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Probabilistic nonlinear dimensionality reduction through gaussian process latent variable models: An overview
Published in Arun Kumar Sinha, John Pradeep Darsy, Computer-Aided Developments: Electronics and Communication, 2019
Tipping and Bishop introduced a probabilistic framework for principal component analysis by constraining the noise distribution of a LVM [26]. A LVM transforms a set of n d-dimensional observed variables encoded as a design matrix, =[y1,…yn]T, to a set of n q-dimensional latent (unobserved) variables, X =[x1,…xn]T. Latent variables are parsimonious, it is generally the case that q ≪ d, explaining the original data with fewer variables. A notable latent variable model is that of factor analysis, one that assumes linearity in relation of the observed data set. For each observed data point, yi ∊ Y,1≤i≤n, there is an associated latent variable xi. The original data can be represented in terms of the corresponding latent variable as () yi=Wxi+μi+∈i
Frequency-Domain Fast Maximum Likelihood Estimation of Complex Modes
Published in Jian Zhang, Zhishen Wu, Mohammad Noori, Yong Li, Experimental Vibration Analysis for Civil Structures, 2020
The EM algorithm (Dempster, Laird and Rubin, 1977) is widely used to infer the statistical model that can be formulated as a latent variable model (Li and Der Kiureghian, 2017). In our model, the measurement 𝓎k is the observed variable and the modal response xk can be regarded as the latent variable. When applying the EM algorithm to our model, the closed-form update of mode shapes Φ is not available due to the constraints on some of its elements. To resolve this difficulty, the parameter-expanded EM (PX-EM) is employed here.
Incorporating the extended theory of planned behavior in a school travel mode choice model: a case study of Shaoxing, China
Published in Transportation Planning and Technology, 2018
Peng Jing, Jing Wang, Long Chen, Qi-fen Zha
As illustrated in Figure 2, the MIMIC model includes demographic characteristics of travelers, the latent variables that construct the expand TPB and endogenous observed indicators. Specifically this model hypothesizes that the socioeconomic variables influence all latent variables of TPB, which are also explained by indicators from questionnaires for respondents. Figure 3 presents the detailed path analysis diagram, which specifies the hypothesized relationships among the latent factors, where ellipses represent unobservable variables and rectangles represent observable indicators. Dashed arrows represent measurement equations while solid arrows represent the structural equations. The latent variable model describes the relationships between the latent variables and their indicators and causes.