LitCovid-sentences  

PMC:7553147 / 16674-19256 JSONTXT 2 Projects

Annnotations TAB TSV DIC JSON TextAE

Id Subject Object Predicate Lexical cue
T127 0-4 Sentence denotes 2.7.
T128 6-36 Sentence denotes Principal component analysis  
T129 37-194 Sentence denotes The principal component analysis used the expectation–maximization (EM) algorithm presented in Tagare et al. (2015 ▸) with the following minor modifications.
T130 195-496 Sentence denotes Firstly, in contrast to Tagare et al. (2015 ▸), the images were not Wiener filtered, nor was the projected mean subtracted from the images; instead, the CTF of each image was incorporated into the projection operator of that image and a variable contrast was allowed for the mean volume in each image.
T131 497-588 Sentence denotes The extent of the variable contrast was determined by the principal component EM algorithm.
T132 589-749 Sentence denotes Secondly, the mean volume was projected along each projection direction and an image mask was constructed with a liberal soft margin to allow for heterogeneity.
T133 750-891 Sentence denotes The different masks thus created, with one mask per projection direction, were applied to the images and the masked images were used as data.
T134 892-1077 Sentence denotes This step corresponds to imposing a form of sparsity on the data, which is known to improve the estimation of principal components in high-dimensional spaces (Johnstone & Paul, 2018 ▸).
T135 1078-1189 Sentence denotes All images were downsampled by a factor of two to improve the signal-to-noise ratio and to speed up processing.
T136 1190-1330 Sentence denotes Finally, during each EM iteration, the principal components were low-pass filtered with a very broad filter whose pass band extended to 4 Å.
T137 1331-1447 Sentence denotes This helped with the convergence of the algorithm without significantly limiting the principal component resolution.
T138 1448-1685 Sentence denotes As part of the EM iteration, the algorithm in Tagare et al. (2015 ▸) conveniently estimates the expected amount by which each principal component is present in each image (this is the term E[z_j] in equation 15 of Tagare et al., 2015 ▸).
T139 1686-1727 Sentence denotes Fig. 3(b) shows a scatter plot of E[z_j].
T140 1728-1918 Sentence denotes It is interesting to note that in the algorithm of Tagare et al. (2015 ▸) the latent variables (representing the contributions of the principal components to each particle) are marginalized.
T141 1919-2110 Sentence denotes Because of this marginalization, the number of unknown parameters that need to be estimated (the principal components and variances) is fixed and does not change with the number of particles.
T142 2111-2345 Sentence denotes We have found this feature to be very valuable for relatively small sets of images (say 100 000 images), which is the case in our work, in order to prevent the number of parameters to be estimated growing with the number of particles.
T143 2346-2482 Sentence denotes Statistically speaking, nonmarginalization is known to be a problem when there are few particles, where the estimates can be unreliable.
T144 2483-2582 Sentence denotes Since the method developed by Tagare and coworkers does not suffer from this, we chose this method.