60 research outputs found

    Applications of No-Collision Transportation Maps in Manifold Learning

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    In this work, we investigate applications of no-collision transportation maps introduced in [Nurbekyan et. al., 2020] in manifold learning for image data. Recently, there has been a surge in applying transportation-based distances and features for data representing motion-like or deformation-like phenomena. Indeed, comparing intensities at fixed locations often does not reveal the data structure. No-collision maps and distances developed in [Nurbekyan et. al., 2020] are sensitive to geometric features similar to optimal transportation (OT) maps but much cheaper to compute due to the absence of optimization. In this work, we prove that no-collision distances provide an isometry between translations (respectively dilations) of a single probability measure and the translation (respectively dilation) vectors equipped with a Euclidean distance. Furthermore, we prove that no-collision transportation maps, as well as OT and linearized OT maps, do not in general provide an isometry for rotations. The numerical experiments confirm our theoretical findings and show that no-collision distances achieve similar or better performance on several manifold learning tasks compared to other OT and Euclidean-based methods at a fraction of a computational cost

    Manifold learning in Wasserstein space

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    This paper aims at building the theoretical foundations for manifold learning algorithms in the space of absolutely continuous probability measures on a compact and convex subset of Rd\mathbb{R}^d, metrized with the Wasserstein-2 distance WW. We begin by introducing a natural construction of submanifolds Λ\Lambda of probability measures equipped with metric WΛW_\Lambda, the geodesic restriction of WW to Λ\Lambda. In contrast to other constructions, these submanifolds are not necessarily flat, but still allow for local linearizations in a similar fashion to Riemannian submanifolds of Rd\mathbb{R}^d. We then show how the latent manifold structure of (Λ,WΛ)(\Lambda,W_{\Lambda}) can be learned from samples {λi}i=1N\{\lambda_i\}_{i=1}^N of Λ\Lambda and pairwise extrinsic Wasserstein distances WW only. In particular, we show that the metric space (Λ,WΛ)(\Lambda,W_{\Lambda}) can be asymptotically recovered in the sense of Gromov--Wasserstein from a graph with nodes {λi}i=1N\{\lambda_i\}_{i=1}^N and edge weights W(λi,λj)W(\lambda_i,\lambda_j). In addition, we demonstrate how the tangent space at a sample λ\lambda can be asymptotically recovered via spectral analysis of a suitable "covariance operator" using optimal transport maps from λ\lambda to sufficiently close and diverse samples {λi}i=1N\{\lambda_i\}_{i=1}^N. The paper closes with some explicit constructions of submanifolds Λ\Lambda and numerical examples on the recovery of tangent spaces through spectral analysis

    Carbon translocation from glacial and terrestrial to aqueous systems – characteristics and processing of dissolved organic matter in the endorheic Tibetan Lake Nam Co watershed

