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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

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

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

Predicting gastric cancer response to anti-HER2 therapy or anti-HER2 combined immunotherapy based on multimodal data

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Signal Transduction and Targeted Therapy 2024年第9期9卷 4137-4148页

作者： Zifan Chen Yang Chen Yu Sun Lei Tang Li Zhang Yajie Hu Meng He Zhiwei Li Siyuan Cheng Jiajia Yuan Zhenghang Wang Yakun Wang Jie Zhao Jifang Gong Liying Zhao Baoshan Cao Guoxin Li Xiaotian Zhang Bin Dong Lin Shen Center for Data Science Peking UniversityBeijingChina Department of Gastrointestinal Oncology Key Laboratory of Carcinogenesis and Translational Research(Ministry of Education)Peking University Cancer Hospital and InstituteBeijingChina Department of Pathology Key Laboratory of Carcinogenesis and Translational Research(Ministry of Education)Peking University Cancer Hospital and InstituteBeijingChina Department of Radiology Key Laboratory of Carcinogenesis and Translational Research(Ministry of Education)Peking University Cancer Hospital and InstituteBeijingChina National Biomedical Imaging Center Peking UniversityBeijingChina Department of General Surgery Nanfang HospitalSouthern Medical UniversityGuangzhouChina Guangdong Provincial Key Laboratory of Precision Medicine for Gastrointestinal Tumor GuangzhouChina Department of Medical Oncology and Radiation Sickness Peking University Third HospitalBeijingChina National Engineering Laboratory for Big Data Analysis and Applications Peking UniversityBeijingChina Beijing International Center for Mathematical Research(BICMR) Peking UniversityBeijingChina Center for Machine Learning Research Peking UniversityBeijingChina

The sole use of single modality data often fails to capture the complex heterogeneity among patients,including the variability in resistance to anti-HER2 therapy and outcomes of combined treatment regimens,for the treatment of HER2-positive gastric cancer(GC).This modality deficit has not been fully considered in many ***,the application of artificial intelligence in predicting the treatment response,particularly in complex diseases such as GC,is still in its ***,this study aimed to use a comprehensive analytic approach to accurately predict treatment responses to anti-HER2 therapy or anti-HER2 combined immunotherapy in patients with HER2-positive *** collected multi-modal data,comprising radiology,pathology,and clinical information from a cohort of 429 patients:310 treated with anti-HER2 therapy and 119 treated with a combination of anti-HER2 and anti-PD-1/PD-L1 inhibitors *** introduced a deep learning model,called the Multi-Modal model(MuMo),that integrates these data to make precise treatment response *** achieved an area under the curve score of 0.821 for anti-HER2 therapy and 0.914 for combined ***,patients classified as low-risk by MuMo exhibited significantly prolonged progression-free survival and overall survival(log-rank test,P<0.05).These findings not only highlight the significance of multi-modal data analysis in enhancing treatment evaluation and personalized medicine for HER2-positive gastric cancer,but also the potential and clinical value of our model.

关键词： immunotherapy HER2 cancer

Locally linear embedding and its variants: Tutorial and survey

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arXiv 2020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 for Locally Linear Embedding (LLE) and its variants. The idea of LLE is fitting the local structure of manifold in the embedding space. In this paper, we first cover LLE, kernel LLE, inverse LLE, and feature fusion with LLE. Then, we cover out-of-sample embedding using linear reconstruction, eigenfunctions, and kernel mapping. Incremental LLE is explained for embedding streaming data. Landmark LLE methods using the Nystrom approximation and locally linear landmarks are explained for big data embedding. We introduce the methods for parameter selection of number of neighbors using residual variance, Procrustes statistics, preservation neighborhood error, and local neighborhood selection. Afterwards, Supervised LLE (SLLE), enhanced SLLE, SLLE projection, probabilistic SLLE, supervised guided LLE (using Hilbert-Schmidt independence criterion), and semi-supervised LLE are explained for supervised and semi-supervised embedding. Robust LLE methods using least squares problem and penalty functions are also introduced for embedding in the presence of outliers and noise. Then, we introduce fusion of LLE with other manifold learning methods including Isomap (i.e., ISOLLE), principal component analysis, Fisher discriminant analysis, discriminant LLE, and Isotop. Finally, we explain weighted LLE in which the distances, reconstruction weights, or the embeddings are adjusted for better embedding;we cover weighted LLE for deformed distributed data, weighted LLE using probability of occurrence, SLLE by adjusting weights, modified LLE, and iterative LLE. Copyright © 2020, The Authors. All rights reserved.

