Imperial College London

ProfessorMichaelBronstein

Faculty of EngineeringDepartment of Computing

Chair in Machine Learning and Pattern Recognition
 
 
 
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Contact

 

m.bronstein Website

 
 
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Location

 

569Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
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228 results found

Croquet B, Matthews H, Mertens J, Fan Y, Nauwelaers N, Mahdi S, Hoskens H, El Sergani A, Xu T, Vandermeulen D, Bronstein M, Marazita M, Weinberg S, Claes Pet al., 2021, Automated landmarking for palatal shape analysis using geometric deep learning, ORTHODONTICS & CRANIOFACIAL RESEARCH, ISSN: 1601-6335

Journal article

Bahri M, O' Sullivan E, Gong S, Liu F, Liu X, Bronstein MM, Zafeiriou Set al., 2021, Shape My Face: Registering 3D Face Scans by Surface-to-Surface Translation, INTERNATIONAL JOURNAL OF COMPUTER VISION, Vol: 129, Pages: 2680-2713, ISSN: 0920-5691

Journal article

Gonzalez G, Gong S, Laponogov I, Bronstein M, Veselkov Ket al., 2021, Predicting anticancer hyperfoods with graph convolutional networks, Human Genomics, Vol: 15, ISSN: 1479-7364

Background:Recent efforts in the field of nutritional science have allowed the discovery of disease-beating molecules within foods based on the commonality of bioactive food molecules to FDA-approved drugs. The pioneering work in this field used an unsupervised network propagation algorithm to learn the systemic-wide effect on the human interactome of 1962 FDA-approved drugs and a supervised algorithm to predict anticancer therapeutics using the learned representations. Then, a set of bioactive molecules within foods was fed into the model, which predicted molecules with cancer-beating potential.The employed methodology consisted of disjoint unsupervised feature generation and classification tasks, which can result in sub-optimal learned drug representations with respect to the classification task. Additionally, due to the disjoint nature of the tasks, the employed approach proved cumbersome to optimize, requiring testing of thousands of hyperparameter combinations and significant computational resources.To overcome the technical limitations highlighted above, we represent each drug as a graph (human interactome) with its targets as binary node features on the graph and formulate the problem as a graph classification task. To solve this task, inspired by the success of graph neural networks in graph classification problems, we use an end-to-end graph neural network model operating directly on the graphs, which learns drug representations to optimize model performance in the prediction of anticancer therapeutics.Results:The proposed model outperforms the baseline approach in the anticancer therapeutic prediction task, achieving an F1 score of 67.99%±2.52% and an AUPR of 73.91%±3.49%. It is also shown that the model is able to capture knowledge of biological pathways to predict anticancer molecules based on the molecules’ effects on cancer-related pathways.Conclusions:We introduce an end-to-end graph convolutional model to predict cancer-beating mo

Journal article

Maggioli F, Melzi S, Ovsjanikov M, Bronstein MM, Rodola Eet al., 2021, Orthogonalized Fourier Polynomials for Signal Approximation and Transfer, COMPUTER GRAPHICS FORUM, Vol: 40, Pages: 435-447, ISSN: 0167-7055

Journal article

Schonsheck SC, Bronstein MM, Lai R, 2021, Nonisometric Surface Registration via Conformal Laplace–Beltrami Basis Pursuit, Journal of Scientific Computing, Vol: 86, ISSN: 0885-7474

Surface registration is one of the most fundamental problems in geometry processing. Many approaches have been developed to tackle this problem in cases where the surfaces are nearly isometric. However, it is much more challenging to compute correspondence between surfaces which are intrinsically less similar. In this paper, we propose a variational model to align the Laplace-Beltrami (LB) eigensytems of two non-isometric genus zero shapes via conformal deformations. This method enables us to compute geometrically meaningful point-to-point maps between non-isometric shapes. Our model is based on a novel basis pursuit scheme whereby we simultaneously compute a conformal deformation of a ’target shape’ and its deformed LB eigensystem. We solve the model using a proximal alternating minimization algorithm hybridized with the augmented Lagrangian method which produces accurate correspondences given only a few landmark points. We also propose a re-initialization scheme to overcome some of the difficulties caused by the non-convexity of the variational problem. Intensive numerical experiments illustrate the effectiveness and robustness of the proposed method to handle non-isometric surfaces with large deformation with respect to both noises on the underlying manifolds and errors within the given landmarks or feature functions.

