Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLearning Common Harmonic Waves on Stiefel Manifold -- A New Mathematical Approach for Brain Network Analyses
47
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Converging evidence shows that disease-relevant brain alterations do not appear in random brain locations, instead, its spatial pattern follows large scale brain networks. In this context, a powerful network analysis approach with a mathematical foundation is indispensable to understand the mechanism of neuropathological events spreading throughout the brain. Indeed, the topology of each brain network is governed by its native harmonic waves, which are a set of orthogonal bases derived from the Eigen-system of the underlying Laplacian matrix. To that end, we propose a novel connectome harmonic analysis framework to provide enhanced mathematical insights by detecting frequency-based alterations relevant to brain disorders. The backbone of our framework is a novel manifold algebra appropriate for inference across harmonic waves that overcomes the limitations of using classic Euclidean operations on irregular data structures. The individual harmonic difference is measured by a set of common harmonic waves learned from a population of individual Eigen systems, where each native Eigen-system is regarded as a sample drawn from the Stiefel manifold. Specifically, a manifold optimization scheme is tailored to find the common harmonic waves which reside at the center of Stiefel manifold. To that end, the common harmonic waves constitute the new neuro-biological bases to understand disease progression. Each harmonic wave exhibits a unique propagation pattern of neuro-pathological burdens spreading across brain networks. The statistical power of our novel connectome harmonic analysis approach is evaluated by identifying frequency-based alterations relevant to Alzheimers disease, where our learning-based manifold approach discovers more significant and reproducible network dysfunction patterns compared to Euclidian methods.
rate research
Read More
Understanding the connectivity in the brain is an important prerequisite for understanding how the brain processes information. In the Brain/MINDS project, a connectivity study on marmoset brains uses two-photon microscopy fluorescence images of axonal projections to collect the neuron connectivity from defined brain regions at the mesoscopic scale. The processing of the images requires the detection and segmentation of the axonal tracer signal. The objective is to detect as much tracer signal as possible while not misclassifying other background structures as the signal. This can be challenging because of imaging noise, a cluttered image background, distortions or varying image contrast cause problems. We are developing MarmoNet, a pipeline that processes and analyzes tracer image data of the common marmoset brain. The pipeline incorporates state-of-the-art machine learning techniques based on artificial convolutional neural networks (CNN) and image registration techniques to extract and map all relevant information in a robust manner. The pipeline processes new images in a fully automated way. This report introduces the current state of the tracer signal analysis part of the pipeline.
Riemannian optimization has drawn a lot of attention due to its wide applications in practice. Riemannian stochastic first-order algorithms have been studied in the literature to solve large-scale machine learning problems over Riemannian manifolds. However, most of the existing Riemannian stochastic algorithms require the objective function to be differentiable, and they do not apply to the case where the objective function is nonsmooth. In this paper, we present two Riemannian stochastic proximal gradient methods for minimizing nonsmooth function over the Stiefel manifold. The two methods, named R-ProxSGD and R-ProxSPB, are generalizations of proximal SGD and proximal SpiderBoost in Euclidean setting to the Riemannian setting. Analysis on the incremental first-order oracle (IFO) complexity of the proposed algorithms is provided. Specifically, the R-ProxSPB algorithm finds an $epsilon$-stationary point with $mathcal{O}(epsilon^{-3})$ IFOs in the online case, and $mathcal{O}(n+sqrt{n}epsilon^{-3})$ IFOs in the finite-sum case with $n$ being the number of summands in the objective. Experimental results on online sparse PCA and robust low-rank matrix completion show that our proposed methods significantly outperform the existing methods that uses Riemannian subgradient information.
Detecting and segmenting brain metastases is a tedious and time-consuming task for many radiologists, particularly with the growing use of multi-sequence 3D imaging. This study demonstrates automated detection and segmentation of brain metastases on multi-sequence MRI using a deep learning approach based on a fully convolution neural network (CNN). In this retrospective study, a total of 156 patients with brain metastases from several primary cancers were included. Pre-therapy MR images (1.5T and 3T) included pre- and post-gadolinium T1-weighted 3D fast spin echo, post-gadolinium T1-weighted 3D axial IR-prepped FSPGR, and 3D fluid attenuated inversion recovery. The ground truth was established by manual delineation by two experienced neuroradiologists. CNN training/development was performed using 100 and 5 patients, respectively, with a 2.5D network based on a GoogLeNet architecture. The results were evaluated in 51 patients, equally separated into those with few (1-3), multiple (4-10), and many (>10) lesions. Network performance was evaluated using precision, recall, Dice/F1 score, and ROC-curve statistics. For an optimal probability threshold, detection and segmentation performance was assessed on a per metastasis basis. The area under the ROC-curve (AUC), averaged across all patients, was 0.98. The AUC in the subgroups was 0.99, 0.97, and 0.97 for patients having 1-3, 4-10, and >10 metastases, respectively. Using an average optimal probability threshold determined by the development set, precision, recall, and Dice-score were 0.79, 0.53, and 0.79, respectively. At the same probability threshold, the network showed an average false positive rate of 8.3/patient (no lesion-size limit) and 3.4/patient (10 mm3 lesion size limit). In conclusion, a deep learning approach using multi-sequence MRI can aid in the detection and segmentation of brain metastases.
The symplectic Stiefel manifold, denoted by $mathrm{Sp}(2p,2n)$, is the set of linear symplectic maps between the standard symplectic spaces $mathbb{R}^{2p}$ and $mathbb{R}^{2n}$. When $p=n$, it reduces to the well-known set of $2ntimes 2n$ symplectic matrices. Optimization problems on $mathrm{Sp}(2p,2n)$ find applications in various areas, such as optics, quantum physics, numerical linear algebra and model order reduction of dynamical systems. The purpose of this paper is to propose and analyze gradient-descent methods on $mathrm{Sp}(2p,2n)$, where the notion of gradient stems from a Riemannian metric. We consider a novel Riemannian metric on $mathrm{Sp}(2p,2n)$ akin to the canonical metric of the (standard) Stiefel manifold. In order to perform a feasible step along the antigradient, we develop two types of search strategies: one is based on quasi-geodesic curves, and the other one on the symplectic Cayley transform. The resulting optimization algorithms are proved to converge globally to critical points of the objective function. Numerical experiments illustrate the efficiency of the proposed methods.
Automatic segmentation of liver tumors in medical images is crucial for the computer-aided diagnosis and therapy. It is a challenging task, since the tumors are notoriously small against the background voxels. This paper proposes a new three-stage curriculum learning approach for training deep networks to tackle this small object segmentation problem. The learning in the first stage is performed on the whole input to obtain an initial deep network for tumor segmenta-tion. Then the second stage of learning focuses the strength-ening of tumor specific features by continuing training the network on the tumor patches. Finally, we retrain the net-work on the whole input in the third stage, in order that the tumor specific features and the global context can be inte-grated ideally under the segmentation objective. Benefitting from the proposed learning approach, we only need to em-ploy one single network to segment the tumors directly. We evaluated our approach on the 2017 MICCAI Liver Tumor Segmentation challenge dataset. In the experiments, our approach exhibits significant improvement compared with the commonly used cascaded counterpart.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
