ManiNetCluster: a novel manifold learning approach to reveal the functional links between gene networks.

BACKGROUND:The coordination of genomic functions is a critical and complex process across biological systems such as phenotypes or states (e.g., time, disease, organism, environmental perturbation). Understanding how the complexity of genomic function relates to these states remains a challenge. To address this, we have developed a novel computational method, ManiNetCluster, which simultaneously aligns and clusters gene networks (e.g., co-expression) to systematically reveal the links of genomic function between different conditions. Specifically, ManiNetCluster employs manifold learning to uncover and match local and non-linear structures among networks, and identifies cross-network functional links. RESULTS:We demonstrated that ManiNetCluster better aligns the orthologous genes from their developmental expression profiles across model organisms than state-of-the-art methods (p-value <2.2×10-16). This indicates the potential non-linear interactions of evolutionarily conserved genes across species in development. Furthermore, we applied ManiNetCluster to time series transcriptome data measured in the green alga Chlamydomonas reinhardtii to discover the genomic functions linking various metabolic processes between the light and dark periods of a diurnally cycling culture. We identified a number of genes putatively regulating processes across each lighting regime. CONCLUSIONS:ManiNetCluster provides a novel computational tool to uncover the genes linking various functions from different networks, providing new insight on how gene functions coordinate across different conditions. ManiNetCluster is publicly available as an R package at https://github.com/daifengwanglab/ManiNetCluster

Making Laplacians commute

In this paper, we construct multimodal spectral geometry by finding a pair of closest commuting operators (CCO) to a given pair of Laplacians. The CCOs are jointly diagonalizable and hence have the same eigenbasis. Our construction naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of applications in dimensionality reduction, shape analysis, and clustering, demonstrating that our method better captures the inherent structure of multi-modal data

Aligning Manifolds of Double Pendulum Dynamics Under the Influence of Noise

This study presents the results of a series of simulation experiments that evaluate and compare four different manifold alignment methods under the influence of noise. The data was created by simulating the dynamics of two slightly different double pendulums in three-dimensional space. The method of semi-supervised feature-level manifold alignment using global distance resulted in the most convincing visualisations. However, the semi-supervised feature-level local alignment methods resulted in smaller alignment errors. These local alignment methods were also more robust to noise and faster than the other methods.Comment: The final version will appear in ICONIP 2018. A DOI identifier to the final version will be added to the preprint, as soon as it is availabl