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Journal ArticleDOI

Pattern Recognition and Machine Learning

01 Aug 2007-Technometrics (Taylor & Francis)-Vol. 49, Iss: 3, pp 366-366
TL;DR: This book covers a broad range of topics for regular factorial designs and presents all of the material in very mathematical fashion and will surely become an invaluable resource for researchers and graduate students doing research in the design of factorial experiments.
Abstract: (2007). Pattern Recognition and Machine Learning. Technometrics: Vol. 49, No. 3, pp. 366-366.
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Journal ArticleDOI
Yang Chen1, Xiangyong Cao1, Qian Zhao1, Deyu Meng1, Zongben Xu1 
TL;DR: This paper attempts the first effort to model the HSI noise using a non-i.i.d. mixture of Gaussians (NMoGs) noise assumption, which finely accords with the noise characteristics possessed by a natural HSI and thus is capable of adapting various practical noise shapes.
Abstract: Hyperspectral image (HSI) denoising has been attracting much research attention in remote sensing area due to its importance in improving the HSI qualities. The existing HSI denoising methods mainly focus on specific spectral and spatial prior knowledge in HSIs, and share a common underlying assumption that the embedded noise in HSI is independent and identically distributed (i.i.d.). In real scenarios, however, the noise existed in a natural HSI is always with much more complicated non-i.i.d. statistical structures and the under-estimation to this noise complexity often tends to evidently degenerate the robustness of current methods. To alleviate this issue, this paper attempts the first effort to model the HSI noise using a non-i.i.d. mixture of Gaussians (NMoGs) noise assumption, which finely accords with the noise characteristics possessed by a natural HSI and thus is capable of adapting various practical noise shapes. Then we integrate such noise modeling strategy into the low-rank matrix factorization (LRMF) model and propose an NMoG-LRMF model in the Bayesian framework. A variational Bayes algorithm is then designed to infer the posterior of the proposed model. As substantiated by our experiments implemented on synthetic and real noisy HSIs, the proposed method performs more robust beyond the state-of-the-arts.

150 citations


Cites methods from "Pattern Recognition and Machine Lea..."

  • ...3) Setting of Hyper-Parameters: We set all the hyperparameters involved in our model in a noninformative manner to make them possibly less affect the inference of posterior distributions [3]....

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  • ...We use variational Bayes (VB) method [3] for posterior inference....

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Journal ArticleDOI
TL;DR: A state-of-the-art analysis of the ongoing machine learning (ML) and deep learning (DL) methods in the diagnosis and prediction of COVID-19 has been done and a comparative analysis on the impact of machine learning and other competitive approaches like mathematical and statistical models on CO VID-19 problem has been conducted.
Abstract: The World Health Organization (WHO) declared novel coronavirus 2019 (COVID-19), an infectious epidemic caused by SARS-CoV-2, as Pandemic in March 2020. It has affected more than 40 million people in 216 countries. Almost in all the affected countries, the number of infected and deceased patients has been enhancing at a distressing rate. As the early prediction can reduce the spread of the virus, it is highly desirable to have intelligent prediction and diagnosis tools. The inculcation of efficient forecasting and prediction models may assist the government in implementing better design strategies to prevent the spread of virus. In this paper, a state-of-the-art analysis of the ongoing machine learning (ML) and deep learning (DL) methods in the diagnosis and prediction of COVID-19 has been done. Moreover, a comparative analysis on the impact of machine learning and other competitive approaches like mathematical and statistical models on COVID-19 problem has been conducted. In this study, some factors such as type of methods(machine learning, deep learning, statistical & mathematical) and the impact of COVID research on the nature of data used for the forecasting and prediction of pandemic using computing approaches has been presented. Finally some important research directions for further research on COVID-19 are highlighted which may facilitate the researchers and technocrats to develop competent intelligent models for the prediction and forecasting of COVID-19 real time data.