Journal article

Laponogov I, Gonzalez G, Shepherd M, Qureshi A, Veselkov D, Charkoftaki G, Vasiliou V, Youssef J, Mirnezami R, Bronstein M, Veselkov Ket al., 2021, Network machine learning maps phytochemically rich "Hyperfoods" to fight COVID-19, Human Genomics, Vol: 15, Pages: 1-1, ISSN: 1479-7364

In this paper, we introduce a network machine learning method to identify potential bioactive anti-COVID-19 molecules in foods based on their capacity to target the SARS-CoV-2-host gene-gene (protein-protein) interactome. Our analyses were performed using a supercomputing DreamLab App platform, harnessing the idle computational power of thousands of smartphones. Machine learning models were initially calibrated by demonstrating that the proposed method can predict anti-COVID-19 candidates among experimental and clinically approved drugs (5658 in total) targeting COVID-19 interactomics with the balanced classification accuracy of 80-85% in 5-fold cross-validated settings. This identified the most promising drug candidates that can be potentially "repurposed" against COVID-19 including common drugs used to combat cardiovascular and metabolic disorders, such as simvastatin, atorvastatin and metformin. A database of 7694 bioactive food-based molecules was run through the calibrated machine learning algorithm, which identified 52 biologically active molecules, from varied chemical classes, including flavonoids, terpenoids, coumarins and indoles predicted to target SARS-CoV-2-host interactome networks. This in turn was used to construct a "food map" with the theoretical anti-COVID-19 potential of each ingredient estimated based on the diversity and relative levels of candidate compounds with antiviral properties. We expect this in silico predicted food map to play an important role in future clinical studies of precision nutrition interventions against COVID-19 and other viral diseases.

Journal article

Mahdi SS, Nauwelaers N, Joris P, Bouritsas G, Gong S, Bokhnyak S, Walsh S, Shriver MD, Bronstein M, Claes Pet al., 2021, 3D Facial Matching by Spiral Convolutional Metric Learning and a Biometric Fusion-Net of Demographic Properties, 2020 25TH INTERNATIONAL CONFERENCE ON PATTERN RECOGNITION (ICPR), Pages: 1757-1764, ISSN: 1051-4651

Journal article

Dong X, Thanou D, Toni L, Bronstein M, Frossard Pet al., 2020, Graph Signal Processing for Machine Learning: A Review and New Perspectives, IEEE SIGNAL PROCESSING MAGAZINE, Vol: 37, Pages: 117-127, ISSN: 1053-5888

Journal article

Zabatani A, Surazhsky V, Sperling E, Ben Moshe S, Menashe O, Silver DH, Karni Z, Bronstein AM, Bronstein MM, Kimmel Ret al., 2020, Intel (R) RealSense (TM) SR300 Coded Light Depth Camera, IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, Vol: 42, Pages: 2333-2345, ISSN: 0162-8828

Journal article

Svoboda J, Astolfi P, Boscaini D, Masci J, Bronstein Met al., 2020, Clustered Dynamic Graph CNN for Biometric 3D Hand Shape Recognition

The research in biometric recognition using hand shape has been somewhat stagnating in the last decade. Meanwhile, computer vision and machine learning have experienced a paradigm shift with the renaissance of deep learning, which has set the new state-of-the-art in many related fields. Inspired by successful applications of deep learning for other biometric modalities, we propose a novel approach to 3D hand shape recognition from RGB-D data based on geometric deep learning techniques. We show how to train our model on synthetic data and retain the performance on real samples during test time. To evaluate our method, we provide a new dataset NNHand RGB- D of short video sequences and show encouraging performance compared to diverse baselines on the new data, as well as current benchmark dataset HKPolyU. Moreover, the new dataset opens door to many new research directions in hand shape recognition.

Conference paper

Chamberlain BP, Rossi E, Shiebler D, Sedhain S, Bronstein MMet al., 2020, Tuning Word2vec for Large Scale Recommendation Systems, Pages: 732-737

Word2vec is a powerful machine learning tool that emerged from Natural Language Processing (NLP) and is now applied in multiple domains, including recommender systems, forecasting, and network analysis. As Word2vec is often used off the shelf, we address the question of whether the default hyperparameters are suitable for recommender systems. The answer is emphatically no. In this paper, we first elucidate the importance of hyperparameter optimization and show that unconstrained optimization yields an average 221% improvement in hit rate over the default parameters. However, unconstrained optimization leads to hyperparameter settings that are very expensive and not feasible for large scale recommendation tasks. To this end, we demonstrate 138% average improvement in hit rate with a runtime budget-constrained hyperparameter optimization. Furthermore, to make hyperparameter optimization applicable for large scale recommendation problems where the target dataset is too large to search over, we investigate generalizing hyperparameters settings from samples. We show that applying constrained hyperparameter optimization using only a 10% sample of the data still yields a 91% average improvement in hit rate over the default parameters when applied to the full datasets. Finally, we apply hyperparameters learned using our method of constrained optimization on a sample to the Who To Follow recommendation service at Twitter and are able to increase follow rates by 15%.

