scholarly journals Time-Lagged Independent Component Analysis of Random Walks and Protein Dynamics

2021 ◽  
Vol 17 (9) ◽  
pp. 5766-5776
Author(s):  
Steffen Schultze ◽  
Helmut Grubmüller
Keyword(s):  
Independent Component Analysis ◽  
Random Walks ◽  
Protein Dynamics ◽  
Component Analysis ◽  
Independent Component ◽  
Time Lagged

scholarly journals Time-lagged Independent Component Analysis of Random Walks and Protein Dynamics

2021 ◽  
Author(s):  
Steffen Schultze ◽  
Helmut Grubmueller
Keyword(s):  
Free Energy ◽  
Independent Component Analysis ◽  
Random Walks ◽  
Protein Dynamics ◽  
Energy Landscape ◽  
Component Analysis ◽  
Lag Time ◽  
Independent Component ◽  
Free Energy Landscape ◽  
Time Lagged

Time-lagged independent component analysis (tICA) is a widely used dimension reduction method for the analysis of molecular dynamics (MD) trajectories and has proven particularly useful for the construction of protein dynamics Markov models. It identifies those 'slow' collective degrees of freedom onto which the projections of a given trajectory show maximal autocorrelation for a given lag time. Here we ask how much information on the actual protein dynamics and, in particular, the free energy landscape that governs these dynamics the tICA-projections of MD-trajectories contain, as opposed to noise due to the inherently stochastic nature of each trajectory. To answer this question, we have analyzed the tICA-projections of high dimensional random walks using a combination of analytical and numerical methods. We find that the projections resemble cosine functions and strongly depend on the lag time, exhibiting strikingly complex behaviour. In particular, and contrary to previous studies of principal component projections, the projections change non-continuously with increasing lag time. The tICA-projections of selected 1 μs protein trajectories and those of random walks are strikingly similar, particularly for larger proteins, suggesting that these trajectories contain only little information on the energy landscape that governs the actual protein dynamics. Further the tICA-projections of random walks show clusters very similar to those observed for the protein trajectories, suggesting that clusters in the tICA-projections of protein trajectories do not necessarily reflect local minima in the free energy landscape. We also conclude that, in addition to the previous finding that certain ensemble properties of non-converged protein trajectories resemble those of random walks, this is also true for their time correlations. Due to the higher complexity of the latter, this result also suggests tICA analyses as a more sensitive tool to test MD simulations for proper convergence.

Skin Chromophore Estimation from Mobile Selfie Images using Constrained Independent Component Analysis

2020 ◽  
Vol 2020 (14) ◽  
pp. 357-1-357-6
Author(s):  
Luisa F. Polanía ◽  
Raja Bala ◽  
Ankur Purwar ◽  
Paul Matts ◽  
Martin Maltz
Keyword(s):  
Independent Component Analysis ◽  
Spectral Reflectance ◽  
Source Separation ◽  
Principal Component ◽  
Component Analysis ◽  
Previous Method ◽  
Independent Component ◽  
Light Transport ◽  
Camera Model ◽  
Constrained Independent Component Analysis

Human skin is made up of two primary chromophores: melanin, the pigment in the epidermis giving skin its color; and hemoglobin, the pigment in the red blood cells of the vascular network within the dermis. The relative concentrations of these chromophores provide a vital indicator for skin health and appearance. We present a technique to automatically estimate chromophore maps from RGB images of human faces captured with mobile devices such as smartphones. The ultimate goal is to provide a diagnostic aid for individuals to monitor and improve the quality of their facial skin. A previous method approaches the problem as one of blind source separation, and applies Independent Component Analysis (ICA) in camera RGB space to estimate the chromophores. We extend this technique in two important ways. First we observe that models for light transport in skin call for source separation to be performed in log spectral reflectance coordinates rather than in RGB. Thus we transform camera RGB to a spectral reflectance space prior to applying ICA. This process involves the use of a linear camera model and Principal Component Analysis to represent skin spectral reflectance as a lowdimensional manifold. The camera model requires knowledge of the incident illuminant, which we obtain via a novel technique that uses the human lip as a calibration object. Second, we address an inherent limitation with ICA that the ordering of the separated signals is random and ambiguous. We incorporate a domain-specific prior model for human chromophore spectra as a constraint in solving ICA. Results on a dataset of mobile camera images show high quality and unambiguous recovery of chromophores.

Exploring Independent Component Analysis for GPR Signal Processing

PIERS Online ◽  
2005 ◽  
Vol 1 (6) ◽  
pp. 750-753 ◽  
Author(s):  
Anxing Zhao ◽  
Yansheng Jiang ◽  
Wenbing Wang
Keyword(s):  
Signal Processing ◽  
Independent Component Analysis ◽  
Component Analysis ◽  
Independent Component
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