150 citations

Journal ArticleDOI
Wenlong Lyu1, Pan Xue1, Fan Yang1, Changhao Yan1, Zhiliang Hong1, Xuan Zeng1, Dian Zhou1 
TL;DR: A weighted expected improvement-based Bayesian optimization approach for automated analog circuit sizing using Gaussian processes as the online surrogate models for circuit performances and extended to handle multi-objective optimization problems.
Abstract: The computation-intensive circuit simulation makes the analog circuit sizing challenging for large-scale/complicated analog/RF circuits. A Bayesian optimization approach has been proposed recently for the optimization problems involving the evaluations of black-box functions with high computational cost in either objective functions or constraints. In this paper, we propose a weighted expected improvement-based Bayesian optimization approach for automated analog circuit sizing. Gaussian processes (GP) are used as the online surrogate models for circuit performances. Expected improvement is selected as the acquisition function to balance the exploration and exploitation during the optimization procedure. The expected improvement is weighted by the probability of satisfying the constraints. In this paper, we propose a complete Bayesian optimization framework for the optimization of analog circuits with constraints for the first time. The existing GP model-based optimization methods for analog circuits take the GP models as either offline models or as assistance for the evolutionary algorithms. We also extend the Bayesian optimization algorithm to handle multi-objective optimization problems. Compared with the state-of-the-art approaches listed in this paper, the proposed Bayesian optimization method achieves better optimization results with significantly less number of simulations.

150 citations


Cites background from "Pattern Recognition and Machine Lea..."

  • ...Note that y∗ conditioned by y also follows the normal distribution [31]....

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Journal ArticleDOI
TL;DR: A new way to incorporate spatial information between neighboring pixels into the Gaussian mixture model based on Markov random field (MRF) to demonstrate its robustness, accuracy, and effectiveness, compared with other mixture models.
Abstract: In this paper, a new mixture model for image segmentation is presented. We propose a new way to incorporate spatial information between neighboring pixels into the Gaussian mixture model based on Markov random field (MRF). In comparison to other mixture models that are complex and computationally expensive, the proposed method is fast and easy to implement. In mixture models based on MRF, the M-step of the expectation-maximization (EM) algorithm cannot be directly applied to the prior distribution ${\pi_{ij}}$ for maximization of the log-likelihood with respect to the corresponding parameters. Compared with these models, our proposed method directly applies the EM algorithm to optimize the parameters, which makes it much simpler. Experimental results obtained by employing the proposed method on many synthetic and real-world grayscale and colored images demonstrate its robustness, accuracy, and effectiveness, compared with other mixture models.

150 citations


Cites background or methods from "Pattern Recognition and Machine Lea..."

  • ...In the model-based techniques, standard Gaussian mixture model (GMM) [8]–[10], [18], [19], is a wellknown method that has been widely used due to its simplicity and ease of implementation....

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  • ...In order to partition an image consisting of N pixels into K labels, GMM [10], [29] assumes that each observation xi is considered independent of the label j ....

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  • ...Over the past decades, a number of algorithms based on the model-based techniques [8]–[10] have been proposed....

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Journal ArticleDOI
TL;DR: This work introduces two new methods of deriving the classical PCA in the framework of minimizing the mean square error upon performing a lower-dimensional approximation of the data and derives the optimal basis and the minimum error of approximation in this framework.
Abstract: We introduce two new methods of deriving the classical PCA in the framework of minimizing the mean square error upon performing a lower-dimensional approximation of the data. These methods are based on two forms of the mean square error function. One of the novelties of the presented methods is that the commonly employed process of subtraction of the mean of the data becomes part of the solution of the optimization problem and not a pre-analysis heuristic. We also derive the optimal basis and the minimum error of approximation in this framework and demonstrate the elegance of our solution in comparison with a recent solution in the framework.

150 citations


Cites background or methods or result from "Pattern Recognition and Machine Lea..."

  • ...3 Comparison of the Reviewed Solution with the Present Work In order to compare the solution of [1] reviewed in Sect....

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  • ...4 Review of a Recent Solution The most recent PCA solution in the framework of approximation error minimization, derived in [1], is reviewed here....

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  • ...(29) If ̃ W ̃ W = B, we have the approximation according to [1] in (10) of Sect....

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  • ...But [1] necessitates an orthogonal projection of certain data-independent components b ∈ Rp−q to μ ∈ R to achieve the same objective....

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  • ...We will also be reviewing [1] who derives PCA in the same framework as that of ours....

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