Conference paper

Anelli VW, Delic A, Sottocornola G, Smith J, Andrade N, Belli L, Bronstein M, Gupta A, Ira Ktena S, Lung-Yut-Fong A, Portman F, Tejani A, Xie Y, Zhu X, Shi Wet al., 2020, RecSys 2020 ChallengeWorkshop: Engagement Prediction on Twitter's Home Timeline, Pages: 623-627

The workshop features presentations of accepted contributions to the RecSys Challenge 2020, organized by Politecnico di Bari, Free University of Bozen-Bolzano, TU Wien, University of Colorado, Boulder, and Universidade Federal de Campina Grande, and sponsored by Twitter. The challenge focuses on a real-world task of Tweet engagement prediction in a dynamic environment. The goal is to predict the probability for different types of engagement (Like, Reply, Retweet, and Retweet with comment) of a target user for a set of Tweets, based on heterogeneous input data. To this end, Twitter has released a large public dataset of ~160M public Tweets, obtained by subsampling within ~2 weeks, that contains engagement features, user features, and Tweet features. A peculiarity of this challenge is related to the recent regulations on data protection and privacy. The challenge data set was compliant: if a user deleted a Tweet, or their data from Twitter, the dataset was promptly updated. Moreover, each change in the dataset implied new evaluations of all submissions and the update of the leaderboard metrics. The challenge was well received with 1,131 registered users. In the final phase, 20 teams were competing for the winning position. These teams had an average size of approximately 4 participants and developed an overall number of 127 different methods.

Conference paper

Gainza P, Sverrisson F, Monti F, Rodola E, Boscaini D, Bronstein MM, Correia BEet al., 2020, Deciphering interaction fingerprints from protein molecular surfaces using geometric deep learning, NATURE METHODS, Vol: 17, Pages: 184-+, ISSN: 1548-7091

Journal article

Gonzalez G, Gong S, Laponogov I, Veselkov K, Bronstein Met al., 2020, Graph attentional autoencoder for anticancer hyperfood prediction, Publisher: arXiv

Recent research efforts have shown the possibility to discover anticancerdrug-like molecules in food from their effect on protein-protein interactionnetworks, opening a potential pathway to disease-beating diet design. Weformulate this task as a graph classification problem on which graph neuralnetworks (GNNs) have achieved state-of-the-art results. However, GNNs aredifficult to train on sparse low-dimensional features according to ourempirical evidence. Here, we present graph augmented features, integratinggraph structural information and raw node attributes with varying ratios, toease the training of networks. We further introduce a novel neural networkarchitecture on graphs, the Graph Attentional Autoencoder (GAA) to predict foodcompounds with anticancer properties based on perturbed protein networks. Wedemonstrate that the method outperforms the baseline approach andstate-of-the-art graph classification models in this task.

Working paper

Kulon D, Wang H, Güler RA, Bronstein M, Zafeiriou Set al., 2020, Single image 3D hand reconstruction with mesh convolutions

Monocular 3D reconstruction of deformable objects, such as human body parts, has been typically approached by predicting parameters of heavyweight linear models. In this paper, we demonstrate an alternative solution that is based on the idea of encoding images into a latent non-linear representation of meshes. The prior on 3D hand shapes is learned by training an autoencoder with intrinsic graph convolutions performed in the spectral domain. The pre-trained decoder acts as a non-linear statistical deformable model. The latent parameters that reconstruct the shape and articulated pose of hands in the image are predicted using an image encoder. We show that our system reconstructs plausible meshes and operates in real-time. We evaluate the quality of the mesh reconstructions produced by the decoder on a new dataset and show latent space interpolation results. Our code, data, and models will be made publicly available.

