1,721,118 research outputs found
Estimating the Manifold Dimension of a Complex Network Using Weyl’s Law
No full textThe dimension of the space underlying real-world networks has been shown to strongly influence the networks structural properties, from the degree distribution to the way the networks respond to diffusion and percolation processes. In this paper we propose a way to estimate the dimension of the manifold underlying a network that is based on Weyl’s law, a mathematical result that describes the asymptotic behaviour of the eigenvalues of the graph Laplacian. For the case of manifold graphs, the dimension we estimate is equivalent to the fractal dimension of the network, a measure of structural self-similarity. Through an extensive set of experiments on both synthetic and real-world networks we show that our approach is able to correctly estimate the manifold dimension. We compare this with alternative methods to compute the fractal dimension and we show that our approach yields a better estimate on both synthetic and real-world examples
Smaller is Better: An Analysis of Instance Quantity/Quality Trade-off in Rehearsal-based Continual Learning
No full textThe design of machines and algorithms capable of learning in a dynamically changing environment has become an increasingly topical problem with the increase of the size and heterogeneity of data available to learning systems. As a consequence, the key issue of Continual Learning has become that of addressing the stability-plasticity dilemma of connectionist systems, as they need to adapt their model without forgetting previously acquired knowledge. Within this context, rehearsal-based methods i.e., solutions in where the learner exploits memory to revisit past data, has proven to be very effective, leading to performance at state-of-the-art. In our study, we propose an analysis of the memory quantity/quality trade-off adopting various data reduction approaches to increase the number of instances storable in memory. In particular, we investigate complex instance compression techniques such as deep encoders, but also trivial approaches such as image resizing and linear dimensionality reduction. Our findings suggest that the optimal trade-off is severely skewed toward instance quantity, where rehearsal approaches with several heavily compressed instances easily outperform state-of-the-art approaches with the same amount of memory at their disposal. Further, in high memory configurations, deep approaches extracting spatial structure combined with extreme resizing (of the order of 8 × 8 images) yield the best results, while in memory-constrained configurations where deep approaches cannot be used due to their memory requirement in training, a variation of Extreme Learning Machines (ELM) offer a clear advantage. Code and experiments available at https://github.com/francesco-p/smaller-is-bette
A Novel Graph Kernel Based on the Wasserstein Distance and Spectral Signatures
No full textSpectral signatures have been used with great success in computer vision to characterise the local and global topology of 3D meshes. In this paper, we propose to use two widely used spectral signatures, the Heat Kernel Signature and the Wave Kernel Signature, to create node embeddings able to capture local and global structural information for a given graph. For each node, we concatenate its structural embedding with the one-hot encoding vector of the node feature (if available) and we define a kernel between two input graphs in terms of the Wasserstein distance between the respective node embeddings. Experiments on standard graph classification benchmarks show that our kernel performs favourably when compared to widely used alternative kernels as well as graph neural networks
Can a Quantum Walk Tell Which Is Which?A Study of Quantum Walk-Based Graph Similarity
No full textWe consider the problem of measuring the similarity between two graphs using continuous-time quantum walks and comparing their time-evolution by means of the quantum Jensen-Shannon divergence. Contrary to previous works that focused solely on undirected graphs, here we consider the case of both directed and undirected graphs. We also consider the use of alternative Hamiltonians as well as the possibility of integrating additional node-level topological information into the proposed framework. We set up a graph classification task and we provide empirical evidence that: (1) our similarity measure can effectively incorporate the edge directionality information, leading to a significant improvement in classification accuracy; (2) the choice of the quantum walk Hamiltonian does not have a significant effect on the classification accuracy; (3) the addition of node-level topological information improves the classification accuracy in some but not all cases. We also theoretically prove that under certain constraints, the proposed similarity measure is positive definite and thus a valid kernel measure. Finally, we describe a fully quantum procedure to compute the kernel
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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