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Bi-clustering refers to the task of finding sub-matrices (indexed by a group of columns and a group of rows) within a matrix of data such that the elements of each sub-matrix (data and features) are related in a particular way, for instance, that they are similar with respect to some metric. In this paper, after analyzing the well-known Cheng and Church bi-clustering algorithm which has been proved to be an effective tool for mining co-expressed genes. However, Cheng and Church bi-clustering algorithm and summarizing its limitations (such as interference of random numbers in the greedy strategy; ignoring overlapping bi-clusters), we propose a novel enhancement of the adaptive bi-clustering algorithm, where a shielding complex sub-matrix is constructed to shield the bi-clusters that have been obtained and to discover the overlapping bi-clusters. In the shielding complex sub-matrix, the imaginary and the real parts are used to shield and extend the new bi-clusters, respectively, and to form a series of optimal bi-clusters. To assure that the obtained bi-clusters have no effect on the bi-clusters already produced, a unit impulse signal is introduced to adaptively detect and shield the constructed bi-clusters. Meanwhile, to effectively shield the null data (zero-size data), another unit impulse signal is set for adaptive detecting and shielding. In addition, we add a shielding factor to adjust the mean squared residue score of the rows (or columns), which contains the shielded data of the sub-matrix, to decide whether to retain them or not. We offer a thorough analysis of the developed scheme. The experimental results are in agreement with the theoretical analysis. The results obtained on a publicly available real microarray dataset show the enhancement of the bi-clusters performance thanks to the proposed method.

Fusarium head blight (FHB) of wheat is an important disease worldwide, affecting the yield, end-use quality and threatening food safety. Genetic resources or stable loci for FHB resistance are still limited in breeding programs. A panel of 265 bread wheat accessions from China, CIMMYT-Mexico and other countries was screened for FHB resistance under 5 field experiments in Mexico and China, and a genome-wide association analysis was performed to identify QTLs associated with FHB resistance. The major locus Fhb1 was significantly associated with FHB severity and Deoxynivalenol content in grains. FHB screening experiments in multiple environments showed that Fhb1-harbouring accessions Sumai3, Sumai5, Ningmai9, Yangmai18 and Tokai66 had low FHB index, disease severity and DON content in grains in response to different Fusarium species and ecological conditions in Mexico and China. Accessions Klein Don Enrique, Chuko and Yumai34 did not have Fhb1 but still showed good FHB resistance and low mycotoxin accumulation. Sixteen loci associated with FHB resistance or DON content in grains were identified on chromosomes 1A, 1B, 2B, 3A, 3D, 4B, 4D, 5A, 5B, 7A, and 7B in multiple environments, explaining phenotypic variation of 4.43–10.49%. The sources with good FHB resistance reported here could be used in breeding programs for resistance improvement in Mexico and China, and the significant loci could be further studied and introgressed for resistance improvement against FHB and mycotoxin accumulation in grains.