Conference paper

Cosmo L, Kazi A, Ahmadi SA, Navab N, Bronstein Met al., 2020, Latent-Graph Learning for Disease Prediction, Pages: 643-653, ISSN: 0302-9743

Recently, Graph Convolutional Networks (GCNs) have proven to be a powerful machine learning tool for Computer Aided Diagnosis (CADx) and disease prediction. A key component in these models is to build a population graph, where the graph adjacency matrix represents pair-wise patient similarities. Until now, the similarity metrics have been defined manually, usually based on meta-features like demographics or clinical scores. The definition of the metric, however, needs careful tuning, as GCNs are very sensitive to the graph structure. In this paper, we demonstrate for the first time in the CADx domain that it is possible to learn a single, optimal graph towards the GCN’s downstream task of disease classification. To this end, we propose a novel, end-to-end trainable graph learning architecture for dynamic and localized graph pruning. Unlike commonly employed spectral GCN approaches, our GCN is spatial and inductive, and can thus infer previously unseen patients as well. We demonstrate significant classification improvements with our learned graph on two CADx problems in medicine. We further explain and visualize this result using an artificial dataset, underlining the importance of graph learning for more accurate and robust inference with GCNs in medical applications.

Conference paper

Bronstein MV, Pennycook G, Buonomano L, Cannon TDet al., 2020, Belief in fake news, responsiveness to cognitive conflict, and analytic reasoning engagement, Thinking and Reasoning, ISSN: 1354-6783

Analytic and intuitive reasoning processes have been implicated as important determinants of belief in (or skepticism of) fake news. However, the underlying cognitive mechanisms that encourage endorsement of fake news remain unclear. The present study investigated cognitive decoupling/response inhibition and the potential role of conflict processing in the initiation of analytic thought about fake news as factors that may facilitate skepticism. A base-rate task was used to test the hypotheses that conflict processing deficits and inefficient response inhibition would be related to stronger endorsement of fake news. In support of these hypotheses, increased belief in fake (but not real) news was associated with a smaller decrease in response confidence in the presence (vs. absence) of conflict and with inefficient (in terms of response latency) inhibition of prepotent responses. Through its support for these hypotheses, the present study advances efforts to determine who will fall for fake news, and why.

Journal article

Cosmo L, Minello G, Bronstein M, Rossi L, Torsello Aet al., 2020, The Average Mixing Kernel Signature, Pages: 1-17, ISSN: 0302-9743

We introduce the Average Mixing Kernel Signature (AMKS), a novel signature for points on non-rigid three-dimensional shapes based on the average mixing kernel and continuous-time quantum walks. The average mixing kernel holds information on the average transition probabilities of a quantum walk between each pair of vertices of the mesh until a time T. We define the AMKS by decomposing the spectral contributions of the kernel into several bands, allowing us to limit the influence of noise-dominated high-frequency components and obtain a more descriptive signature. We also show through a perturbation theory analysis of the kernel that choosing a finite stopping time T leads to noise and deformation robustness for the AMKS. We perform an extensive experimental evaluation on two widely used shape matching datasets under varying level of noise, showing that the AMKS outperforms two state-of-the-art descriptors, namely the Heat Kernel Signature (HKS) and the similarly quantum-walk based Wave Kernel Signature (WKS).

Conference paper

Kulon D, Guler RA, Kokkinos I, Bronstein MM, Zafeiriou Set al., 2020, Weakly-Supervised Mesh-Convolutional Hand Reconstruction in the Wild, 2020 IEEE/CVF CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR), Pages: 4989-4999, ISSN: 1063-6919

Journal article

Gong S, Bahri M, Bronstein MM, Zafeiriou Set al., 2020, Geometrically principled connections in graph neural networks, Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Pages: 11412-11421, ISSN: 1063-6919

Graph convolution operators bring the advantages of deep learning to a variety of graph and mesh processing tasks previously deemed out of reach. With their continued success comes the desire to design more powerful architectures, often by adapting existing deep learning techniques to non-Euclidean data. In this paper, we argue geometry should remain the primary driving force behind innovation in the emerging field of geometric deep learning. We relate graph neural networks to widely successful computer graphics and data approximation models: radial basis functions (RBFs). We conjecture that, like RBFs, graph convolution layers would benefit from the addition of simple functions to the powerful convolution kernels. We introduce affine skip connections, a novel building block formed by combining a fully connected layer with any graph convolution operator. We experimentally demonstrate the effectiveness of our technique, and show the improved performance is the consequence of more than the increased number of parameters. Operators equipped with the affine skip connection markedly outperform their base performance on every task we evaluated, i.e., shape reconstruction, dense shape correspondence, and graph classification. We hope our simple and effective approach will serve as a solid baseline and help ease future research in graph neural networks.

