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Mach. Learn. Knowl. Extr., Volume 2, Issue 1 (March 2020) – 4 articles

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Article
Deep Theory of Functional Connections: A New Method for Estimating the Solutions of Partial Differential Equations
Mach. Learn. Knowl. Extr. 2020, 2(1), 37-55; https://doi.org/10.3390/make2010004 - 12 Mar 2020
Cited by 20 | Viewed by 2390
Abstract
This article presents a new methodology called Deep Theory of Functional Connections (TFC) that estimates the solutions of partial differential equations (PDEs) by combining neural networks with the TFC. The TFC is used to transform PDEs into unconstrained optimization problems by analytically embedding [...] Read more.
This article presents a new methodology called Deep Theory of Functional Connections (TFC) that estimates the solutions of partial differential equations (PDEs) by combining neural networks with the TFC. The TFC is used to transform PDEs into unconstrained optimization problems by analytically embedding the PDE’s constraints into a “constrained expression” containing a free function. In this research, the free function is chosen to be a neural network, which is used to solve the now unconstrained optimization problem. This optimization problem consists of minimizing a loss function that is chosen to be the square of the residuals of the PDE. The neural network is trained in an unsupervised manner to minimize this loss function. This methodology has two major differences when compared with popular methods used to estimate the solutions of PDEs. First, this methodology does not need to discretize the domain into a grid, rather, this methodology can randomly sample points from the domain during the training phase. Second, after training, this methodology produces an accurate analytical approximation of the solution throughout the entire training domain. Because the methodology produces an analytical solution, it is straightforward to obtain the solution at any point within the domain and to perform further manipulation if needed, such as differentiation. In contrast, other popular methods require extra numerical techniques if the estimated solution is desired at points that do not lie on the discretized grid, or if further manipulation to the estimated solution must be performed. Full article
(This article belongs to the Section Learning)
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Article
Canopy Height Estimation at Landsat Resolution Using Convolutional Neural Networks
Mach. Learn. Knowl. Extr. 2020, 2(1), 23-36; https://doi.org/10.3390/make2010003 - 09 Feb 2020
Cited by 5 | Viewed by 1867
Abstract
Forest structure estimation is very important in geological, ecological and environmental studies. It provides the basis for the carbon stock estimation and effective means of sequestration of carbon sources and sinks. Multiple parameters are used to estimate the forest structure like above ground [...] Read more.
Forest structure estimation is very important in geological, ecological and environmental studies. It provides the basis for the carbon stock estimation and effective means of sequestration of carbon sources and sinks. Multiple parameters are used to estimate the forest structure like above ground biomass, leaf area index and diameter at breast height. Among all these parameters, vegetation height has unique standing. In addition to forest structure estimation it provides the insight into long term historical changes and the estimates of stand age of the forests as well. There are multiple techniques available to estimate the canopy height. Light detection and ranging (LiDAR) based methods, being the accurate and useful ones, are very expensive to obtain and have no global coverage. There is a need to establish a mechanism to estimate the canopy height using freely available satellite imagery like Landsat images. Multiple studies are available which contribute in this area. The majority use Landsat images with random forest models. Although random forest based models are widely used in remote sensing applications, they lack the ability to utilize the spatial association of neighboring pixels in modeling process. In this research work, we define Convolutional Neural Network based model and analyze that model for three test configurations. We replicate the random forest based setup of Grant et al., which is a similar state-of-the-art study, and compare our results and show that the convolutional neural networks (CNN) based models not only capture the spatial association of neighboring pixels but also outperform the state-of-the-art. Full article
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Editorial
Acknowledgement to Reviewers of MAKE in 2019
Mach. Learn. Knowl. Extr. 2020, 2(1), 20-22; https://doi.org/10.3390/make2010002 - 26 Jan 2020
Viewed by 1184
Abstract
The editorial team greatly appreciates the reviewers who have dedicated their considerable time and expertise to the journal’s rigorous editorial process over the past 12 months, regardless of whether the papers are finally published or not [...] Full article
Article
Statistical Aspects of High-Dimensional Sparse Artificial Neural Network Models
Mach. Learn. Knowl. Extr. 2020, 2(1), 1-19; https://doi.org/10.3390/make2010001 - 02 Jan 2020
Cited by 4 | Viewed by 1563
Abstract
An artificial neural network (ANN) is an automatic way of capturing linear and nonlinear correlations, spatial and other structural dependence among features. This machine performs well in many application areas such as classification and prediction from magnetic resonance imaging, spatial data and computer [...] Read more.
An artificial neural network (ANN) is an automatic way of capturing linear and nonlinear correlations, spatial and other structural dependence among features. This machine performs well in many application areas such as classification and prediction from magnetic resonance imaging, spatial data and computer vision tasks. Most commonly used ANNs assume the availability of large training data compared to the dimension of feature vector. However, in modern applications, as mentioned above, the training sample sizes are often low, and may be even lower than the dimension of feature vector. In this paper, we consider a single layer ANN classification model that is suitable for analyzing high-dimensional low sample-size (HDLSS) data. We investigate the theoretical properties of the sparse group lasso regularized neural network and show that under mild conditions, the classification risk converges to the optimal Bayes classifier’s risk (universal consistency). Moreover, we proposed a variation on the regularization term. A few examples in popular research fields are also provided to illustrate the theory and methods. Full article
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