The Cox proportional hazard model has been widely applied to cancer prognosis prediction. Nowadays, multi-modal data, such as histopathological images and gene data, have advanced this field by providing histologic phenotype and genotype information. However, how to efficiently fuse and select the complementary information of high-dimensional multi-modal data remains challenging for Cox model, as it generally does not equip with feature fusion/selection mechanism. Many previous studies typically perform feature fusion/selection in the original feature space before Cox modeling. Alternatively, learning a latent shared feature space that is tailored for Cox model and simultaneously keeps sparsity is desirable. In addition, existing Cox-based models commonly pay little attention to the actual length of the observed time that may help to boost the model’s performance. In this article, we propose a novel Cox-driven multi-constraint latent representation learning framework for prognosis analysis with multi-modal data. Specifically, for efficient feature fusion, a multi-modal latent space is learned via a bi-mapping approach under ranking and regression constraints. The ranking constraint utilizes the log-partial likelihood of Cox model to induce learning discriminative representations in a task-oriented manner. Meanwhile, the representations also benefit from regression constraint, which imposes the supervision of specific survival time on representation learning. To improve generalization and alleviate overfitting, we further introduce similarity and sparsity constraints to encourage extra consistency and sparseness. Extensive experiments on three datasets acquired from The Cancer Genome Atlas (TCGA) demonstrate that the proposed method is superior to state-of-the-art Cox-based models.

中文翻译：

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使用多模态数据进行预后分析的多约束潜在表示学习

Cox比例风险模型已广泛应用于癌症预后预测。如今，组织病理学图像和基因数据等多模态数据通过提供组织学表型和基因型信息推动了这一领域的发展。然而，如何有效地融合和选择高维多模态数据的互补信息对于Cox模型来说仍然是一个挑战，因为它通常不具备特征融合/选择机制。之前的许多研究通常在 Cox 建模之前在原始特征空间中进行特征融合/选择。或者，学习为 Cox 模型量身定制并同时保持稀疏性的潜在共享特征空间是可取的。此外，现有的基于 Cox 的模型通常很少关注可能有助于提高模型性能的观察时间的实际长度。在本文中，我们提出了一种新颖的 Cox 驱动的多约束潜在表示学习框架，用于多模态数据的预后分析。具体来说，为了有效的特征融合，在排序和回归约束下通过双映射方法学习多模态潜在空间。排序约束利用 Cox 模型的对数部分似然来以面向任务的方式诱导学习判别表示。同时，表示还受益于回归约束，回归约束对表示学习施加了特定生存时间的监督。为了提高泛化能力并减轻过度拟合，我们进一步引入相似性和稀疏性约束，以鼓励额外的一致性和稀疏性。对从癌症基因组图谱 (TCGA) 获取的三个数据集进行的广泛实验表明，所提出的方法优于最先进的基于 Cox 的模型。