416 research outputs found
Robot skill learning system of multi-space fusion based on dynamic movement primitives and adaptive neural network control
This article develops a robot skill learning system with multi-space fusion, simultaneously considering motion/stiffness generation and trajectory tracking. To begin with, surface electromyography (sEMG) signals from the human arm is captured based on the MYO armband to estimate endpoint stiffness. Gaussian Process Regression (GPR) is combined with dynamic movement primitive (DMP) to extract more skills features from multi-demonstrations. Then, the traditional DMP formulation is improved based on the Riemannian metric to encode the robot's quaternions with non-Euclidean properties. Furthermore, an adaptive neural network (NN)-based finite-time admittance controller is designed to track the trajectory generated by the motion model and to reflect the learned stiffness characteristics. In this controller, a radial basis function neural network (RBFNN) is employed to compensate for the uncertainty of the robot dynamics. Finally, experimental validation is conducted using the ROKAE collaborative robot, confirming the effectiveness of the proposed approach. In summary, the presented framework is suitable for human-robot skill transfer method that require simultaneous consideration of position and stiffness in Euclidean space, as well as orientation on Riemannian manifolds
Deep Learning Techniques for Electroencephalography Analysis
In this thesis we design deep learning techniques for training deep neural networks on electroencephalography (EEG) data and in particular on two problems, namely EEG-based motor imagery decoding and EEG-based affect recognition, addressing challenges associated with them. Regarding the problem of motor imagery (MI) decoding, we first consider the various kinds of domain shifts in the EEG signals, caused by inter-individual differences (e.g. brain anatomy, personality and cognitive profile). These domain shifts render multi-subject training a challenging task and impede robust cross-subject generalization. We build a two-stage model ensemble architecture and propose two objectives to train it, combining the strengths of curriculum learning and collaborative training. Our subject-independent experiments on the large datasets of Physionet and OpenBMI, verify the effectiveness of our approach. Next, we explore the utilization of the spatial covariance of EEG signals through alignment techniques, with the goal of learning domain-invariant representations. We introduce a Riemannian framework that concurrently performs covariance-based signal alignment and data augmentation, while training a convolutional neural network (CNN) on EEG time-series. Experiments on the BCI IV-2a dataset show that our method performs superiorly over traditional alignment, by inducing regularization to the weights of the CNN. We also study the problem of EEG-based affect recognition, inspired by works suggesting that emotions can be expressed in relative terms, i.e. through ordinal comparisons between different affective state levels. We propose treating data samples in a pairwise manner to infer the ordinal relation between their corresponding affective state labels, as an auxiliary training objective. We incorporate our objective in a deep network architecture which we jointly train on the tasks of sample-wise classification and pairwise ordinal ranking. We evaluate our method on the affective datasets of DEAP and SEED and obtain performance improvements over deep networks trained without the additional ranking objective
Classical and quantum algorithms for scaling problems
This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size
An Explainable Geometric-Weighted Graph Attention Network for Identifying Functional Networks Associated with Gait Impairment
One of the hallmark symptoms of Parkinson's Disease (PD) is the progressive
loss of postural reflexes, which eventually leads to gait difficulties and
balance problems. Identifying disruptions in brain function associated with
gait impairment could be crucial in better understanding PD motor progression,
thus advancing the development of more effective and personalized therapeutics.
In this work, we present an explainable, geometric, weighted-graph attention
neural network (xGW-GAT) to identify functional networks predictive of the
progression of gait difficulties in individuals with PD. xGW-GAT predicts the
multi-class gait impairment on the MDS Unified PD Rating Scale (MDS-UPDRS). Our
computational- and data-efficient model represents functional connectomes as
symmetric positive definite (SPD) matrices on a Riemannian manifold to
explicitly encode pairwise interactions of entire connectomes, based on which
we learn an attention mask yielding individual- and group-level explainability.
Applied to our resting-state functional MRI (rs-fMRI) dataset of individuals
with PD, xGW-GAT identifies functional connectivity patterns associated with
gait impairment in PD and offers interpretable explanations of functional
subnetworks associated with motor impairment. Our model successfully
outperforms several existing methods while simultaneously revealing
clinically-relevant connectivity patterns. The source code is available at
https://github.com/favour-nerrise/xGW-GAT .Comment: Accepted by the 26th International Conference on Medical Image
Computing and Computer Assisted Intervention (MICCAI 2023). MICCAI
Student-Author Registration (STAR) Award. 11 pages, 2 figures, 1 table,
appendix. Source Code: https://github.com/favour-nerrise/xGW-GA
Curvature corrected tangent space-based approximation of manifold-valued data
When generalizing schemes for real-valued data approximation or decomposition
to data living in Riemannian manifolds, tangent space-based schemes are very
attractive for the simple reason that these spaces are linear. An open
challenge is to do this in such a way that the generalized scheme is applicable
to general Riemannian manifolds, is global-geometry aware and is
computationally feasible. Existing schemes have been unable to account for all
three of these key factors at the same time.
