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Graph Hyperalignment for Multi-subject fMRI Functional Alignment 1

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1st International Workshop on Graph Learning in Medical Imaging, GLMI 2019 held in conjunction with the 22nd International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2019

作者： Li, Weida Chen, Fang Zhang, Daoqiang College of Computer Science and Technology MIIT Key Laboratory of Pattern Analysis and Machine Intelligence Nanjing University of Aeronautics and Astronautics Nanjing China

ISBN: (数字)9783030358174

ISBN: (纸本)9783030358167

In fMRI analysis, the scientist seeks to aggregate multi-subject fMRI data so that inferences shared across subjects can be achieved. The challenge is to eliminate the variability of anatomical structure and functional topography of the human brain, which calls for aligning fMRI data across subjects. However, the existing methods do not exploit the geometry of the stimuli, which can be inferred by using certain domain knowledge and then serve as a priori. In this paper, such geometry is encoded in a graph matrix, and we propose an algorithm named Graph Hyperalignment for leveraging it. Specifically, a kernel-based optimization is developed to allow for non-linear feature extraction. To tackle overfitting caused by the high-spatial-and-low-temporal resolution of fMRI, the data in the new feature space are assumed to lie in a low-dimensional affine subspace, which can be implicitly integrated into the proposed optimization. Unlike other iterative existing methods, GHA reaches an optimal solution directly. Examining over four real datasets, Graph Hyperaligment achieves superior results to other methods. © 2019, Springer Nature Switzerland AG.

关键词： Domain Knowledge

Factor analysis, Probabilistic Principal Component analysis, Variational Inference, and Variational Autoencoder: Tutorial and Survey

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arXiv 2021年

This is a tutorial and survey paper on factor analysis, probabilistic Principal Component analysis (PCA), variational inference, and Variational Autoencoder (VAE). These methods, which are tightly related, are dimensionality reduction and generative models. They assume that every data point is generated from or caused by a lowdimensional latent factor. By learning the parameters of distribution of latent space, the corresponding low-dimensional factors are found for the sake of dimensionality reduction. For their stochastic and generative behaviour, these models can also be used for generation of new data points in the data space. In this paper, we first start with variational inference where we derive the Evidence Lower Bound (ELBO) and Expectation Maximization (EM) for learning the parameters. Then, we introduce factor analysis, derive its joint and marginal distributions, and work out its EM steps. Probabilistic PCA is then explained, as a special case of factor analysis, and its closed-form solutions are derived. Finally, VAE is explained where the encoder, decoder and sampling from the latent space are introduced. Training VAE using both EM and backpropagation are explained. Copyright © 2021, The Authors. All rights reserved.

关键词： Maximum principle

Sufficient dimension reduction for high-dimensional regression and low-dimensional embedding: tutorial and survey

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arXiv 2021年

作者： Ghojogh, Benyamin Ghodsi, Ali Karray, Fakhri Crowley, Mark Department of Electrical and Computer Engineering Machine Learning Laboratory University of Waterloo WaterlooON Canada Department of Statistics and Actuarial Science & David R. Cheriton School of Computer Science Data Analytics Laboratory University of Waterloo WaterlooON Canada Department of Electrical and Computer Engineering Centre for Pattern Analysis and Machine Intelligence University of Waterloo WaterlooON Canada

This is a tutorial and survey paper on various methods for Sufficient Dimension Reduction (SDR). We cover these methods with both statistical high-dimensional regression perspective and machine learning approach for dimensionality reduction. We start with introducing inverse regression methods including Sliced Inverse Regression (SIR), Sliced Average Variance Estimation (SAVE), contour regression, directional regression, Principal Fitted Components (PFC), Likelihood Acquired Direction (LAD), and graphical regression. Then, we introduce forward regression methods including Principal Hessian Directions (pHd), Minimum Average Variance Estimation (MAVE), Conditional Variance Estimation (CVE), and deep SDR methods. Finally, we explain Kernel Dimension Reduction (KDR) both for supervised and unsupervised learning. We also show that supervised KDR and supervised PCA are equivalent. Copyright © 2021, The Authors. All rights reserved.

