One of the major problems in cancer subtype discovery from multimodal omic data is that all the available modalities may not encode relevant and homogeneous information about the subtypes. Moreover, the high-dimensional nature of the modalities makes sample clustering computationally expensive. In this regard, a novel algorithm is proposed to extract a low-rank joint subspace of the integrated data matrix. The proposed algorithm first evaluates the quality of subtype information provided by each of the modalities, and then judiciously selects only relevant ones to construct the joint subspace. The problem of incrementally updating the singular value decomposition of a data matrix is formulated for the multimodal data framework. The analytical formulation enables efficient construction of the joint subspace of integrated data from low-rank subspaces of the individual modalities. The construction of joint subspace by the proposed method is shown to be computationally more efficient compared to performing the principal component analysis (PCA) on the integrated data matrix. Some new quantitative indices are introduced to measure theoretically the accuracy of subspace construction by the proposed approach with respect to the principal subspace extracted by the PCA. The efficacy of clustering on the joint subspace constructed by the proposed algorithm is established over existing integrative clustering approaches on several real-life multimodal cancer data sets.

中文翻译：

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多模态数据集成聚类相关特征空间的选择性更新


从多模式组学数据发现癌症亚型的主要问题之一是所有可用的模式可能无法编码有关亚型的相关且同质的信息。此外，模态的高维性质使得样本聚类的计算成本昂贵。在这方面，提出了一种新的算法来提取集成数据矩阵的低秩联合子空间。所提出的算法首先评估每种模态提供的子类型信息的质量，然后明智地仅选择相关的子类型信息来构造联合子空间。针对多模态数据框架制定了增量更新数据矩阵的奇异值分解的问题。该分析公式能够有效地构建来自各个模态的低秩子空间的集成数据的联合子空间。与在集成数据矩阵上执行主成分分析（PCA）相比，所提出的方法构建联合子空间的计算效率更高。针对PCA提取的主子空间，引入了一些新的定量指标，从理论上衡量所提出的方法构建子空间的准确性。所提出的算法构建的联合子空间上的聚类效果是在几个现实生活中的多模态癌症数据集上建立在现有的综合聚类方法之上的。