In this work, we take a systematic approach to developing a framework that is
able to account for all three factors. First, we will restrict ourselves to the
-- still general -- class of symmetric Riemannian manifolds and show how
curvature affects general manifold-valued tensor approximation schemes. Next,
we show how the latter observations can be used in a general strategy for
developing approximation schemes that are also global-geometry aware. Finally,
having general applicability and global-geometry awareness taken into account
we restrict ourselves once more in a case study on low-rank approximation. Here
we show how computational feasibility can be achieved and propose the
curvature-corrected truncated higher-order singular value decomposition
(CC-tHOSVD), whose performance is subsequently tested in numerical experiments
with both synthetic and real data living in symmetric Riemannian manifolds with
both positive and negative curvature
Building Neural Networks on Matrix Manifolds: A Gyrovector Space Approach
Matrix manifolds, such as manifolds of Symmetric Positive Definite (SPD)
matrices and Grassmann manifolds, appear in many applications. Recently, by
applying the theory of gyrogroups and gyrovector spaces that is a powerful
framework for studying hyperbolic geometry, some works have attempted to build
principled generalizations of Euclidean neural networks on matrix manifolds.
However, due to the lack of many concepts in gyrovector spaces for the
considered manifolds, e.g., the inner product and gyroangles, techniques and
mathematical tools provided by these works are still limited compared to those
developed for studying hyperbolic geometry. In this paper, we generalize some
notions in gyrovector spaces for SPD and Grassmann manifolds, and propose new
models and layers for building neural networks on these manifolds. We show the
effectiveness of our approach in two applications, i.e., human action
recognition and knowledge graph completion
Riemannian statistical techniques with applications in fMRI
Over the past 30 years functional magnetic resonance imaging (fMRI) has become a fundamental
tool in cognitive neuroimaging studies. In particular, the emergence of restingstate
fMRI has gained popularity in determining biomarkers of mental health disorders
(Woodward & Cascio, 2015). Resting-state fMRI can be analysed using the functional
connectivity matrix, an object that encodes the temporal correlation of blood activity
within the brain. Functional connectivity matrices are symmetric positive definite (SPD)
matrices, but common analysis methods either reduce the functional connectivity matrices
to summary statistics or fail to account for the positive definite criteria. However,
through the lens of Riemannian geometry functional connectivity matrices have an intrinsic
non-linear shape that respects the positive definite criteria (the affine-invariant
geometry (Pennec, Fillard, & Ayache, 2006)). With methods from Riemannian geometric
statistics, we can begin to explore the shape of the functional brain to understand this
non-linear structure and reduce data-loss in our analyses.
This thesis o↵ers two novel methodological developments to the field of Riemannian geometric
statistics inspired by methods used in fMRI research. First we propose geometric-
MDMR, a generalisation of multivariate distance matrix regression (MDMR) (McArdle &
Anderson, 2001) to Riemannian manifolds. Our second development is Riemannian partial
least squares (R-PLS), the generalisation of the predictive modelling technique partial least squares (PLS) (H. Wold, 1975) to Riemannian manifolds. R-PLS extends geodesic
regression (Fletcher, 2013) to manifold-valued response and predictor variables, similar to
how PLS extends multiple linear regression. We also generalise the NIPALS algorithm to
Riemannian manifolds and suggest a tangent space approximation as a proposed method
to fit R-PLS.
In addition to our methodological developments, this thesis o↵ers three more contributions
to the literature. Firstly, we develop a novel simulation procedure to simulate
realistic functional connectivity matrices through a combination of bootstrapping and the
Wishart distribution. Second, we propose the R2S
statistic for measuring subspace similarity
using the theory of principal angles between subspaces. Finally, we propose an
extension of the VIP statistic from PLS (S. Wold, Johansson, & Cocchi, 1993) to describe
the relationship between individual predictors and response variables when predicting a
multivariate response with PLS.
All methods in this thesis are applied to two fMRI datasets: the COBRE dataset
relating to schizophrenia, and the ABIDE dataset relating to Autism Spectrum Disorder
(ASD). We show that geometric-MDMR can detect group-based di↵erences between ASD
and neurotypical controls (NTC), unlike its Euclidean counterparts. We also demonstrate
the efficacy of R-PLS through the detection of functional connections related to
schizophrenia and ASD. These results are encouraging for the role of Riemannian geometric
statistics in the future of neuroscientific research.Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 202
Geometric Data Analysis: Advancements of the Statistical Methodology and Applications
Data analysis has become fundamental to our society and comes in multiple facets and approaches. Nevertheless, in research and applications, the focus was primarily on data from Euclidean vector spaces. Consequently, the majority of methods that are applied today are not suited for more general data types. Driven by needs from fields like image processing, (medical) shape analysis, and network analysis, more and more attention has recently been given to data from non-Euclidean spaces–particularly (curved) manifolds. It has led to the field of geometric data analysis whose methods explicitly take the structure (for example, the topology and geometry) of the underlying space into account.
