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Data Tours
Published in Wendy L. Martinez, Angel R. Martinez, Jeffrey L. Solka, Exploratory Data Analysis with MATLAB®, 2017
Wendy L. Martinez, Angel R. Martinez, Jeffrey L. Solka
Like independent component analysis, PCA looks for a set of components that are a linear transformation of the observed variables and will produce transformed variables or (principal components) that are uncorrelated with each other. One difference between the two approaches has to do with their goals. PCA seeks components that explain the maximum amount of variance, while independence and nonnormality are maximized in ICA. Thus, both of these methods have an objective that defines the interestingness of the linear transformation and then find components that optimize that function. We also know that uncorrelatedness does not imply statistical independence. So, the principal components are not guaranteed to be independent, while those in ICA are optimized for independence.
Multiple Random Variables
Published in X. Rong Li, Probability, Random Signals, and Statistics, 2017
Two RVs X and Y are independent if FX,Y(x,y) = Fx(x)FY(y) or equivalently fx,y(x,y) = fx(x)fy(y). They are uncorrelated (i.e., surely not related linearly) if E[XY] = E[X]E[Y], or their covariance Cxy = 0 or their correlation coefficient ρxy = 0. If they are independent then they are uncorrelated, but uncorrelatedness does not imply independence in general unless they are jointly Gaussian.
Proposal of new performance measures for ICA
Published in Rajesh Singh, Anita Gehlot, Intelligent Circuits and Systems, 2021
ICA needs independent components (yis) from the correlated mixtures (xis) of them. Independence implies uncorrelatedness (the opposite is true only for Gaussian random variable). There are techniques available to get zero mean uncorrelated components of the data matrix. So, if we think of a transformation, from the former to the latter, then it must be an orthogonal transformation. Overall, the algorithm is two steps. First, let a zero mean observed mixture data matrix X be linearly transformed through a whitening matrix V to give a zero mean univariant whiten data matrix Z, i.e., Z=VX=VAS. As a next step, let R be the optimal orthogonal matrix for rotation giving m.i.p. components with respect to a given contrast. Then, Y=RZ=RVAS=WAS, where W=RV is the estimated unmixing matrix. The first step is obtained through standard techniques for PCA through eigen value decomposition (EVD) or singular value decomposition (SVD). This article achieves the optimal rotation matrix R through the Search for Rotation based ICA (SRICA) algorithm [7], which uses the genetic algorithm (GA) as a global search based optimization technique.
A novel approach to investigate the mechanical properties of the material for bridge health monitoring using convolutional neural network
Published in Structure and Infrastructure Engineering, 2022
Toan Pham-Bao, Tam Nguyen-Nhat, Nhi Ngo-Kieu
Traditionally, VBDD focuses on the extraction of damage-sensitive features to identify the damage conditions of structures. A set of non-modal vibration parameters as damage indicator features is detailed and selected to detect damage using ambient and vehicle excitations in two real bridges (Delgadillo & Casas, 2020). Two damage features with changes in mass and stiffness using output-only vibration data are first developed to evaluate structural damage and mass change separately (Do & Gül, 2020). Most VBDD methods can be classified into two approaches: model-based methods and non-model-based methods. Model-based methods are more often used because it is easier to control the mechanical variations that result in changes to the vibration characteristics. Random-vibration-based damage identification with the Generalised Functional Model-based method was applied to detect and localise defects for a lab-scale aircraft stabiliser structure (Sakaris, Sakellariou, & Fassois, 2017). Furthermore, Random vibration-based damage detection using the residual variance or uncorrelatedness (whiteness) of a conventional functional model was employed by Aravanis et al. (Aravanis, Sakellariou, & Fassois, 2021). The authors have revealed that the performance of the proposed method performance is equal to that of the multiple model-based methods but superior to that of the principal component analysis–based method. However, the main limitation of this approach is that the mechanical changes may not match the alterations occurring in experiments on actual structures. In contrast, non-model-based methods face difficulty in creating a rich database that conforms with good practicality. Y. Xu & Zhu presented a new non-model-based damage identification method that uses measured mode shape as damage index to successfully localize thickness reduction area in plates (Y. Xu & Zhu, 2017).
The Moran Spectrum as a Geoinformatic Tupu: implications for the First Law of Geography
Published in Annals of GIS, 2022
The properties of orthogonality and uncorrelatedness guarantee that each eigenvector represents a distinct map pattern, and hence the eigenvector maps represent all distinct patterns for a given geographic landscape (as represented by the given SWM ). Uncorrelatedness is a critical property when eigenvectors are selected for inclusion in spatial regression models, to be shown later in the paper.