Higher order analysis of gene correlations by tensor decomposition

This study advances our understanding of inter- and intra-pathways higher order signaling in the cellular system and it leads to new discovery of multiple intracellular structures in signal transduction pathways in yeast Saccharomyces. We present a new tensor decomposition algorithm in reconstructing the pathways based on higher correlations among genes that compose a cellular system. The higher order gene correlation (HOGC) analysis has the power to elucidate genes higher interaction dependencies which has been barely understood. Recent studies i.e. [24] have experimentally revealed that multiple signaling proteins, yet sometimes infinite, may assemble to meaningful structure to transmit a receptor activation information. In this paper we reveal 3-order genomic correlations among significant component of the cellular system. This is the first time such a systematic and computational model provided for analysis of higher order correlations among genes. We use new fast algorithm to formulate a genes x genes x genes x decorrelated rank-1 sub-tensors (complexes) which can be associated with functionally independent pathways. Then we model higher order tensor decomposition [Formula] which is constructed by K tensors of genes x genes x genes. Each new tensor is constructed by an orthogonal projection of data signal onto a designated basis signal to keep common sub-tensors in both signals. Our model for decomposing tensor order-4 approximates series of tensors as linear components of deccorelated rank-1 sub-tensors over tensor of order-3 and rank-3 triplings among sub-tensors. The linear components represent intra-pathway in cell signaling and triplings implicate inter-pathways higher order signaling. Through structural studies of inter- and intra-higher order signaling pathways, we uncover different scenario that involves triple formation of signaling proteins into higher order signaling machines for transmission of receptor activation information to cellular responses.