Artificial intelligence has been applied in wildfire science and management since the 1990s, with early applications including neural networks and expert systems. Since then the field has rapidly progressed congruently with the wide adoption of machine learning (ML) methods in the environmental sciences. Here, we present a scoping review of ML applications in wildfire science and management. Our overall objective is to improve awareness of ML methods among wildfire researchers and managers, as well as illustrate the diverse and challenging range of problems in wildfire science available to ML data scientists. To that end, we first present an overview of popular ML approaches used in wildfire science to date, and then review the use of ML in wildfire science as broadly categorized into six problem domains, including: 1) fuels characterization, fire detection, and mapping; 2) fire weather and climate change; 3) fire occurrence, susceptibility, and risk; 4) fire behavior prediction; 5) fire effects; and 6) fire management. Furthermore, we discuss the advantages and limitations of various ML approaches relating to data size, computational requirements, generalizability, and interpretability, as well as identify opportunities for future advances in the science and management of wildfires within a data science context. In total, we identfied 300 relevant publications up to the end of 2019, where the most frequently used ML methods across problem domains included random forests, MaxEnt, artificial neural networks, decision trees, support vector machines, and genetic algorithms. As such, there exists opportunities to apply more current ML methods — including deep learning and agent based learning — in the wildfire sciences, especially in instances involving very large multivariate datasets. We must recognize, however, that despite the ability of ML methods to learn on their own, expertise in wildfire science is necessary to ensure realistic modelling of fire processes across multiple scales, while the complexity of some ML methods, such as deep learning, requires a dedicated and sophisticated knowledge of their application. Finally, we stress that the wildfire research and management communities play an active role in providing relevant, high quality, and freely available wildfire data for use by practitioners of ML methods.

This paper is a tutorial for eigenvalue and generalized eigenvalue problems. We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem. Then, we mention the optimization problems which yield to the eigenvalue and generalized eigenvalue problems. We also provide examples from machine learning, including principal component analysis, kernel supervised principal component analysis, and Fisher discriminant analysis, which result in eigenvalue and generalized eigenvalue problems. Finally, we introduce the solutions to both eigenvalue and generalized eigenvalue problems.

In this tutorial paper, we first define mean squared error, variance, covariance, and bias of both random variables and classification/predictor models. Then, we formulate the true and generalization errors of the model for both training and validation/test instances where we make use of the Stein's Unbiased Risk Estimator (SURE). We define overfitting, underfitting, and generalization using the obtained true and generalization errors. We introduce cross validation and two well-known examples which are K-fold and leave-one-out cross validations. We briefly introduce generalized cross validation and then move on to regularization where we use the SURE again. We work on both 2 and 1 norm regularizations. Then, we show that bootstrap aggregating (bagging) reduces the variance of estimation. Boosting, specifically AdaBoost, is introduced and it is explained as both an additive model and a maximum margin model, i.e., Support Vector Machine (SVM). The upper bound on the generalization error of boosting is also provided to show why boosting prevents from overfitting. As examples of regularization, the theory of ridge and lasso regressions, weight decay, noise injection to input/weights, and early stopping are explained. Random forest, dropout, histogram of oriented gradients, and single shot multi-box detector are explained as examples of bagging in machine learning and computer vision. Finally, boosting tree and SVM models are mentioned as examples of boosting. Mean Squared Error, Variance, and Bias Measures for a Random VariableAssume we have variable X and we estimate it. Let the random variable X denote the estimate of X. The variance

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Where a legacy of aggressive wildland fire suppression has left forests in need of fuel reduction, allowing wildland fire to burn may provide fuel treatment benefits, thereby reducing suppression costs from subsequent fires. The least-cost-plus-net-value-change model of wildland fire economics includes benefits of wildfire in a framework for evaluating suppression options. In this study, we estimated one component of that benefit – the expected present value of the reduction in suppression costs for subsequent fires arising from the fuel treatment effect of a current fire. To that end, we employed Monte Carlo methods to generate a set of scenarios for subsequent fire ignition and weather events, which are referred to as sample paths, for a study area in central Oregon. We simulated fire on the landscape over a 100-year time horizon using existing models of fire behaviour, vegetation and fuels development, and suppression effectiveness, and we estimated suppression costs using an existing suppression cost model. Our estimates suggest that the potential cost savings may be substantial. Further research is needed to estimate the full least-cost-plus-net-value-change model. This line of research will extend the set of tools available for developing wildfire management plans for forested landscapes.

This is a detailed tutorial paper which explains the Principal Component Analysis (PCA), Supervised PCA (SPCA), kernel PCA, and kernel SPCA. We start with projection, PCA with eigendecomposition, PCA with one and multiple projection directions, properties of the projection matrix, reconstruction error minimization, and we connect to auto-encoder. Then, PCA with singular value decomposition, dual PCA, and kernel PCA are covered. SPCA using both scoring and Hilbert-Schmidt independence criterion are explained. Kernel SPCA using both direct and dual approaches are then introduced. We cover all cases of projection and reconstruction of training and out-of-sample data. Finally, some simulations are provided on Frey and AT&T face datasets for verifying the theory in practice.

To appear as a part of an upcoming textbook on dimensionality reduction and manifold learning.

This is a detailed tutorial paper which explains the Fisher discriminant Analysis (FDA) and kernel FDA. We start with projection and reconstruction. Then, one-and multi-dimensional FDA subspaces are covered. Scatters in two-and then multi-classes are explained in FDA. Then, we discuss on the rank of the scatters and the dimensionality of the subspace. A real-life example is also provided for interpreting FDA. Then, possible singularity of the scatter is discussed to introduce robust FDA. PCA and FDA directions are also compared. We also prove that FDA and linear discriminant analysis are equivalent. Fisher forest is also introduced as an ensemble of fisher subspaces useful for handling data with different features and dimensionality. Afterwards, kernel FDA is explained for both one-and multi-dimensional subspaces with both two-and multi-classes. Finally, some simulations are performed on AT&T face dataset to illustrate FDA and compare it with PCA.