arXiv subjects

Jefrey Lijffijt

Publications and source records attributed to Jefrey Lijffijt.

At least 37 records · Page 2Linked to original sources

arXiv2022

Topologically Regularized Data Embeddings

Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may lead to higher quality embeddings. For example, this may help one to embed the data into a given number of clusters, or to accommodate for noise that prevents one from deriving the distribution of the data over the model directly, which can then be learned more effectively. However, a general tool for integrating different prior topological knowledge into embeddings is lacking. Although differentiable topology layers have been recently developed that can (re)shape embeddings into prespecified topological models, they have two important limitations for representation learning, which we address in this paper. First, the currently suggested topological losses fail to represent simple models such as clusters and flares in a natural manner. Second, these losses neglect all original structural (such as neighborhood) information in the data that is useful for learning. We overcome these limitations by introducing a new set of topological losses, and proposing their usage as a way for topologically regularizing data embeddings to naturally represent a prespecified model. We include thorough experiments on synthetic and real data that highlight the usefulness and versatility of this approach, with applications ranging from modeling high-dimensional single-cell data, to graph embedding.

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arXiv2021

ExClus: Explainable Clustering on Low-dimensional Data Representations

Dimensionality reduction and clustering techniques are frequently used to analyze complex data sets, but their results are often not easy to interpret. We consider how to support users in interpreting apparent cluster structure on scatter plots where the axes are not directly interpretable, such as when the data is projected onto a two-dimensional space using a dimensionality-reduction method. Specifically, we propose a new method to compute an interpretable clustering automatically, where the explanation is in the original high-dimensional space and the clustering is coherent in the low-dimensional projection. It provides a tunable balance between the complexity and the amount of information provided, through the use of information theory. We study the computational complexity of this problem and introduce restrictions on the search space of solutions to arrive at an efficient, tunable, greedy optimization algorithm. This algorithm is furthermore implemented in an interactive tool called ExClus. Experiments on several data sets highlight that ExClus can provide informative and easy-to-understand patterns, and they expose where the algorithm is efficient and where there is room for improvement considering tunability and scalability.

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arXiv2021

Adversarial Robustness of Probabilistic Network Embedding for Link Prediction

In today's networked society, many real-world problems can be formalized as predicting links in networks, such as Facebook friendship suggestions, e-commerce recommendations, and the prediction of scientific collaborations in citation networks. Increasingly often, link prediction problem is tackled by means of network embedding methods, owing to their state-of-the-art performance. However, these methods lack transparency when compared to simpler baselines, and as a result their robustness against adversarial attacks is a possible point of concern: could one or a few small adversarial modifications to the network have a large impact on the link prediction performance when using a network embedding model? Prior research has already investigated adversarial robustness for network embedding models, focused on classification at the node and graph level. Robustness with respect to the link prediction downstream task, on the other hand, has been explored much less. This paper contributes to filling this gap, by studying adversarial robustness of Conditional Network Embedding (CNE), a state-of-the-art probabilistic network embedding model, for link prediction. More specifically, given CNE and a network, we measure the sensitivity of the link predictions of the model to small adversarial perturbations of the network, namely changes of the link status of a node pair. Thus, our approach allows one to identify the links and non-links in the network that are most vulnerable to such perturbations, for further investigation by an analyst. We analyze the characteristics of the most and least sensitive perturbations, and empirically confirm that our approach not only succeeds in identifying the most vulnerable links and non-links, but also that it does so in a time-efficient manner thanks to an effective approximation.

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arXiv2020

Benchmarking Network Embedding Models for Link Prediction: Are We Making Progress?