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    The Tibetan Plateau (TP) comprises sensitive alpine environments such as grassland biomes. Climatic changes and intensifying land use threaten these ecosystems. Therefore, it is important to understand the response of ecosystems to changing biotic and abiotic factors. The translocation of dissolved organic matter from glacial and terrestrial to aqueous systems is an important aspect of this response, specifically when characterizing changing conditions of freshwater resources and sensitive limnic ecosystems on the TP. Via changes in its chemical composition, characteristics, transformation and processing of DOM can be tracked. Three catchments of the Nam Co watershed of the TP (Niyaqu, Qugaqie and Zhagu) and the lake were investigated to understand how site specific terrestrial processes and seasonality affect the composition of DOM and alteration of organic compounds in streams and the lake of this endorheic basin. Four hypotheses were tested: H1 The natural diversity in the Nam Co watershed controls site specific effects on DOM composition. H2 Seasonal effects on DOM composition are driven by warm and moist summers influenced from the Indian summer monsoon (ISM) and cold and dry winters. H3/ H4a Site specific effects on DOM diminish by means of biological decomposition and photooxidation of DOM during the stream path / in the lake. Alongside H4b organic matter of the Nam Co Lake is independent from catchment influences, given by an autochthonous source of DOM. A multi-parameter approach was applied, consitsing of water chemistry parameters (pH, electric conductivity, cations and anions, dissolved inorganic carbon), concentration of dissolved organic carbon (DOC), DOM characteristics (chromophoric DOM, fluorescence DOM and δ13C of DOM) and DOM ultra-high resolution Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS). Sampling was conducted for three seasons, freshet in 2018, the phase of the ISM in 2019 and post-ISM baseflow in 2019. Alongside a watershed-wide plant cover estimate was composed, to explore the link between differences in DOM characteristics and degree of green plant cover. Sampling covers stream water, as well as endmember samples such as: glacial effluents, water of springs and water from an alpine wetland. The lake was covered by sampling the brackish zone and the lake pelagial and the lake surface. The composition of DOM differed between the three endmember groups and between stream samples of catchments. Glaciers showed a dual DOM source, indicating a glacial microbiome and compounds derived from burned fossil fuels. Springs differed based on their geographic location. Upland waters showed limited inputs of alpine pastures: lowland springs displayed influences of yak faeces with microbial reworked DOM, indicated by less negative δ13C and nitrogen. Wetlands were distinguished by more eutrophic conditions by highest concentrations in DOC and high amounts in N-heteroatoms. Streams were site specific with input sources derived from glaciers, wetlands, groundwater, intense animal husbandry and a plant-derived phenolic signature from alpine pastures aligned to the degree of plant cover. Seasonality affected DOM characteristics in stream water. During freshet, DOM was plant-derived, as was during baseflow conditions. A flush of dissolved organic carbon, accompanied by a compositional shift towards more microbial derived DOM was observed during the ISM season. Processing of DOM in streams was limited to the biolabile fraction of DOM of the glacial biome. Transformation of DOM was overruled by the constant input of plant derived phenolic DOM compounds from alpine pastures. Consequentially, the brackish intermixing zone showed the inflow of terrestrial DOM into the lake. In contrast, lake water exhibited distinct DOM characteristics, by lowest amounts in aromatic molecular compounds and DOM rich in 13C. This suggested intense processing of phenolic, terrestrial derived DOM by photooxidation, as well as a seasonally stable autochthonous DOM source derived from algae and microorganisms in lake water. In conclusion, DOM characteristics are largely influenced by local endmembers such as glaciers, springs and wetlands. Seasonality shows that shifts in the onset, and changes in the intensity of the ISM can largely modify DOM composition. Processing of DOM took place mainly in the lake. The study revealed that DOM is suited to function as a monitoring agent in this lake watershed. Hence, DOM is a helpful tool to understand changes in ecosystems, and forthcoming, to safeguard sensitive ecosystems of the TP.Deutsche Forschungsgemeinschaft (DFG)/International Research Training Group (GRK 2309/1)/317513741/E

    Reciprocal feature encoding by cortical excitatory and inhibitory neurons

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    In the cortex, the interplay between excitation and inhibition determines the fidelity of neuronal representations. However, while the receptive fields of excitatory neurons are often fine-tuned to the encoded features, the principles governing the tuning of inhibitory neurons are still elusive. We addressed this problem by recording populations of neurons in the postsubiculum (PoSub), a cortical area where the receptive fields of most excitatory neurons correspond to a specific head-direction (HD). In contrast to PoSub-HD cells, the tuning of fast-spiking (FS) cells, the largest class of cortical inhibitory neurons, was broad and heterogeneous. However, we found that PoSub-FS cell tuning curves were often fine-tuned in the spatial frequency domain, which resulted in various radial symmetries in their HD tuning. In addition, the average frequency spectrum of PoSub-FS cell populations was virtually indistinguishable from that of PoSub-HD cells but different from that of the upstream thalamic HD cells, suggesting that this population cotuning in the frequency domain has a local origin. Two observations corroborated this hypothesis. First, PoSub-FS cell tuning was independent of upstream thalamic inputs. Second, PoSub-FS cell tuning was tightly coupled to PoSub-HD cell activity even during sleep. Together, these findings provide evidence that the resolution of neuronal tuning is an intrinsic property of local cortical networks, shared by both excitatory and inhibitory cell populations. We hypothesize that this reciprocal feature encoding supports two parallel streams of information processing in thalamocortical networks.Canadian Institutes of Health ResearchIsrael Science FoundationAzrieli FoundationEMBO Long-Term Postdoctoral FellowshipSir Henry Wellcome Fellowship (A.J.D.

    Facial expression recognition and intensity estimation.

