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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

Uniform manifold approximation and projection (UMAP) and its variants: Tutorial and survey

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arXiv 2021年

Uniform Manifold Approximation and Projection (UMAP) is one of the state-of-the-art methods for dimensionality reduction and data visualization. This is a tutorial and survey paper on UMAP and its variants. We start with UMAP algorithm where we explain probabilities of neighborhood in the input and embedding spaces, optimization of cost function, training algorithm, derivation of gradients, and supervised and semisupervised embedding by UMAP. Then, we introduce the theory behind UMAP by algebraic topology and category theory. Then, we introduce UMAP as a neighbor embedding method and compare it with t-SNE and LargeVis algorithms. We discuss negative sampling and repulsive forces in UMAP's cost function. DensMAP is then explained for density-preserving embedding. We then introduce parametric UMAP for embedding by deep learning and progressive UMAP for streaming and out-of-sample data embedding. Copyright © 2021, The Authors. All rights reserved.

关键词： Embeddings

End-to-end simultaneous learning of single-particle orientation and 3D map reconstruction from cryo-electron microscopy data

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arXiv 2021年

作者： Nashed, Youssef S.G. Poitevin, Frederic Gupta, Harshit Woollard, Geoffrey Kagan, Michael Yoon, Chuck Ratner, Daniel Machine Learning Initiative SLAC National Accelerator Laboratory United States Department of LCLS Data Analytics SLAC National Accelerator Laboratory United States Department of Mathematics University of British Columbia Canada Fundamental Physics Directorate SLAC National Accelerator Laboratory United States

Cryogenic electron microscopy (cryo-EM) provides images from different copies of the same biomolecule in arbitrary orientations. Here, we present an end-to-end unsupervised approach that learns individual particle orientations from cryo-EM data while reconstructing the average 3D map of the biomolecule, starting from a random initialization. The approach relies on an auto-encoder architecture where the latent space is explicitly interpreted as orientations used by the decoder to form an image according to the linear projection model. We evaluate our method on simulated data and show that it is able to reconstruct 3D particle maps from noisy- and CTF-corrupted 2D projection images of unknown particle orientations. © 2021, CC BY.

关键词： Biomolecules

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

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

Reducing over-smoothness in speech synthesis using Generative Adversarial Networks

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Reducing over-smoothness in speech synthesis using Generativ...

2019 International Multi-Conference on Engineering, Computer and Information Sciences, SIBIRCON 2019

作者： Sheng, Leyuan Pavlovskiy, Evgeniy N. Novosibirsk State University Department of Mathematics and Mechanics Novosibirsk Russia Stream Data Analytics and Machine Learning Laboratory Novosibirsk State University Novosibirsk Russia

ISBN: (纸本)9781728144016

Speech synthesis is widely used in many practical applications. In recent years, speech synthesis technology has developed rapidly. However, one of the reasons why synthetic speech is unnatural is that it often has over-smoothness. In order to improve the naturalness of synthetic speech, we first extract the mel-spectrogram of speech and convert it into a real image, then take the over-smooth mel-spectrogram image as input, and use image-To-image translation Generative Adversarial Networks(GANs) framework to generate a more realistic mel-spectrogram. Finally, the results show that this method greatly reduces the over-smoothness of synthesized speech and is more close to the mel-spectrogram of real speech. © 2019 IEEE.

关键词： Speech synthesis

System Design for a data-driven and Explainable Customer Sentiment Monitor

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arXiv 2021年

作者： Nguyen, An Foerstel, Stefan Kittler, Thomas Kurzyukov, Andrey Schwinn, Leo Zanca, Dario Hipp, Tobias Sun, Da Jun Schrapp, Michael Rothgang, Eva Eskofier, Bjoern Machine Learning and Data Analytics Lab Friedrich-Alexander-Universität Erlangen-Nürnberg Germany University of Applied Sciences Amberg Weiden Germany Siemens Healthcare GmbH Germany Siemens Shanghai Medical Equipment Ltd. China infoteam Software AG Germany

The most important goal of customer services is to keep the customer satisfied. However, service resources are always limited and must be prioritized. Therefore, it is important to identify customers who potentially become unsatisfied and might lead to escalations. Today this prioritization of customers is often done manually. data science on IoT data (esp. log data) for machine health monitoring, as well as analytics on enterprise data for customer relationship management (CRM) have mainly been researched and applied independently. In this paper, we present a framework for a data-driven decision support system which combines IoT and enterprise data to model customer sentiment. Such decision support systems can help to prioritize customers and service resources to effectively troubleshoot problems or even avoid them. The framework is applied in a real-world case study with a major medical device manufacturer. This includes a fully automated and interpretable machine learning pipeline designed to meet the requirements defined with domain experts and end users. The overall framework is currently deployed, learns and evaluates predictive models from terabytes of IoT and enterprise data to actively monitor the customer sentiment for a fleet of thousands of high-end medical devices. Furthermore, we provide an anonymized industrial benchmark dataset for the research community. Copyright © 2021, The Authors. All rights reserved.

关键词： Sales

Laplacian-Based Dimensionality Reduction Including Spectral Clustering, Laplacian Eigenmap, Locality Preserving Projection, Graph Embedding, and Diffusion Map: Tutorial and Survey

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arXiv 2021年

This is a tutorial and survey paper for nonlinear dimensionality and feature extraction methods which are based on the Laplacian of graph of data. We first introduce adjacency matrix, definition of Laplacian matrix, and the interpretation of Laplacian. Then, we cover the cuts of graph and spectral clustering which applies clustering in a subspace of data. Different optimization variants of Laplacian eigenmap and its out-of-sample extension are explained. Thereafter, we introduce the locality preserving projection and its kernel variant as linear special cases of Laplacian eigenmap. Versions of graph embedding are then explained which are generalized versions of Laplacian eigenmap and locality preserving projection. Finally, diffusion map is introduced which is a method based on Laplacian of data and random walks on the data graph. Copyright © 2021, The Authors. All rights reserved.

关键词： Surveys

Digitizing Handwriting with a Sensor Pen: A Writer-Independent Recognizer

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Digitizing Handwriting with a Sensor Pen: A Writer-Independe...

International Workshop on Frontiers in Handwriting Recognition

作者： Mohamad Wehbi Tim Hamann Jens Barth Bjoern Eskofier Machine Learning and Data Analytics Lab Friedrich-Alexander-Universität Erlangen-Nürnberg Erlangen Germany STABILO International GmbH Heroldsberg Germany

ISBN: (数字)9781728199665

ISBN: (纸本)9781728199672

Online handwriting recognition has been studied for a long time with only few practicable results when writing on normal paper. Previous approaches using sensor-based devices encountered problems that limited the usage of the developed systems in real-world applications. This paper presents a writer-independent system that recognizes characters written on plain paper with the use of a sensor-equipped pen. This system is applicable in real-world applications and requires no user-specific training for recognition. The pen provides linear acceleration, angular velocity, magnetic field, and force applied by the user, and acts as a digitizer that transforms the analogue signals of the sensors into timeseries data while writing on regular paper. The dataset we collected with this pen consists of Latin lower-case and upper-case alphabets. We present the results of a convolutional neural network model for letter classification and show that this approach is practical and achieves promising results for writer-independent character recognition. This work aims at providing a real-time handwriting recognition system to be used for writing on normal paper.

关键词： Writing Character recognition Handwriting recognition Optical character recognition software data models Training Real-time systems