Heterogeneity is a hallmark of cancer, diabetes, cardiovascular diseases, and many other complex diseases. This study has been partly motivated by the unsupervised heterogeneity analysis for complex diseases based on molecular and imaging data, for which, network-based analysis, by accommodating the interconnections among variables, can be more informative than that limited to mean, variance, and other simple distributional properties. In the literature, there has been very limited research on network-based heterogeneity analysis, and a common limitation shared by the existing techniques is that the number of subgroups needs to be specified a priori or in an ad hoc manner. In this article, we develop a penalized fusion approach for heterogeneity analysis based on the Gaussian graphical model. It applies penalization to the mean and precision matrix parameters to generate regularized and interpretable estimates. More importantly, a fusion penalty is imposed to “automatedly” determine the number of subgroups and generate more concise, reliable, and interpretable estimation. Consistency properties are rigorously established, and an effective computational algorithm is developed. The heterogeneity analysis of non-small-cell lung cancer based on single-cell gene expression data of the Wnt pathway and that of lung adenocarcinoma based on histopathological imaging data not only demonstrate the practical applicability of the proposed approach but also lead to interesting new findings.

中文翻译：

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通过惩罚融合进行基于高斯图模型的异质性分析

异质性是癌症、糖尿病、心血管疾病和许多其他复杂疾病的标志。这项研究的部分动机是基于分子和影像数据对复杂疾病进行无监督异质性分析，为此，基于网络的分析通过适应变量之间的相互联系，可以比仅限于均值、方差和其他分析提供更多信息简单的分布特性。在文献中，对基于网络的异质性分析的研究非常有限，现有技术的一个共同限制是需要先验或以临时方式指定子组的数量。在本文中，我们基于高斯图模型开发了一种用于异质性分析的惩罚融合方法。它将惩罚应用于均值和精度矩阵参数，以生成正则化和可解释的估计值。更重要的是，施加融合惩罚以“自动”确定子组的数量并生成更简洁、可靠和可解释的估计。严格建立一致性属性，并开发有效的计算算法。基于 Wnt 通路单细胞基因表达数据的非小细胞肺癌异质性分析和基于组织病理学成像数据的肺腺癌异质性分析不仅证明了所提出方法的实际适用性，而且还带来了有趣的新发现. 施加融合惩罚以“自动”确定子组的数量并生成更简洁、可靠和可解释的估计。严格建立一致性属性，并开发有效的计算算法。基于 Wnt 通路单细胞基因表达数据的非小细胞肺癌异质性分析和基于组织病理学成像数据的肺腺癌异质性分析不仅证明了所提出方法的实际适用性，而且还带来了有趣的新发现. 施加融合惩罚以“自动”确定子组的数量并生成更简洁、可靠和可解释的估计。严格建立一致性属性，并开发有效的计算算法。基于 Wnt 通路单细胞基因表达数据的非小细胞肺癌异质性分析和基于组织病理学成像数据的肺腺癌异质性分析不仅证明了所提出方法的实际适用性，而且还带来了有趣的新发现.