Optimization Techniques to Deeply Mine the Transcriptomic Profile of the Sub-Genomes in Hybrid Fish Lineage

It has been shown that reciprocal cross allodiploid lineage with sub-genomes derived from the cross of Megalobrama amblycephala (BSB) × Culter alburnus (TC) generates the variations in phenotypes and genotypes, but it is still a challenge to deeply mine biological information in the transcriptomic profile of this lineage owing to its genomic complexity and lack of efficient data mining methods. In this paper, we establish an optimization model by non-negative matrix factorization approach for deeply mining the transcriptomic profile of the sub-genomes in hybrid fish lineage. A new so-called spectral conjugate gradient algorithm is developed to solve a sequence of large-scale subproblems such that the original complicated model can be efficiently solved. It is shown that the proposed method can provide a satisfactory result of taxonomy for the hybrid fish lineage such that their genetic characteristics are revealed, even for the samples with larger detection errors. Particularly, highly expressed shared genes are found for each class of the fish. The hybrid progeny of TC and BSB displays significant hybrid characteristics. The third generation of TC-BSB hybrid progeny ( $$ and $$ ) shows larger trait separation.