between nodes and appli…
Advanced Digital Sciences Center(高级数字科学中心);Nanyang Technological University(南洋理工大学);University of Illinois at Urbana-Champaign(伊利诺伊大学厄巴纳-香槟分校)
Most of the existing graph embedding methods focus on nodes, which aim to output a vector representation for each node in the graph such that two nodes being "close" on the graph are close too in the low-dimensional space. Despite the success of embedding individual nodes for graph analytics, we notice that an important concept of embedding communities (i.e., groups of nodes) is missing. Embedding communities is useful, not only for supporting various community-level applications, but also to help preserve community structure in graph embedding. In fact, we see community embedding as providing…
Toronto Metropolitan University(多伦多都会大学);SGH Warsaw School of Economics(华沙经济学院);Tutte Institute for Mathematics and Computing(塔特数学与计算研究所)
Graph embedding is a transformation of nodes of a graph into a set of vectors. A~good embedding should capture the graph topology, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes. If these objectives are achieved, an embedding is a meaningful, understandable, compressed representations of a network that can be used for other machine learning tools such as node classification, community detection, or link prediction. The main challenge is that one needs to make sure that embeddings describe the properties of the graphs well. As a result, selec…
Neural node embeddings have recently emerged as a powerful representation for supervised learning tasks involving graph-structured data. We leverage this recent advance to develop a novel algorithm for unsupervised community discovery in graphs. Through extensive experimental studies on simulated and real-world data, we demonstrate that the proposed approach consistently improves over the current state-of-the-art. Specifically, our approach empirically attains the information-theoretic limits for community recovery under the benchmark Stochastic Block Models for graph generation and exhibits b…
Networks have been widely used as the data structure for abstracting real-world systems as well as organizing the relations among entities. Network embedding models are powerful tools in mapping nodes in a network into continuous vector-space representations in order to facilitate subsequent tasks such as classification and link prediction. Existing network embedding models comprehensively integrate all information of each node, such as links and attributes, towards a single embedding vector to represent the node's general role in the network. However, a real-world entity could be multifaceted…
Representation learning of textual networks poses a significant challenge as it involves capturing amalgamated information from two modalities: (i) underlying network structure, and (ii) node textual attributes. For this, most existing approaches learn embeddings of text and network structure by enforcing embeddings of connected nodes to be similar. Then for achieving a modality fusion they use the similarities between text embedding of a node with the structure embedding of its connected node and vice versa. This implies that these approaches require edge information for learning embeddings a…
Dartmouth College(达特茅斯学院);Millennium Management, LLC(千禧管理有限责任公司);Georgia Institute of Technology(佐治亚理工学院)
Recent years have seen a rise in the development of representational learning methods for graph data. Most of these methods, however, focus on node-level representation learning at various scales (e.g., microscopic, mesoscopic, and macroscopic node embedding). In comparison, methods for representation learning on whole graphs are currently relatively sparse. In this paper, we propose a novel unsupervised whole graph embedding method. Our method uses spectral graph wavelets to capture topological similarities on each k-hop sub-graph between nodes and uses them to learn embeddings for the whole …
In real-world complex networks, understanding the dynamics of their evolution has been of great interest to the scientific community. Predicting future links is an essential task of social network analysis as the addition or removal of the links over time leads to the network evolution. In a network, links can be categorized as intra-community links if both end nodes of the link belong to the same community, otherwise inter-community links. The existing link-prediction methods have mainly focused on achieving high accuracy for intra-community link prediction. In this work, we propose a network…
Network embedding in heterogeneous information networks (HINs) is a challenging task, due to complications of different node types and rich relationships between nodes. As a result, conventional network embedding techniques cannot work on such HINs. Recently, metapath-based approaches have been proposed to characterize relationships in HINs, but they are ineffective in capturing rich contexts and semantics between nodes for embedding learning, mainly because (1) metapath is a rather strict single path node-node relationship descriptor, which is unable to accommodate variance in relationships, …