arXiv subjects

Davide Mottin

Publications and source records attributed to Davide Mottin.

27 records · Page 2Linked to original sources

arXiv2021

GRASP: Graph Alignment through Spectral Signatures

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 paper, 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. Our experimental study, featuring noise levels higher than anything used in previous studies, shows that GRASP outperforms state-of-the-art methods for graph alignment across noise levels and graph types.

cs.IR↗

arXiv2021

SOFOS: Demonstrating the Challenges of Materialized View Selection on Knowledge Graphs

Analytical queries over RDF data are becoming prominent as a result of the proliferation of knowledge graphs. Yet, RDF databases are not optimized to perform such queries efficiently, leading to long processing times. A well known technique to improve the performance of analytical queries is to exploit materialized views. Although popular in relational databases, view materialization for RDF and SPARQL has not yet transitioned into practice, due to the non-trivial application to the RDF graph model. Motivated by a lack of understanding of the impact of view materialization alternatives for RDF data, we demonstrate SOFOS, a system that implements and compares several cost models for view materialization. SOFOS is, to the best of our knowledge, the first attempt to adapt cost models, initially studied in relational data, to the generic RDF setting, and to propose new ones, analyzing their pitfalls and merits. SOFOS takes an RDF dataset and an analytical query for some facet in the data, and compares and evaluates alternative cost models, displaying statistics and insights about time, memory consumption, and query characteristics.

cs.DB↗

arXiv2021

Bandits for Learning to Explain from Explanations

We introduce Explearn, an online algorithm that learns to jointly output predictions and explanations for those predictions. Explearn leverages Gaussian Processes (GP)-based contextual bandits. This brings two key benefits. First, GPs naturally capture different kinds of explanations and enable the system designer to control how explanations generalize across the space by virtue of choosing a suitable kernel. Second, Explearn builds on recent results in contextual bandits which guarantee convergence with high probability. Our initial experiments hint at the promise of the approach.

cs.LG↗

arXiv2020

What if Neural Networks had SVDs?

Various Neural Networks employ time-consuming matrix operations like matrix inversion. Many such matrix operations are faster to compute given the Singular Value Decomposition (SVD). Previous work allows using the SVD in Neural Networks without computing it. In theory, the techniques can speed up matrix operations, however, in practice, they are not fast enough. We present an algorithm that is fast enough to speed up several matrix operations. The algorithm increases the degree of parallelism of an underlying matrix multiplication $H\cdot X$ where $H$ is an orthogonal matrix represented by a product of Householder matrices. Code is available at www.github.com/AlexanderMath/fasth .

cs.LG↗

arXiv2020

The Shape of Data: Intrinsic Distance for Data Distributions

The ability to represent and compare machine learning models is crucial in order to quantify subtle model changes, evaluate generative models, and gather insights on neural network architectures. Existing techniques for comparing data distributions focus on global data properties such as mean and covariance; in that sense, they are extrinsic and uni-scale. We develop a first-of-its-kind intrinsic and multi-scale method for characterizing and comparing data manifolds, using a lower-bound of the spectral variant of the Gromov-Wasserstein inter-manifold distance, which compares all data moments. In a thorough experimental study, we demonstrate that our method effectively discerns the structure of data manifolds even on unaligned data of different dimensionalities; moreover, we showcase its efficacy in evaluating the quality of generative models.

stat.ML↗

arXiv2018

SGR: Self-Supervised Spectral Graph Representation Learning

Representing a graph as a vector is a challenging task; ideally, the representation should be easily computable and conducive to efficient comparisons among graphs, tailored to the particular data and analytical task at hand. Unfortunately, a "one-size-fits-all" solution is unattainable, as different analytical tasks may require different attention to global or local graph features. We develop SGR, the first, to our knowledge, method for learning graph representations in a self-supervised manner. Grounded on spectral graph analysis, SGR seamlessly combines all aforementioned desirable properties. In extensive experiments, we show how our approach works on large graph collections, facilitates self-supervised representation learning across a variety of application domains, and performs competitively to state-of-the-art methods without re-training.

cs.SI↗

arXiv2018

NetLSD: Hearing the Shape of a Graph

Comparison among graphs is ubiquitous in graph analytics. However, it is a hard task in terms of the expressiveness of the employed similarity measure and the efficiency of its computation. Ideally, graph comparison should be invariant to the order of nodes and the sizes of compared graphs, adaptive to the scale of graph patterns, and scalable. Unfortunately, these properties have not been addressed together. Graph comparisons still rely on direct approaches, graph kernels, or representation-based methods, which are all inefficient and impractical for large graph collections. In this paper, we propose the Network Laplacian Spectral Descriptor (NetLSD): the first, to our knowledge, permutation- and size-invariant, scale-adaptive, and efficiently computable graph representation method that allows for straightforward comparisons of large graphs. NetLSD extracts a compact signature that inherits the formal properties of the Laplacian spectrum, specifically its heat or wave kernel; thus, it hears the shape of a graph. Our evaluation on a variety of real-world graphs demonstrates that it outperforms previous works in both expressiveness and efficiency.

cs.SI↗

arXiv2018

VERSE: Versatile Graph Embeddings from Similarity Measures

Embedding a web-scale information network into a low-dimensional vector space facilitates tasks such as link prediction, classification, and visualization. Past research has addressed the problem of extracting such embeddings by adopting methods from words to graphs, without defining a clearly comprehensible graph-related objective. Yet, as we show, the objectives used in past works implicitly utilize similarity measures among graph nodes. In this paper, we carry the similarity orientation of previous works to its logical conclusion; we propose VERtex Similarity Embeddings (VERSE), a simple, versatile, and memory-efficient method that derives graph embeddings explicitly calibrated to preserve the distributions of a selected vertex-to-vertex similarity measure. VERSE learns such embeddings by training a single-layer neural network. While its default, scalable version does so via sampling similarity information, we also develop a variant using the full information per vertex. Our experimental study on standard benchmarks and real-world datasets demonstrates that VERSE, instantiated with diverse similarity measures, outperforms state-of-the-art methods in terms of precision and recall in major data mining tasks and supersedes them in time and space efficiency, while the scalable sampling-based variant achieves equally good results as the non-scalable full variant.

cs.SI↗

arXiv2018

Notable Characteristics Search through Knowledge Graphs

Query answering routinely employs knowledge graphs to assist the user in the search process. Given a knowledge graph that represents entities and relationships among them, one aims at complementing the search with intuitive but effective mechanisms. In particular, we focus on the comparison of two or more entities and the detection of unexpected, surprising properties, called notable characteristics. Such characteristics provide intuitive explanations of the peculiarities of the selected entities with respect to similar entities. We propose a solid probabilistic approach that first retrieves entity nodes similar to the query nodes provided by the user, and then exploits distributional properties to understand whether a certain attribute is interesting or not. Our preliminary experiments demonstrate the solidity of our approach and show that we are able to discover notable characteristics that are indeed interesting and relevant for the user.

cs.DB↗