Network embedding methods map a network's nodes to vectors in an embedding space, in such a way that these representations are useful for estimating some notion of similarity or proximity between pairs of nodes in the network. The quality of these node representations is then showcased through results of downstream prediction tasks. Commonly used benchmark tasks such as link prediction, however, present complex evaluation pipelines and an abundance of design choices. This, together with a lack of standardized evaluation setups can obscure the real progress in the field. In this paper, we aim to shed light on the state-of-the-art of network embedding methods for link prediction and show, using a consistent evaluation pipeline, that only thin progress has been made over the last years. The newly conducted benchmark that we present here, including 17 embedding methods, also shows that many approaches are outperformed even by simple heuristics. Finally, we argue that standardized evaluation tools can repair this situation and boost future progress in this field.

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arXiv2020

Block-Approximated Exponential Random Graphs

An important challenge in the field of exponential random graphs (ERGs) is the fitting of non-trivial ERGs on large graphs. By utilizing fast matrix block-approximation techniques, we propose an approximative framework to such non-trivial ERGs that result in dyadic independence (i.e., edge independent) distributions, while being able to meaningfully model both local information of the graph (e.g., degrees) as well as global information (e.g., clustering coefficient, assortativity, etc.) if desired. This allows one to efficiently generate random networks with similar properties as an observed network, and the models can be used for several downstream tasks such as link prediction. Our methods are scalable to sparse graphs consisting of millions of nodes. Empirical evaluation demonstrates competitiveness in terms of both speed and accuracy with state-of-the-art methods -- which are typically based on embedding the graph into some low-dimensional space -- for link prediction, showcasing the potential of a more direct and interpretable probabalistic model for this task.

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arXiv2020

CSNE: Conditional Signed Network Embedding

Signed networks are mathematical structures that encode positive and negative relations between entities such as friend/foe or trust/distrust. Recently, several papers studied the construction of useful low-dimensional representations (embeddings) of these networks for the prediction of missing relations or signs. Existing embedding methods for sign prediction generally enforce different notions of status or balance theories in their optimization function. These theories, however, are often inaccurate or incomplete, which negatively impacts method performance. In this context, we introduce conditional signed network embedding (CSNE). Our probabilistic approach models structural information about the signs in the network separately from fine-grained detail. Structural information is represented in the form of a prior, while the embedding itself is used for capturing fine-grained information. These components are then integrated in a rigorous manner. CSNE's accuracy depends on the existence of sufficiently powerful structural priors for modelling signed networks, currently unavailable in the literature. Thus, as a second main contribution, which we find to be highly valuable in its own right, we also introduce a novel approach to construct priors based on the Maximum Entropy (MaxEnt) principle. These priors can model the \emph{polarity} of nodes (degree to which their links are positive) as well as signed \emph{triangle counts} (a measure of the degree structural balance holds to in a network). Experiments on a variety of real-world networks confirm that CSNE outperforms the state-of-the-art on the task of sign prediction. Moreover, the MaxEnt priors on their own, while less accurate than full CSNE, achieve accuracies competitive with the state-of-the-art at very limited computational cost, thus providing an excellent runtime-accuracy trade-off in resource-constrained situations.

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arXiv2020

FONDUE: A Framework for Node Disambiguation Using Network Embeddings

Real-world data often presents itself in the form of a network. Examples include social networks, citation networks, biological networks, and knowledge graphs. In their simplest form, networks represent real-life entities (e.g. people, papers, proteins, concepts) as nodes, and describe them in terms of their relations with other entities by means of edges between these nodes. This can be valuable for a range of purposes from the study of information diffusion to bibliographic analysis, bioinformatics research, and question-answering. The quality of networks is often problematic though, affecting downstream tasks. This paper focuses on the common problem where a node in the network in fact corresponds to multiple real-life entities. In particular, we introduce FONDUE, an algorithm based on network embedding for node disambiguation. Given a network, FONDUE identifies nodes that correspond to multiple entities, for subsequent splitting. Extensive experiments on twelve benchmark datasets demonstrate that FONDUE is substantially and uniformly more accurate for ambiguous node identification compared to the existing state-of-the-art, at a comparable computational cost, while less optimal for determining the best way to split ambiguous nodes.