关键词： Regression analysis

TIDE: Test Time Few Shot Object Detection

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arXiv 2023年

作者： Li, Weikai Wei, Hongfeng Wu, Yanlai Yang, Jie Ruan, Yudi Li, Yuan Tang, Ying The School of Mathematics and Statistics Chongqing Jiaotong University Chongqing400074 China MIIT Key Laboratory of Pattern Analysis and Machine Intelligence Nanjing210016 China China Science IntelliCloud Technology Co. Ltd. Anhui230000 China The China Science IntelliCloud Technology Co. Ltd. Anhui230000 China The School of Information Science and Technology Chongqing Jiaotong University Chongqing400074 China The Department of Electrical and Computer Engineering Rowan University GlassboroNJ08028 United States

Few-shot object detection (FSOD) aims to extract semantic knowledge from limited object instances of novel categories within a target domain. Recent advances in FSOD focus on fine-tuning the base model based on a few objects via meta-learning or data augmentation. Despite their success, the majority of them are grounded with parametric readjustment to generalize on novel objects, which face considerable challenges in Industry 5.0, such as (i) a certain amount of fine-tuning time is required, and (ii) the parameters of the constructed model being unavailable due to the privilege protection, making the fine-tuning fail. Such constraints naturally limit its application in scenarios with real-time configuration requirements or within black-box settings. To tackle the challenges mentioned above, we formalize a novel FSOD task, referred to as Test TIme Few Shot DEtection (TIDE), where the model is un-tuned in the configuration procedure. To that end, we introduce an asymmetric architecture for learning a support-instance-guided dynamic category classifier. Further, a cross-attention module and a multi-scale resizer are provided to enhance the model performance. Experimental results on multiple few-shot object detection platforms reveal that the proposed TIDE significantly outperforms existing contemporary methods. The implementation codes are available at https://***/deku-0621/TIDE. © 2023, CC BY-NC-ND.

关键词： Object detection

KKT conditions, first-order and second-order optimization, and distributed optimization: Tutorial and survey

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arXiv 2021年

作者： Ghojogh, Benyamin Ghodsi, Ali Karray, Fakhri Crowley, Mark Department of Electrical and Computer Engineering Machine Learning Laboratory University of Waterloo WaterlooON Canada Department of Statistics and Actuarial Science & David R. Cheriton School of Computer Science Data Analytics Laboratory University of Waterloo WaterlooON Canada Department of Electrical and Computer Engineering Centre for Pattern Analysis and Machine Intelligence University of Waterloo WaterlooON Canada

This is a tutorial and survey paper on Karush-Kuhn-Tucker (KKT) conditions, first-order and second-order numerical optimization, and distributed optimization. After a brief review of history of optimization, we start with some preliminaries on properties of sets, norms, functions, and concepts of optimization. Then, we introduce the optimization problem, standard optimization problems (including linear programming, quadratic programming, and semidefinite programming), and convex problems. We also introduce some techniques such as eliminating inequality, equality, and set constraints, adding slack variables, and epigraph form. We introduce Lagrangian function, dual variables, KKT conditions (including primal feasibility, dual feasibility, weak and strong duality, complementary slackness, and stationarity condition), and solving optimization by method of Lagrange multipliers. Then, we cover first-order optimization including gradient descent, line-search, convergence of gradient methods, momentum, steepest descent, and backpropagation. Other first-order methods are explained, such as accelerated gradient method, stochastic gradient descent, mini-batch gradient descent, stochastic average gradient, stochastic variance reduced gradient, AdaGrad, RMSProp, and Adam optimizer, proximal methods (including proximal mapping, proximal point algorithm, and proximal gradient method), and constrained gradient methods (including projected gradient method, projection onto convex sets, and Frank-Wolfe method). We also cover non-smooth and `1 optimization methods including lasso regularization, convex conjugate, Huber function, soft-thresholding, coordinate descent, and subgradient methods. Then, we explain second-order methods including Newton’s method for unconstrained, equality constrained, and inequality constrained problems. We explain the interior-point method, barrier methods, Wolfe conditions for line-search, fast solving system of equations (including decomposition methods a

关键词： Quadratic programming

Unified Framework for Spectral Dimensionality Reduction, Maximum Variance Unfolding, and Kernel Learning By Semidefinite Programming: Tutorial and Survey

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arXiv 2021年

This is a tutorial and survey paper on unification of spectral dimensionality reduction methods, kernel learning by Semidefinite Programming (SDP), Maximum Variance Unfolding (MVU) or Semidefinite Embedding (SDE), and its variants. We first explain how the spectral dimensionality reduction methods can be unified as kernel Principal Component analysis (PCA) with different kernels. This unification can be interpreted as eigenfunction learning or representation of kernel in terms of distance matrix. Then, since the spectral methods are unified as kernel PCA, we say let us learn the best kernel for unfolding the manifold of data to its maximum variance. We first briefly introduce kernel learning by SDP for the transduction task. Then, we explain MVU in detail. Various versions of supervised MVU using nearest neighbors graph, by class-wise unfolding, by Fisher criterion, and by colored MVU are explained. We also explain out-of-sample extension of MVU using eigenfunctions and kernel mapping. Finally, we introduce other variants of MVU including action respecting embedding, relaxed MVU, and landmark MVU for big data. Copyright © 2021, The Authors. All rights reserved.