Journal article

Feydy J, Glaunès JA, Charlier B, Bronstein MMet al., 2020, Fast geometric learning with symbolic matrices, ISSN: 1049-5258

Geometric methods rely on tensors that can be encoded using a symbolic formula and data arrays, such as kernel and distance matrices. We present an extension for standard machine learning frameworks that provides comprehensive support for this abstraction on CPUs and GPUs: our toolbox combines a versatile, transparent user interface with fast runtimes and low memory usage. Unlike general purpose acceleration frameworks such as XLA, our library turns generic Python code into binaries whose performances are competitive with state-of-the-art geometric libraries – such as FAISS for nearest neighbor search – with the added benefit of flexibility. We perform an extensive evaluation on a broad class of problems: Gaussian modelling, K-nearest neighbors search, geometric deep learning, non-Euclidean embeddings and optimal transport theory. In practice, for geometric problems that involve 103 to 106 samples in dimension 1 to 100, our library speeds up baseline GPU implementations by up to two orders of magnitude.

Conference paper

Bermant PC, Bronstein MM, Wood RJ, Gero S, Gruber DFet al., 2019, Publisher Correction: Deep Machine Learning Techniques for the Detection and Classification of Sperm Whale Bioacoustics., Sci Rep, Vol: 9

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Journal article

Wang Y, Sun Y, Liu Z, Sarma SE, Bronstein MM, Solomon JMet al., 2019, Dynamic Graph CNN for Learning on Point Clouds, ACM TRANSACTIONS ON GRAPHICS, Vol: 38, ISSN: 0730-0301

Journal article

Frasca F, Galeano D, Gonzalez G, Laponogov I, Veselkov K, Paccanaro A, Bronstein MMet al., 2019, Learning interpretable disease self-representations for drug repositioning, Publisher: arxiv

Drug repositioning is an attractive cost-efficient strategy for thedevelopment of treatments for human diseases. Here, we propose an interpretablemodel that learns disease self-representations for drug repositioning. Ourself-representation model represents each disease as a linear combination of afew other diseases. We enforce proximity in the learnt representations in a wayto preserve the geometric structure of the human phenome network - adomain-specific knowledge that naturally adds relational inductive bias to thedisease self-representations. We prove that our method is globally optimal andshow results outperforming state-of-the-art drug repositioning approaches. Wefurther show that the disease self-representations are biologicallyinterpretable.

Working paper

Bermant PC, Bronstein MM, Wood RJ, Gero S, Gruber DFet al., 2019, Deep Machine Learning Techniques for the Detection and Classification of Sperm Whale Bioacoustics., Sci Rep, Vol: 9

We implemented Machine Learning (ML) techniques to advance the study of sperm whale (Physeter macrocephalus) bioacoustics. This entailed employing Convolutional Neural Networks (CNNs) to construct an echolocation click detector designed to classify spectrograms generated from sperm whale acoustic data according to the presence or absence of a click. The click detector achieved 99.5% accuracy in classifying 650 spectrograms. The successful application of CNNs to clicks reveals the potential of future studies to train CNN-based architectures to extract finer-scale details from cetacean spectrograms. Long short-term memory and gated recurrent unit recurrent neural networks were trained to perform classification tasks, including (1) "coda type classification" where we obtained 97.5% accuracy in categorizing 23 coda types from a Dominica dataset containing 8,719 codas and 93.6% accuracy in categorizing 43 coda types from an Eastern Tropical Pacific (ETP) dataset with 16,995 codas; (2) "vocal clan classification" where we obtained 95.3% accuracy for two clan classes from Dominica and 93.1% for four ETP clan types; and (3) "individual whale identification" where we obtained 99.4% accuracy using two Dominica sperm whales. These results demonstrate the feasibility of applying ML to sperm whale bioacoustics and establish the validity of constructing neural networks to learn meaningful representations of whale vocalizations.

