These robust contigs also performed better in the tests assessing representation of reference datasets (Table 10 and Table 11).
A great benefit of such technologies is that they allow the representation of complete datasets without the need for algorithms dedicated to dimensionality reduction, which might lead to information loss.
Several key initiatives in the past decade have led to the formal representation of biomedical datasets on the web and integration across these diverse data sources through identification using Unique Resource Identifiers (URIs).
These are the two largest data sets for annelids explored to date in terms of amount of numbers of characters for a full range of taxa, and it is our hope that the taxonomic representation of these datasets will continue to grow in order to provide a more holistic comparison to morphological hypotheses.
A sensitivity analysis was performed to determine the optimal sparsity of the network and the cut-off for the partial correlation among transcript profiles, through which we established that the network was a robust representation of the datasets (supplemental note 4 in Supplementary file 1, Table S7, Figure 6 source data 1).
Unlike the low-rank representation seeking the lowest rank of the dataset, sparse representation finds the sparest representation of a dataset.
A Principal Component Analysis (PCA, a mathematical representation of the dataset diversity [ 25]), performed on the transcriptome dataset, identified two main components that explain 29.5% and 9.6% of the variance.
For subspace segmentation problem, Liu et al. (2010, 2013) use the nuclear norm to find the lowest rank representation of a dataset; in this way, the global structure of the dataset can be well preserved.
Given the Toy dataset as shown in Fig. 3a, the graphical representation of this dataset is demonstrated in Fig. 3b.
For any analyzed dataset, there is a basis set (the best basis set) that can best represent the spatial and frequency domain information in the dataset, and the corresponding "best" multiwavelet packet transform provides the most effective representation of the dataset (denoted as MWPT at below).