关键词： Surveys

Generative Adversarial Networks and adversarial autoencoders: Tutorial and survey

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arXiv 2021年

This is a tutorial and survey paper on Generative Adversarial Network (GAN), adversarial autoencoders, and their variants. We start with explaining adversarial learning and the vanilla GAN. Then, we explain the conditional GAN and DCGAN. The mode collapse problem is introduced and various methods, including minibatch GAN, unrolled GAN, BourGAN, mixture GAN, D2GAN, and Wasserstein GAN, are introduced for resolving this problem. Then, maximum likelihood estimation in GAN are explained along with f-GAN, adversarial variational Bayes, and Bayesian GAN. Then, we cover feature matching in GAN, InfoGAN, GRAN, LSGAN, energy-based GAN, CatGAN, MMD GAN, LapGAN, progressive GAN, triple GAN, LAG, GMAN, AdaGAN, CoGAN, inverse GAN, BiGAN, ALI, SAGAN, Few-shot GAN, SinGAN, and interpolation and evaluation of GAN. Then, we introduce some applications of GAN such as image-to-image translation (including PatchGAN, CycleGAN, DeepFaceDrawing, simulated GAN, interactive GAN), text-to-image translation (including StackGAN), and mixing image characteristics (including FineGAN and MixNMatch). Finally, we explain the autoencoders based on adversarial learning including adversarial autoencoder, PixelGAN, and implicit autoencoder. Copyright © 2021, The Authors. All rights reserved.

关键词： Generative adversarial networks

Restricted Boltzmann machine and Deep Belief Network: Tutorial and Survey

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arXiv 2021年

This is a tutorial and survey paper on Boltzmann machine (BM), Restricted Boltzmann machine (RBM), and Deep Belief Network (DBN). We start with the required background on probabilistic graphical models, Markov random field, Gibbs sampling, statistical physics, Ising model, and the Hopfield network. Then, we introduce the structures of BM and RBM. The conditional distributions of visible and hidden variables, Gibbs sampling in RBM for generating variables, training BM and RBM by maximum likelihood estimation, and contrastive divergence are explained. Then, we discuss different possible discrete and continuous distributions for the variables. We introduce conditional RBM and how it is trained. Finally, we explain deep belief network as a stack of RBM models. This paper on Boltzmann machines can be useful in various fields including data science, statistics, neural computation, and statistical physics. Copyright © 2021, The Authors. All rights reserved.

关键词： Statistical Physics

Johnson-lindenstrauss lemma, linear and nonlinear random projections, random fourier features, and random kitchen sinks: Tutorial and survey

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arXiv 2021年

作者： Ghojogh, Benyamin Ghodsi, Ali Karray, Fakhri Crowley, Mark Department of Electrical and Computer Engineering Machine Learning Laboratory University of Waterloo WaterlooON Canada Department of Statistics and Actuarial Science & David R. Cheriton School of Computer Science Data Analytics Laboratory University of Waterloo WaterlooON Canada Department of Electrical and Computer Engineering Centre for Pattern Analysis and Machine Intelligence University of Waterloo WaterlooON Canada

This is a tutorial and survey paper on the Johnson-Lindenstrauss (JL) lemma and linear and nonlinear random projections. We start with linear random projection and then justify its correctness by JL lemma and its proof. Then, sparse random projections with `1 norm and interpolation norm are introduced. Two main applications of random projection, which are low-rank matrix approximation and approximate nearest neighbor search by random projection onto hypercube, are explained. Random Fourier Features (RFF) and Random Kitchen Sinks (RKS) are explained as methods for nonlinear random projection. Some other methods for nonlinear random projection, including extreme learning machine, randomly weighted neural networks, and ensemble of random projections, are also introduced. Copyright © 2021, The Authors. All rights reserved.

关键词： Surveys