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arXiv2020

ALPINE: Active Link Prediction using Network Embedding

Many real-world problems can be formalized as predicting links in a partially observed network. Examples include Facebook friendship suggestions, consumer-product recommendations, and the identification of hidden interactions between actors in a crime network. Several link prediction algorithms, notably those recently introduced using network embedding, are capable of doing this by just relying on the observed part of the network. Often, the link status of a node pair can be queried, which can be used as additional information by the link prediction algorithm. Unfortunately, such queries can be expensive or time-consuming, mandating the careful consideration of which node pairs to query. In this paper we estimate the improvement in link prediction accuracy after querying any particular node pair, to use in an active learning setup. Specifically, we propose ALPINE (Active Link Prediction usIng Network Embedding), the first method to achieve this for link prediction based on network embedding. To this end, we generalized the notion of V-optimality from experimental design to this setting, as well as more basic active learning heuristics originally developed in standard classification settings. Empirical results on real data show that ALPINE is scalable, and boosts link prediction accuracy with far fewer queries.

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arXiv2020

Explainable Subgraphs with Surprising Densities: A Subgroup Discovery Approach

The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between two people depends on their attributes, such as their age, address, and hobbies. The connectivity of a graph can thus possibly be understood in terms of patterns of the form 'the subgroup of individuals with properties X are often (or rarely) friends with individuals in another subgroup with properties Y'. Such rules present potentially actionable and generalizable insights into the graph. We present a method that finds pairs of node subgroups between which the edge density is interestingly high or low, using an information-theoretic definition of interestingness. This interestingness is quantified subjectively, to contrast with prior information an analyst may have about the graph. This view immediately enables iterative mining of such patterns. Our work generalizes prior work on dense subgraph mining (i.e. subgraphs induced by a single subgroup). Moreover, not only is the proposed method more general, we also demonstrate considerable practical advantages for the single subgroup special case.

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arXiv2019

Discovering Interesting Cycles in Directed Graphs

Cycles in graphs often signify interesting processes. For example, cyclic trading patterns can indicate inefficiencies or economic dependencies in trade networks, cycles in food webs can identify fragile dependencies in ecosystems, and cycles in financial transaction networks can be an indication of money laundering. Identifying such interesting cycles, which can also be constrained to contain a given set of query nodes, although not extensively studied, is thus a problem of considerable importance. In this paper, we introduce the problem of discovering interesting cycles in graphs. We first address the problem of quantifying the extent to which a given cycle is interesting for a particular analyst. We then show that finding cycles according to this interestingness measure is related to the longest cycle and maximum mean-weight cycle problems (in the unconstrained setting) and to the maximum Steiner cycle and maximum mean Steiner cycle problems (in the constrained setting). A complexity analysis shows that finding interesting cycles is NP-hard, and is NP-hard to approximate within a constant factor in the unconstrained setting, and within a factor polynomial in the input size for the constrained setting. The latter inapproximability result implies a similar result for the maximum Steiner cycle and maximum mean Steiner cycle problems. Motivated by these hardness results, we propose a number of efficient heuristic algorithms. We verify the effectiveness of the proposed methods and demonstrate their practical utility on two real-world use cases: a food web and an international trade-network dataset.

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arXiv2019

Conditional t-SNE: Complementary t-SNE embeddings through factoring out prior information

Dimensionality reduction and manifold learning methods such as t-Distributed Stochastic Neighbor Embedding (t-SNE) are routinely used to map high-dimensional data into a 2-dimensional space to visualize and explore the data. However, two dimensions are typically insufficient to capture all structure in the data, the salient structure is often already known, and it is not obvious how to extract the remaining information in a similarly effective manner. To fill this gap, we introduce \emph{conditional t-SNE} (ct-SNE), a generalization of t-SNE that discounts prior information from the embedding in the form of labels. To achieve this, we propose a conditioned version of the t-SNE objective, obtaining a single, integrated, and elegant method. ct-SNE has one extra parameter over t-SNE; we investigate its effects and show how to efficiently optimize the objective. Factoring out prior knowledge allows complementary structure to be captured in the embedding, providing new insights. Qualitative and quantitative empirical results on synthetic and (large) real data show ct-SNE is effective and achieves its goal.