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    Doctoral Degree. University of KwaZulu-Natal, Durban.Facial Expression is one of the profound non-verbal channels through which human emotion state is inferred from the deformation or movement of face components when facial muscles are activated. Facial Expression Recognition (FER) is one of the relevant research fields in Computer Vision (CV) and Human-Computer Interraction (HCI). Its application is not limited to: robotics, game, medical, education, security and marketing. FER consists of a wealth of information. Categorising the information into primary emotion states only limit its performance. This thesis considers investigating an approach that simultaneously predicts the emotional state of facial expression images and the corresponding degree of intensity. The task also extends to resolving FER ambiguous nature and annotation inconsistencies with a label distribution learning method that considers correlation among data. We first proposed a multi-label approach for FER and its intensity estimation using advanced machine learning techniques. According to our findings, this approach has not been considered for emotion and intensity estimation in the field before. The approach used problem transformation to present FER as a multilabel task, such that every facial expression image has unique emotion information alongside the corresponding degree of intensity at which the emotion is displayed. A Convolutional Neural Network (CNN) with a sigmoid function at the final layer is the classifier for the model. The model termed ML-CNN (Multilabel Convolutional Neural Network) successfully achieve concurrent prediction of emotion and intensity estimation. ML-CNN prediction is challenged with overfitting and intraclass and interclass variations. We employ Visual Geometric Graphics-16 (VGG-16) pretrained network to resolve the overfitting challenge and the aggregation of island loss and binary cross-entropy loss to minimise the effect of intraclass and interclass variations. The enhanced ML-CNN model shows promising results and outstanding performance than other standard multilabel algorithms. Finally, we approach data annotation inconsistency and ambiguity in FER data using isomap manifold learning with Graph Convolutional Networks (GCN). The GCN uses the distance along the isomap manifold as the edge weight, which appropriately models the similarity between adjacent nodes for emotion predictions. The proposed method produces a promising result in comparison with the state-of-the-art methods.Author's List of Publication is on page xi of this thesis

    Recent Advances and Applications of Machine Learning in Metal Forming Processes

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    Machine learning (ML) technologies are emerging in Mechanical Engineering, driven by the increasing availability of datasets, coupled with the exponential growth in computer performance. In fact, there has been a growing interest in evaluating the capabilities of ML algorithms to approach topics related to metal forming processes, such as: Classification, detection and prediction of forming defects; Material parameters identification; Material modelling; Process classification and selection; Process design and optimization. The purpose of this Special Issue is to disseminate state-of-the-art ML applications in metal forming processes, covering 10 papers about the abovementioned and related topics

    Décomposition en valeurs singulières randomisée et positionnement multidimensionel à base de tâches

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    The multidimensional scaling (MDS) is an important and robust algorithm for representing individual cases of a dataset out of their respective dissimilarities. However, heuristics, possibly trading-off with robustness, are often preferred in practice due to the potentially prohibitive memory and computational costs of the MDS. The recent introduction of random projection techniques within the MDS allowed it to be become competitive on larger testcases. The goal of this manuscript is to propose a high-performance distributed-memory MDS based on random projection for processing data sets of even larger size (up to one million items). We propose a task-based design of the whole algorithm and we implement it within an efficient software stack including state-of-the-art numerical solvers, runtime systems and communication layers. The outcome is the ability to efficiently apply robust MDS to large datasets on modern supercomputers. We assess the resulting algorithm and software stack to the point cloud visualization for analyzing distances between sequencesin metabarcoding.Le positionnement multidimensionnel (MDS) est un algorithme important et robuste pour représenter les cas individuels d’un ensemble de données en fonction de leurs dissimilarités respectives. Cependant, les heuristiques, qui peuvent être un compromis avec la robustesse, sont souvent préférées en pratique en raison de sa consommation mémoire et de ses coûts potentiellement prohibitifs. L’introduction récente de techniques de projection aléatoire dans le MDS lui a permis de devenir compétitif sur des cas test plus importants. L’objectif de ce manuscrit est de proposer un MDS haute performance basé sur la projection aléatoire pour le traitement d’ensembles de données de taille encore plus grande (jusqu’à un million d’éléments). Nous proposons une conception de l’algorithme et nous l’implémentons dans une pile logicielle efficace, comprenant des solveurs numériques de pointe ainsi des systèmes d’exécution et des couches de communication optimisés. L’aboutissement de ce travail résultat est la capacité d’appliquer efficacement le MDS robuste à de grands ensembles de données sur des super-ordinateurs modernes. Nous évaluons l’algorithme etla pile logicielle résultants à la visualisation de nuages de points pour l’analyse des distances entre séquences de metabarcoding