This thesis contributes to the methodology of geometric data analysis by generalizing several fundamental notions from multivariate statistics to manifolds. We thereby focus on two different viewpoints.
First, we use Riemannian structures to derive a novel regression scheme for general manifolds that relies on splines of generalized BĂ©zier curves. It can accurately model non-geodesic relationships, for example, time-dependent trends with saturation effects or cyclic trends. Since BĂ©zier curves can be evaluated with the constructive de Casteljau algorithm, working with data from manifolds of high dimensions (for example, a hundred thousand or more) is feasible. Relying on the regression, we further develop
a hierarchical statistical model for an adequate analysis of longitudinal data in manifolds, and a method to control for confounding variables.
We secondly focus on data that is not only manifold- but even Lie group-valued, which is frequently the case in applications. We can only achieve this by endowing the group with an affine connection structure that is generally not Riemannian. Utilizing it, we derive generalizations of several well-known dissimilarity measures between data distributions that can be used for various tasks, including hypothesis testing. Invariance under data translations is proven, and a connection to continuous distributions is given for one measure.
A further central contribution of this thesis is that it shows use cases for all notions in real-world applications, particularly in problems from shape analysis in medical imaging and archaeology. We can replicate or further quantify several known findings for shape changes of the femur and the right hippocampus under osteoarthritis and Alzheimer's, respectively. Furthermore, in an archaeological application, we obtain new insights into the construction principles of ancient sundials. Last but not least, we use the geometric structure underlying human brain connectomes to predict cognitive scores. Utilizing a sample selection procedure, we obtain state-of-the-art results
Unifying over-smoothing and over-squashing in graph neural networks: A physics informed approach and beyond
Graph Neural Networks (GNNs) have emerged as one of the leading approaches
for machine learning on graph-structured data. Despite their great success,
critical computational challenges such as over-smoothing, over-squashing, and
limited expressive power continue to impact the performance of GNNs. In this
study, inspired from the time-reversal principle commonly utilized in classical
and quantum physics, we reverse the time direction of the graph heat equation.
The resulted reversing process yields a class of high pass filtering functions
that enhance the sharpness of graph node features. Leveraging this concept, we
introduce the Multi-Scaled Heat Kernel based GNN (MHKG) by amalgamating diverse
filtering functions' effects on node features. To explore more flexible
filtering conditions, we further generalize MHKG into a model termed G-MHKG and
thoroughly show the roles of each element in controlling over-smoothing,
over-squashing and expressive power. Notably, we illustrate that all
aforementioned issues can be characterized and analyzed via the properties of
the filtering functions, and uncover a trade-off between over-smoothing and
over-squashing: enhancing node feature sharpness will make model suffer more
from over-squashing, and vice versa. Furthermore, we manipulate the time again
to show how G-MHKG can handle both two issues under mild conditions. Our
conclusive experiments highlight the effectiveness of proposed models. It
surpasses several GNN baseline models in performance across graph datasets
characterized by both homophily and heterophily
Towards learning mechanistic models at the right level of abstraction
Das menschliche Gehirn ist in der Lage, Vorhersagen zu treffen, zu planen und sich durch mentale Simulationen kontrafaktische Situationen vorzustellen. Künstliche neuronale Netze sind zwar in bestimmten Bereichen brereits sehr leistungsfähig, scheinen aber immer noch ein mechanistisches Verständnis der Welt zu vermissen. In dieser Arbeit befassen wir uns mit verschiedenen Ansätzen, wie neuronale Netze die zugrundeliegenden Mechanismen des modellierten Systems besser erfassen können. Wir werden uns mit Adaptive skip intervals (ASI) befassen; eine Methode, die es dynamischen Modellen ermöglicht, ihre eigene zeitliche Vergröberung an jedem Punkt zu wählen. Dadurch werden langfristige Vorhersagen sowohl einfacher als auch rechnerisch effizienter. Als Nächstes werden wir uns mit alternativen Möglichkeiten zur Aggregation von Gradienten in verschiedenen Umgebungen befassen, was zum Begriff der Invariant Learning Consistency (ILC) und der Methode AND-mask für einen modifizierten stochastischen Gradientenabstieg führt. Durch das Herausfiltern inkonsistenter Trainingssignale aus verschiedenen Umgebungen bleiben die gemeinsamen Mechanismen erhalten. Schließlich werden wir sehen, dass Lernen auf der Grundlage von Meta-Gradienten Trajektorien von dynamischen Systemen transformieren kann, um nützliche Lernsignale in Richtung eines zugrunde liegenden Ziels zu konstruieren, wie z. B. Reward beim Reinforcement Learning. Dadurch kann das interne Modell sowohl eine zeitliche als auch eine Zustandsabstraktion beinhalten
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