Journal article

Veselkov K, Gonzalez Pigorini G, Aljifri S, Galea D, Mirnezami R, Youssef J, Bronstein M, Laponogov Iet al., 2019, HyperFoods: Machine intelligent mapping of cancer-beating molecules in foods, Scientific Reports, Vol: 9, ISSN: 2045-2322

Recent data indicate that up-to 30–40% of cancers can be prevented by dietary and lifestyle measures alone. Herein, we introduce a unique network-based machine learning platform to identify putative food-based cancer-beating molecules. These have been identified through their molecular biological network commonality with clinically approved anti-cancer therapies. A machine-learning algorithm of random walks on graphs (operating within the supercomputing DreamLab platform) was used to simulate drug actions on human interactome networks to obtain genome-wide activity profiles of 1962 approved drugs (199 of which were classified as “anti-cancer” with their primary indications). A supervised approach was employed to predict cancer-beating molecules using these ‘learned’ interactome activity profiles. The validated model performance predicted anti-cancer therapeutics with classification accuracy of 84–90%. A comprehensive database of 7962 bioactive molecules within foods was fed into the model, which predicted 110 cancer-beating molecules (defined by anti-cancer drug likeness threshold of >70%) with expected capacity comparable to clinically approved anti-cancer drugs from a variety of chemical classes including flavonoids, terpenoids, and polyphenols. This in turn was used to construct a ‘food map’ with anti-cancer potential of each ingredient defined by the number of cancer-beating molecules found therein. Our analysis underpins the design of next-generation cancer preventative and therapeutic nutrition strategies.

Journal article

Cosmo L, Panine M, Rampini A, Ovsjanikov M, Bronstein MM, Rodola Ret al., 2019, Isospectralization, or how to hear shape, style, and correspondence, Pages: 7521-7530, ISSN: 1063-6919

The question whether one can recover the shape of a geometric object from its Laplacian spectrum ('hear the shape of the drum') is a classical problem in spectral geometry with a broad range of implications and applications. While theoretically the answer to this question is negative (there exist examples of iso-spectral but non-isometric manifolds), little is known about the practical possibility of using the spectrum for shape reconstruction and optimization. In this paper, we introduce a numerical procedure called isospectralization, consisting of deforming one shape to make its Laplacian spectrum match that of another. We implement the isospectralization procedure using modern differentiable programming techniques and exemplify its applications in some of the classical and notoriously hard problems in geometry processing, computer vision, and graphics such as shape reconstruction, pose and style transfer, and dense deformable correspondence.

Conference paper

Melzi S, Spezialetti R, Tombari F, Bronstein MM, Stefano LD, Rodola Eet al., 2019, Gframes: Gradient-based local reference frame for 3D shape matching, Pages: 4624-4633, ISSN: 1063-6919

We introduce GFrames, a novel local reference frame (LRF) construction for 3D meshes and point clouds. GFrames are based on the computation of the intrinsic gradient of a scalar field defined on top of the input shape. The resulting tangent vector field defines a repeatable tangent direction of the local frame at each point; importantly, it directly inherits the properties and invariance classes of the underlying scalar function, making it remarkably robust under strong sampling artifacts, vertex noise, as well as non-rigid deformations. Existing local descriptors can directly benefit from our repeatable frames, as we showcase in a selection of 3D vision and shape analysis applications where we demonstrate state-of-the-art performance in a variety of challenging settings.

Conference paper

Rodolà E, Lähner Z, Bronstein AM, Bronstein MM, Solomon Jet al., 2019, Functional Maps Representation On Product Manifolds, Computer Graphics Forum, ISSN: 0167-7055

© 2019 The Authors Computer Graphics Forum © 2019 The Eurographics Association and John Wiley & Sons Ltd. We consider the tasks of representing, analysing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace–Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices.

Journal article

Bronstein MV, Everaert J, Castro A, Joormann J, Cannon TDet al., 2019, Pathways to paranoia: Analytic thinking and belief flexibility., Behav Res Ther, Vol: 113, Pages: 18-24

Delusions have been repeatedly linked to reduced engagement in analytic (i.e., conscious and effortful) reasoning. However, the mechanisms underlying this relationship remain unclear. One hypothesis is that less analytic reasoning might maintain persecutory delusions by reducing belief flexibility. An important aspect of belief flexibility is the ability to revise beliefs in response to disconfirmatory evidence. The present study recruited 231 participants from the general population that represented a wide range of paranoid ideation. Participants completed tasks in which they encountered a series of ambiguous scenarios with initially-appealing explanations that were later disconfirmed by statements supporting alternative interpretations. Three types of scenarios were employed: two presented participants with emotionally valenced explanations (i.e., negative or positive) and one presented participants with emotionally neutral explanations. In each type of reasoning scenario, impaired belief revision ability was found to partially mediate the relationship between reduced engagement in analytic reasoning and persecutory ideation. These results are consistent with the notion that reduced engagement in analytic reasoning may help maintain paranoid delusions by interfering with the ability to revise beliefs in the presence of disconfirmatory information.

Journal article

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