关键词： Iterative methods

Multidimensional scaling, Sammon mapping, and Isomap: Tutorial and survey

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arXiv 2020年

Multidimensional Scaling (MDS) is one of the first fundamental manifold learning methods. It can be categorized into several methods, i.e., classical MDS, kernel classical MDS, metric MDS, and non-metric MDS. Sammon mapping and Isomap can be considered as special cases of metric MDS and kernel classical MDS, respectively. In this tutorial and survey paper, we review the theory of MDS, Sammon mapping, and Isomap in detail. We explain all the mentioned categories of MDS. Then, Sammon mapping, Isomap, and kernel Isomap are explained. Out-of-sample embedding for MDS and Isomap using eigenfunctions and kernel mapping are introduced. Then, Nystrom approximation and its use in landmark MDS and landmark Isomap are introduced for big data embedding. We also provide some simulations for illustrating the embedding by these methods. Copyright © 2020, The Authors. All rights reserved.

关键词： Embeddings

Spectral, Probabilistic, and Deep Metric learning: Tutorial and Survey

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arXiv 2022年

This is a tutorial and survey paper on metric learning. Algorithms are divided into spectral, probabilistic, and deep metric learning. We first start with the definition of distance metric, Mahalanobis distance, and generalized Mahalanobis distance. In spectral methods, we start with methods using scatters of data, including the first spectral metric learning, relevant methods to Fisher discriminant analysis, Relevant Component analysis (RCA), Discriminant Component analysis (DCA), and the Fisher-HSIC method. Then, large-margin metric learning, imbalanced metric learning, locally linear metric adaptation, and adversarial metric learning are covered. We also explain several kernel spectral methods for metric learning in the feature space. We also introduce geometric metric learning methods on the Riemannian manifolds. In probabilistic methods, we start with collapsing classes in both input and feature spaces and then explain the neighborhood component analysis methods, Bayesian metric learning, information theoretic methods, and empirical risk minimization in metric learning. In deep learning methods, we first introduce reconstruction autoencoders and supervised loss functions for metric learning. Then, Siamese networks and its various loss functions, triplet mining, and triplet sampling are explained. Deep discriminant analysis methods, based on Fisher discriminant analysis, are also reviewed. Finally, we introduce multi-modal deep metric learning, geometric metric learning by neural networks, and few-shot metric learning. Copyright © 2022, The Authors. All rights reserved.

关键词： Surveys

Robust learning with implicit residual networks

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arXiv 2019年

作者： Reshniak, Viktor Webster, Clayton G. Data Analysis and Machine Learning Oak Ridge National Laboratory Oak RidgeTN37831 United States Department of Mathematics University of Tennessee at Knoxville KnoxvilleTN37996 United States Lirio LLC KnoxvilleTN37923 United States

In this effort, we propose a new deep architecture utilizing residual blocks inspired by implicit discretization schemes. As opposed to the standard feed-forward networks, the outputs of the proposed implicit residual blocks are defined as the fixed points of the appropriately chosen nonlinear transformations. We show that this choice leads to the improved stability of both forward and backward propagations, has a favorable impact on the generalization power and allows to control the robustness of the network with only a few hyperparameters. In addition, the proposed reformulation of ResNet does not introduce new parameters and can potentially lead to a reduction in the number of required layers due to improved forward stability. Finally, we derive the memory-efficient training algorithm, propose a stochastic regularization technique and provide numerical results in support of our findings. Copyright © 2019, The Authors. All rights reserved.

关键词： Stochastic systems

Developing a Strategy for the Digital Transformation of an Educational Organization Based on Cloud Technology

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Developing a Strategy for the Digital Transformation of an E...

Information Systems Theory and Practice (ISTP), Seminar on

作者： Alexander V. Olifirov Krystina A. Makoveichuk Sergei A. Petrenko Department of Economics and Finance V.I Vernadsky Crimean Federal University Yalta Russia Department of Data Analysis and Machine Learning Financial University under the Government of the Russian Federation Moscow Russia Department of Information Security Saint Petersburg Electrotechnical University “LETI” Saint Petersburg Russia

The article examines the theory and practical implementation of a digital transformation strategy. It was found that the main stages of formation of the digital transformation strategy of the organization are determined by: the use of digital services, individualization of a particular instance of the service, the involvement of the end consumer in the process, customer support throughout the life cycle of the service. Six main stages of implementation of the strategy of digital transformation of the educational process based on the use of cloud technology were formed. Opportunities and threats to the use of cloud technology in the educational space were identified. The experience of using the cloud service “1C: Fresh” in the formation of more than one hundred information bases in the training of specialists in the field of economics and finance was obtained. It was shown that the use of cloud technologies with the provision of students with access to the cloud service of 1C in the educational space of the university simulates the production activities of future specialists in real time. In this case, up-to-date and daily updated for the current legislation programs are used, functionality, cybersecurity and a high degree of data security are maintained at the proper level.

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