Second, each entry is truncated to 0, 1, or 2. For the two-way model, we first add the data across the GeneID mode to form a Sample x Category matrix, then divide each GO vector by its sum, and finally center the data by subtracting the hMSC vector.
The voids are divided into two categories (bubbles and micro-pores), and the cracks are classified into three categories (matrix, intra-bundle, and interfacial).
Hence, each ds-t-m was transformed to a document-section-category-matrix (ds-c-m).
Component numbers are chosen such that the relationship observed in the sample mode coincides with the results of two-way analysis of the Samples x Categories matrix.
Two points should be noted here: i) L i,j)(ℓi,j) and U i,j ui,j) belong to the same category of matrices; therefore, they can be estimated by the same algorithmic procedure just with an emphasis on the relation between the i and j indices (i < j for U i,j ui,j) and j < i for L i,j)(ℓi,j)); ii) for both JD LU + and JD QR + algorithms, the procedure of estimating U i,j ui,j) is identical.
This analytical enterprise includes the arrangement of major parts of the material around detailed lists of factors and combinations of sets of their categories yielding matrices (Skt., mātṛkā, Pali, mātikā) of doctrinal topics.
The last example raises interesting questions on which filtrations arise as length filtrations on the category of matrix factorizations.
The kidney-blue (c = 0.42) and liver-brown (c = 0.74) modules are enriched for GO category extracellular matrix, each containing more than 12 genes of that category.
We input all 24 columns of the category component matrix, which has dimensions (69 × 24), to a k-means (for k = 4) algorithm and ran it up to 100 times to obtain a consensus, or a majority.
The application of batch correction allowed the unequivocal identification of genes differentially expressed between RA and OA and returned the top-ranked GO category "extracellular matrix structural constituent" (8/74 genes; p-value decreased by 4 orders of magnitude).
