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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

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

arXiv

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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 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

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

arXiv

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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 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

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

arXiv

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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

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

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Locally linear embedding and its variants: Tutorial and survey

arXiv

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arXiv 2020年

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

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Collaborative authoring of Walden's paths

Collaborative authoring of Walden's paths

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2nd International Conference on Theory and Practice of Digital Libraries, TPDL 2012

作者： Li, Yuanling Bogen II, Paul Logasa Pogue, Daniel Furuta, Richard Shipman, Frank Center for the Study of Digital Libraries Department of Computer Science and Engineering Texas A and M University College Station TX United States Intelligent Computing Research Team Computational Data Analytics Group Oak Ridge National Laboratory Oak Ridge United States User Experience and Interaction Design Team Production Enhancement Halliburton Energy Services Houston TX United States

ISBN: (纸本)9783642332890

This paper presents a prototype of an authoring tool to allow users to collaboratively build, annotate, manage, share and reuse collections of distributed resources from the World Wide Web. This extends on the Walden's Path project's work to help educators bring resources found on the World Wide Web into a linear contextualized structure. The introduction of collaborative authoring feature fosters collaborative learning activities through social interaction among participants, where participants can coauthor paths in groups. Besides, the prototype supports path sharing, branching and reusing;specifically, individual participant can contribute to the group with private collections of knowledge resources;paths completed by group can be shared among group members, such that participants can tailor, extend, reorder and/or replace nodes to have sub versions of shared paths for different information needs. © 2012 Springer-Verlag.

关键词： World Wide Web

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C-Net: A reliable convolutional neural network for biomedical image classification

arXiv

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arXiv 2020年

作者： Barzekar, Hosein Yu, Zeyun Big Data Analytics and Visualization Laboratory Department of Computer Science University of Wisconsin-Milwaukee MilwaukeeWI53211 United States Department of Biomedical Engineering University of Wisconsin-Milwaukee MilwaukeeWI53211 United States

Cancers are the leading cause of death in many countries. Early diagnosis plays a crucial role in having proper treatment for this debilitating disease. The automated classification of the type of cancer is a challenging task since pathologists must examine a huge number of histopathological images to detect infinitesimal abnormalities. In this study, we propose a novel convolutional neural network (CNN) architecture composed of a Concatenation of multiple Networks, called C-Net, to classify biomedical images. The model incorporates multiple CNNs including Outer, Middle, and Inner. The first two parts of the architecture contain six networks that serve as feature extractors to feed into the Inner network to classify the images in terms of malignancy and benignancy. The C-Net is applied for histopathological image classification on two public datasets, including BreakHis and Osteosarcoma. To evaluate the performance, the model is tested using several evaluation metrics for its reliability. The C-Net model outperforms all other models on the individual metrics for both datasets and achieves zero misclassification. This approach has the potential to be extended to additional classification tasks, as experimental results demonstrate utilizing extensive evaluation metrics. Copyright © 2020, The Authors. All rights reserved.

关键词： computer aided diagnosis

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Facilitated machine learning for image-based fruit quality assessment

arXiv

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arXiv 2022年

作者： Knott, Manuel Perez-Cruz, Fernando Defraeye, Thijs Empa Swiss Federal Laboratories for Materials Science Technology Laboratory for Biomimetic Membranes and Textiles St. Gallen Switzerland Swiss Data Science Center ETH Zurich and EPFL Zurich Switzerland Institute for Machine Learning Department of Computer Science ETH Zurich Switzerland

Image-based machine learning models can be used to make the sorting and grading of agricultural products more efficient. In many regions, implementing such systems can be difficult due to the lack of centralization and automation of postharvest supply chains. Stakeholders are often too small to specialize in machine learning, and large training data sets are unavailable. We propose a machine learning procedure for images based on pre-trained Vision Transformers. It is easier to implement than the current standard approach of training Convolutional Neural Networks (CNNs) as we do not (re-)train deep neural networks. We evaluate our approach based on two data sets for apple defect detection and banana ripeness estimation. Our model achieves a competitive classification accuracy equal to or less than one percent below the best-performing CNN. At the same time, it requires three times fewer training samples to achieve a 90% accuracy. © 2022, CC BY.

关键词： computer vision

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GPTR: Gestalt-Perception Transformer for Diagram Object Detection

arXiv

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arXiv 2022年

作者： Hu, Xin Zhang, Lingling Liu, Jun Fan, Jinfu You, Yang Wu, Yaqiang Shaanxi Provincial Key Laboratory of Big Data Knowledge Engineering School of Computer Science and Technology Xi’an Jiaotong University China National Engineering Lab for Big Data Analytics Xi’an Jiaotong University China Department of Control Science and Engineering Tongji University Shanghai China Department of Computer Science National University of Singapore Singapore Lenovo Research Beijing China

Diagram object detection is the key basis of practical applications such as textbook question answering. Because the diagram mainly consists of simple lines and color blocks, its visual features are sparser than those of natural images. In addition, diagrams usually express diverse knowledge, in which there are many low-frequency object categories in diagrams. These lead to the fact that traditional data-driven detection model is not suitable for diagrams. In this work, we propose a gestalt-perception transformer model for diagram object detection, which is based on an encoder-decoder architecture. Gestalt perception contains a series of laws to explain human perception, that the human visual system tends to perceive patches in an image that are similar, close or connected without abrupt directional changes as a perceptual whole object. Inspired by these thoughts, we build a gestalt-perception graph in transformer encoder, which is composed of diagram patches as nodes and the relationships between patches as edges. This graph aims to group these patches into objects via laws of similarity, proximity, and smoothness implied in these edges, so that the meaningful objects can be effectively detected. The experimental results demonstrate that the proposed GPTR achieves the best results in the diagram object detection task. Our model also obtains comparable results over the competitors in natural image object detection. Copyright © 2022, The Authors. All rights reserved.

关键词： Object detection

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A study of complex deep learning networks on high-performance, neuromorphic, and quantum computers

A study of complex deep learning networks on high-performanc...

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作者： Potok, Thomas E. Schuman, Catherine Young, Steven Patton, Robert Spedalieri, Federico Liu, Jeremy Yao, Ke-Thia Rose, Garrett Chakma, Gangotree Computational Data Analytics Group Oak Ridge National Laboratory P.O. Box 2008 Oak RidgeTN37831 United States University of Southern California Information Sciences Institute 4676 Admiralty Way Marina del ReyCA90292 United States Department of Electrical Engineering and Computer Science University of Tennessee 1520 Middle Dr KnoxvilleTN37996 United States

Current deep learning approaches have been very successful using convolutional neural networks trained on large graphical-processing-unit-based computers. Three limitations of this approach are that (1) they are based on a simple layered network topology, i.e., highly connected layers, without intra-layer connections;(2) the networks are manually configured to achieve optimal results, and (3) the implementation of the network model is expensive in both cost and power. In this article, we evaluate deep learning models using three different computing architectures to address these problems: quantum computing to train complex topologies, high performance computing to automatically determine network topology, and neuromorphic computing for a low-power hardware implementation. We use the MNIST dataset for our experiment, due to input size limitations of current quantum computers. Our results show the feasibility of using the three architectures in tandem to address the above deep learning *** show that a quantum computer can find high quality values of intra-layer connection weights in a tractable time as the complexity of the network increases, a high performance computer can find optimal layer-based topologies, and a neuromorphic computer can represent the complex topology and weights derived from the other architectures in low power memristive hardware. © 2018 ACM.

关键词： Deep learning

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