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This book is aimed at raising awareness of researchers, scientists and engineers on the benefits of Principal Component Analysis (PCA) in data analysis. In this book, the reader will find the applications of PCA in fields such as energy, multi-sensor data fusion, materials science, gas chromatographic analysis, ecology, video and image processing, agriculture, color coating, climate and automatic target recognition.

Principal components analysis. --- Analysis, Principal components --- Components analysis, Principal --- Correlation (Statistics) --- Factor analysis --- Mathematical modelling

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In 1901, Karl Pearson invented Principal Component Analysis (PCA). Since then, PCA serves as a prototype for many other tools of data analysis, visualization and dimension reduction: Independent Component Analysis (ICA), Multidimensional Scaling (MDS), Nonlinear PCA (NLPCA), Self Organizing Maps (SOM), etc. The book starts with the quote of the classical Pearson definition of PCA and includes reviews of various methods: NLPCA, ICA, MDS, embedding and clustering algorithms, principal manifolds and SOM. New approaches to NLPCA, principal manifolds, branching principal components and topology preserving mappings are described as well. Presentation of algorithms is supplemented by case studies, from engineering to astronomy, but mostly of biological data: analysis of microarray and metabolite data. The volume ends with a tutorial "PCA and K-means decipher genome". The book is meant to be useful for practitioners in applied data analysis in life sciences, engineering, physics and chemistry; it will also be valuable to PhD students and researchers in computer sciences, applied mathematics and statistics.

Principal components analysis. --- Principal components analysis --- Statistics --- Mathematical Statistics --- Mathematics - General --- Mathematics --- Physical Sciences & Mathematics --- Graphic methods --- Correlation (Statistics) --- Analysis, Principal components --- Components analysis, Principal --- Engineering. --- Science. --- Computer mathematics. --- Physics. --- Statistics. --- Computational intelligence. --- Control engineering. --- Control. --- Science, general. --- Computational Science and Engineering. --- Mathematical Methods in Physics. --- Computational Intelligence. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Natural science --- Science of science --- Sciences --- Construction --- Industrial arts --- Technology --- Factor analysis --- Least squares --- Mathematical statistics --- Probabilities --- Regression analysis --- Instrumental variables (Statistics) --- Computer science. --- Mathematical physics. --- Control and Systems Theory. --- Science, Humanities and Social Sciences, multidisciplinary. --- Physical mathematics --- Physics --- Informatics --- Science --- Statistics .

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Recently, considerable attention has been placed on the development and application of tools useful for the analysis of the high-dimensional and/or high-frequency datasets that now dominate the landscape. The purpose of this Special Issue is to collect both methodological and empirical papers that develop and utilize state-of-the-art econometric techniques for the analysis of such data.

level, slope, and curvature of the yield curve --- Nelson-Siegel factors --- supervised factor models --- combining forecasts --- principal components --- Minimum variance portfolio --- risk --- shrinkage --- S&amp --- P 500 --- high-frequency --- volatility --- forecasting --- realized measures --- bivariate GARCH --- Japanese candlestick --- ordered fuzzy number --- Kosiński’s number --- oriented fuzzy number --- dynamic analysis of securities --- integrated volatility --- high-frequency data --- jumps --- realized skewness --- cross-sectional stock returns --- signed jump variation --- long-range dependence --- log periodogram regression --- smoothed periodogram --- subsampling --- intraday returns --- portfolio selection --- maximum diversification --- regularization

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This book provides a comprehensive introduction to the latest advances in the mathematical theory and computational tools for modeling high-dimensional data drawn from one or multiple low-dimensional subspaces (or manifolds) and potentially corrupted by noise, gross errors, or outliers. This challenging task requires the development of new algebraic, geometric, statistical, and computational methods for efficient and robust estimation and segmentation of one or multiple subspaces. The book also presents interesting real-world applications of these new methods in image processing, image and video segmentation, face recognition and clustering, and hybrid system identification etc. This book is intended to serve as a textbook for graduate students and beginning researchers in data science, machine learning, computer vision, image and signal processing, and systems theory. It contains ample illustrations, examples, and exercises and is made largely self-contained with three Appendices which survey basic concepts and principles from statistics, optimization, and algebraic-geometry used in this book. René Vidal is a Professor of Biomedical Engineering and Director of the Vision Dynamics and Learning Lab at The Johns Hopkins University. Yi Ma is Executive Dean and Professor at the School of Information Science and Technology at ShanghaiTech University. S. Shankar Sastry is Dean of the College of Engineering, Professor of Electrical Engineering and Computer Science and Professor of Bioengineering at the University of California, Berkeley.

Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Mathematics. --- Image processing. --- Algebraic geometry. --- System theory. --- Statistics. --- Systems Theory, Control. --- Image Processing and Computer Vision. --- Signal, Image and Speech Processing. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Algebraic Geometry. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Systems, Theory of --- Systems science --- Science --- Algebraic geometry --- Geometry --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Math --- Philosophy --- Systems theory. --- Computer vision. --- Geometry, algebraic. --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Principal components analysis. --- Optical data processing. --- Signal processing. --- Speech processing systems. --- Statistics . --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Optical equipment

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Wildfire risk can be perceived as the combination of wildfire hazards (often described by likelihood and intensity) with the susceptibility of people, property, or other valued resources to that hazard. Reflecting the seriousness of wildfire risk to communities around the world, substantial resources are devoted to assessing wildfire hazards and risks. Wildfire hazard and risk assessments are conducted at a wide range of scales, from localized to nationwide, and are often intended to communicate and support decision making about risks, including the prioritization of scarce resources. Improvements in the underlying science of wildfire hazard and risk assessment and in the development, communication, and application of these assessments support effective decisions made on all aspects of societal adaptations to wildfire, including decisions about the prevention, mitigation, and suppression of wildfire risks. To support such efforts, this Special Issue of the journal Fire compiles articles on the understanding, modeling, and addressing of wildfire risks to homes, water resources, firefighters, and landscapes.

wildfire risk --- object-oriented image analysis --- Sentinel-2 --- fire behavior --- flammap --- wildfire management --- water supply --- erosion --- wildfire containment --- Potential fire Operational Delineations --- Monte Carlo simulation --- transmission risk --- WUI --- fire --- defensible space --- prescribed fire --- community vulnerability --- fire suppression costs --- Zillow --- wildfire --- predictive modeling --- fire spread model --- Monte Carlo --- spatial modeling --- area difference index --- statistics --- precision --- recall --- principal components analysis --- risk assessment --- structure loss --- wildland–urban interface --- mitigation --- mapping --- land use --- disaster --- fire spread models --- surrogate modeling --- sensitivity analysis --- global sensitivity analysis --- colour coding --- communication --- forest fire --- ordinal categorization --- palette --- risk --- firefighter safety --- safe separation distance --- safety zones --- LCES --- Google Earth Engine --- lidar --- LANDFIRE --- Landsat --- GEDI --- parcel-level risk --- post-fire analysis --- risk mitigation --- rapid assessment --- natural hazards --- fuels --- fire hazard --- remote sensing --- LiDAR --- Sentinel --- modeling --- simulation