    Collision Avoidance on Unmanned Aerial Vehicles using Deep Neural Networks

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    Unmanned Aerial Vehicles (UAVs), although hardly a new technology, have recently gained a prominent role in many industries, being widely used not only among enthusiastic consumers but also in high demanding professional situations, and will have a massive societal impact over the coming years. However, the operation of UAVs is full of serious safety risks, such as collisions with dynamic obstacles (birds, other UAVs, or randomly thrown objects). These collision scenarios are complex to analyze in real-time, sometimes being computationally impossible to solve with existing State of the Art (SoA) algorithms, making the use of UAVs an operational hazard and therefore significantly reducing their commercial applicability in urban environments. In this work, a conceptual framework for both stand-alone and swarm (networked) UAVs is introduced, focusing on the architectural requirements of the collision avoidance subsystem to achieve acceptable levels of safety and reliability. First, the SoA principles for collision avoidance against stationary objects are reviewed. Afterward, a novel image processing approach that uses deep learning and optical flow is presented. This approach is capable of detecting and generating escape trajectories against potential collisions with dynamic objects. Finally, novel models and algorithms combinations were tested, providing a new approach for the collision avoidance of UAVs using Deep Neural Networks. The feasibility of the proposed approach was demonstrated through experimental tests using a UAV, created from scratch using the framework developed.Os veículos aéreos não tripulados (VANTs), embora dificilmente considerados uma nova tecnologia, ganharam recentemente um papel de destaque em muitas indústrias, sendo amplamente utilizados não apenas por amadores, mas também em situações profissionais de alta exigência, sendo expectável um impacto social massivo nos próximos anos. No entanto, a operação de VANTs está repleta de sérios riscos de segurança, como colisões com obstáculos dinâmicos (pássaros, outros VANTs ou objetos arremessados). Estes cenários de colisão são complexos para analisar em tempo real, às vezes sendo computacionalmente impossível de resolver com os algoritmos existentes, tornando o uso de VANTs um risco operacional e, portanto, reduzindo significativamente a sua aplicabilidade comercial em ambientes citadinos. Neste trabalho, uma arquitectura conceptual para VANTs autônomos e em rede é apresentada, com foco nos requisitos arquitetônicos do subsistema de prevenção de colisão para atingir níveis aceitáveis de segurança e confiabilidade. Os estudos presentes na literatura para prevenção de colisão contra objectos estacionários são revistos e uma nova abordagem é descrita. Esta tecnica usa técnicas de aprendizagem profunda e processamento de imagem, para realizar a prevenção de colisões em tempo real com objetos móveis. Por fim, novos modelos e combinações de algoritmos são propostos, fornecendo uma nova abordagem para evitar colisões de VANTs usando Redes Neurais Profundas. A viabilidade da abordagem foi demonstrada através de testes experimentais utilizando um VANT, desenvolvido a partir da arquitectura apresentada

    Expressive movement generation with machine learning

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    Movement is an essential aspect of our lives. Not only do we move to interact with our physical environment, but we also express ourselves and communicate with others through our movements. In an increasingly computerized world where various technologies and devices surround us, our movements are essential parts of our interaction with and consumption of computational devices and artifacts. In this context, incorporating an understanding of our movements within the design of the technologies surrounding us can significantly improve our daily experiences. This need has given rise to the field of movement computing – developing computational models of movement that can perceive, manipulate, and generate movements. In this thesis, we contribute to the field of movement computing by building machine-learning-based solutions for automatic movement generation. In particular, we focus on using machine learning techniques and motion capture data to create controllable, generative movement models. We also contribute to the field by creating datasets, tools, and libraries that we have developed during our research. We start our research by reviewing the works on building automatic movement generation systems using machine learning techniques and motion capture data. Our review covers background topics such as high-level movement characterization, training data, features representation, machine learning models, and evaluation methods. Building on our literature review, we present WalkNet, an interactive agent walking movement controller based on neural networks. The expressivity of virtual, animated agents plays an essential role in their believability. Therefore, WalkNet integrates controlling the expressive qualities of movement with the goal-oriented behaviour of an animated virtual agent. It allows us to control the generation based on the valence and arousal levels of affect, the movement’s walking direction, and the mover’s movement signature in real-time. Following WalkNet, we look at controlling movement generation using more complex stimuli such as music represented by audio signals (i.e., non-symbolic music). Music-driven dance generation involves a highly non-linear mapping between temporally dense stimuli (i.e., the audio signal) and movements, which renders a more challenging modelling movement problem. To this end, we present GrooveNet, a real-time machine learning model for music-driven dance generation
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