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arXiv2019

ExplaiNE: An Approach for Explaining Network Embedding-based Link Predictions

Networks are powerful data structures, but are challenging to work with for conventional machine learning methods. Network Embedding (NE) methods attempt to resolve this by learning vector representations for the nodes, for subsequent use in downstream machine learning tasks. Link Prediction (LP) is one such downstream machine learning task that is an important use case and popular benchmark for NE methods. Unfortunately, while NE methods perform exceedingly well at this task, they are lacking in transparency as compared to simpler LP approaches. We introduce ExplaiNE, an approach to offer counterfactual explanations for NE-based LP methods, by identifying existing links in the network that explain the predicted links. ExplaiNE is applicable to a broad class of NE algorithms. An extensive empirical evaluation for the NE method `Conditional Network Embedding' in particular demonstrates its accuracy and scalability.

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arXiv2019

Mining Subjectively Interesting Attributed Subgraphs

Community detection in graphs, data clustering, and local pattern mining are three mature fields of data mining and machine learning. In recent years, attributed subgraph mining is emerging as a new powerful data mining task in the intersection of these areas. Given a graph and a set of attributes for each vertex, attributed subgraph mining aims to find cohesive subgraphs for which (a subset of) the attribute values has exceptional values in some sense. While research on this task can borrow from the three abovementioned fields, the principled integration of graph and attribute data poses two challenges: the definition of a pattern language that is intuitive and lends itself to efficient search strategies, and the formalization of the interestingness of such patterns. We propose an integrated solution to both of these challenges. The proposed pattern language improves upon prior work in being both highly flexible and intuitive. We show how an effective and principled algorithm can enumerate patterns of this language. The proposed approach for quantifying interestingness of patterns of this language is rooted in information theory, and is able to account for prior knowledge on the data. Prior work typically quantifies interestingness based on the cohesion of the subgraph and for the exceptionality of its attributes separately, combining these in a parametrized trade-off. Instead, in our proposal this trade-off is implicitly handled in a principled, parameter-free manner. Extensive empirical results confirm the proposed pattern syntax is intuitive, and the interestingness measure aligns well with actual subjective interestingness.

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arXiv2019

Opinion Dynamics with Backfire Effect and Biased Assimilation

The democratization of AI tools for content generation, combined with unrestricted access to mass media for all (e.g. through microblogging and social media), makes it increasingly hard for people to distinguish fact from fiction. This raises the question of how individual opinions evolve in such a networked environment without grounding in a known reality. The dominant approach to studying this problem uses simple models from the social sciences on how individuals change their opinions when exposed to their social neighborhood, and applies them on large social networks. We propose a novel model that incorporates two known social phenomena: (i) \emph{Biased Assimilation}: the tendency of individuals to adopt other opinions if they are similar to their own; (ii) \emph{Backfire Effect}: the fact that an opposite opinion may further entrench someone in their stance, making their opinion more extreme instead of moderating it. To the best of our knowledge this is the first model that captures the Backfire Effect. A thorough theoretical and empirical analysis of the proposed model reveals intuitive conditions for polarization and consensus to exist, as well as the properties of the resulting opinions.

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arXiv2019

EvalNE: A Framework for Evaluating Network Embeddings on Link Prediction

In this paper we present EvalNE, a Python toolbox for evaluating network embedding methods on link prediction tasks. Link prediction is one of the most popular choices for evaluating the quality of network embeddings. However, the complexity of this task requires a carefully designed evaluation pipeline in order to provide consistent, reproducible and comparable results. EvalNE simplifies this process by providing automation and abstraction of tasks such as hyper-parameter tuning and model validation, edge sampling and negative edge sampling, computation of edge embeddings from node embeddings, and evaluation metrics. The toolbox allows for the evaluation of any off-the-shelf embedding method without the need to write extra code. Moreover, it can also be used for evaluating any other link prediction method, and integrates several link prediction heuristics as baselines.

