The explosion of multiomics data poses new challenges to existing data mining methods. Joint analysis of multiomics data can make the best of the complementary information that is provided by different types of data. Therefore, they can more accurately explore the biological mechanism of diseases. In this article, two forms of joint nonnegative matrix factorization based on the sparse and graph Laplacian regularization (SG-jNMF) method are proposed. In the method, the graph regularization constraint can preserve the local geometric structure of data. -norm regularization can enhance the sparsity among the rows and remove redundant features in the data. First, SG-jNMF1 projects multiomics data into a common subspace and applies the multiomics fusion characteristic matrix to mine the important information closely related to diseases. Second, multiomics data of the same disease are mapped into the common sample space by SG-jNMF2, and the cluster structures are detected clearly. Experimental results show that SG-jNMF can achieve significant improvement in sample clustering compared with existing joint analysis frameworks. SG-jNMF also effectively integrates multiomics data to identify co-differentially expressed genes (Co-DEGs). SG-jNMF provides an efficient integrative analysis method for mining the biological information hidden in heterogeneous multiomics data.

中文翻译：

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基于稀疏和图拉普拉斯正则化的联合非负矩阵分解用于聚类和协差分表达基因分析

多组学数据的爆炸式增长给现有的数据挖掘方法带来了新的挑战。对多组学数据进行联合分析可以充分利用不同类型数据提供的补充信息。因此，他们可以更准确地探索疾病的生物学机制。本文提出了基于稀疏和图拉普拉斯正则化（SG-jNMF）方法的两种形式的联合非负矩阵分解。在该方法中，图正则化约束可以保留数据的局部几何结构。--规范正则化可以增强行之间的稀疏性，并删除数据中的冗余特征。首先，SG-jNMF1将多组学数据投影到一个公共子空间中，并应用多组学融合特征矩阵来挖掘与疾病密切相关的重要信息。其次，将相同疾病的多组学数据通过SG-jNMF2映射到公共样本空间中，并清晰地检测出簇结构。实验结果表明，与现有的联合分析框架相比，SG-jNMF可以显着改善样本聚类。SG-jNMF还可以有效地整合多组学数据，以识别共差异表达的基因（Co-DEG）。SG-jNMF为挖掘隐藏在异构多组学数据中的生物信息提供了一种有效的综合分析方法。