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arXiv2018

Conditional Network Embeddings

Network Embeddings (NEs) map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that `similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such as link prediction (if `similar' means being `more likely to be connected') or classification (if `similar' means `being more likely to have the same label'). In recent years various methods for NE have been introduced, all following a similar strategy: defining a notion of similarity between nodes (typically some distance measure within the network), a distance measure in the embedding space, and a loss function that penalizes large distances for similar nodes and small distances for dissimilar nodes. A difficulty faced by existing methods is that certain networks are fundamentally hard to embed due to their structural properties: (approximate) multipartiteness, certain degree distributions, assortativity, etc. To overcome this, we introduce a conceptual innovation to the NE literature and propose to create \emph{Conditional Network Embeddings} (CNEs); embeddings that maximally add information with respect to given structural properties (e.g. node degrees, block densities, etc.). We use a simple Bayesian approach to achieve this, and propose a block stochastic gradient descent algorithm for fitting it efficiently. We demonstrate that CNEs are superior for link prediction and multi-label classification when compared to state-of-the-art methods, and this without adding significant mathematical or computational complexity. Finally, we illustrate the potential of CNE for network visualization.

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arXiv2018

From acquaintance to best friend forever: robust and fine-grained inference of social tie strengths

Social networks often provide only a binary perspective on social ties: two individuals are either connected or not. While sometimes external information can be used to infer the strength of social ties, access to such information may be restricted or impractical. Sintos and Tsaparas (KDD 2014) first suggested to infer the strength of social ties from the topology of the network alone, by leveraging the Strong Triadic Closure (STC) property. The STC property states that if person A has strong social ties with persons B and C, B and C must be connected to each other as well (whether with a weak or strong tie). Sintos and Tsaparas exploited this to formulate the inference of the strength of social ties as NP-hard optimization problem, and proposed two approximation algorithms. We refine and improve upon this landmark paper, by developing a sequence of linear relaxations of this problem that can be solved exactly in polynomial time. Usefully, these relaxations infer more fine-grained levels of tie strength (beyond strong and weak), which also allows to avoid making arbitrary strong/weak strength assignments when the network topology provides inconclusive evidence. One of the relaxations simultaneously infers the presence of a limited number of STC violations. An extensive theoretical analysis leads to two efficient algorithmic approaches. Finally, our experimental results elucidate the strengths of the proposed approach, and sheds new light on the validity of the STC property in practice.

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arXiv2017

Interactive Visual Data Exploration with Subjective Feedback: An Information-Theoretic Approach

Visual exploration of high-dimensional real-valued datasets is a fundamental task in exploratory data analysis (EDA). Existing methods use predefined criteria to choose the representation of data. There is a lack of methods that (i) elicit from the user what she has learned from the data and (ii) show patterns that she does not know yet. We construct a theoretical model where identified patterns can be input as knowledge to the system. The knowledge syntax here is intuitive, such as "this set of points forms a cluster", and requires no knowledge of maths. This background knowledge is used to find a Maximum Entropy distribution of the data, after which the system provides the user data projections in which the data and the Maximum Entropy distribution differ the most, hence showing the user aspects of the data that are maximally informative given the user's current knowledge. We provide an open source EDA system with tailored interactive visualizations to demonstrate these concepts. We study the performance of the system and present use cases on both synthetic and real data. We find that the model and the prototype system allow the user to learn information efficiently from various data sources and the system works sufficiently fast in practice. We conclude that the information theoretic approach to exploratory data analysis where patterns observed by a user are formalized as constraints provides a principled, intuitive, and efficient basis for constructing an EDA system.

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