In clinical routine, high-dimensional descriptors of the cardiac function such as shape and deformation are reduced to scalars (e.g. volumes or ejection fraction), which limit the characterization of complex diseases. Besides, these descriptors undergo interactions depending on disease, which may bias their computational analysis. In this paper, we aim at characterizing such interactions by unsupervised manifold learning. We propose to use a sparsified version of Multiple Manifold Learning to align the latent spaces encoding each descriptor and weighting the strength of the alignment depending on each pair of samples. While this framework was up to now only applied to link different datasets from the same manifold, we demonstrate its relevance to characterize the interactions between different but partially related descriptors of the cardiac function (shape and deformation).

We benchmark our approach against linear and non-linear embedding strategies, among which the fusion of manifolds by Multiple Kernel Learning, the independent embedding of each descriptor by Diffusion Maps, and a strict alignment based on pairwise correspondences. We first evaluated the methods on a synthetic dataset from a 0D cardiac model where the interactions between descriptors are fully controlled. Then, we transfered them to a population of right ventricular meshes from 310 subjects (100 healthy and 210 patients with right ventricular disease) obtained from 3D echocardiography, where the link between shape and deformation is key for disease understanding. Our experiments underline the relevance of jointly considering shape and deformation descriptors, and that manifold alignment is preferable over fusion for our application. They also confirm at a finer scale the characteristic traits of the right ventricular diseases in our population.

在临床常规中，心脏功能的高维描述符（例如形状和变形）被简化为标量（例如体积或射血分数），这限制了复杂疾病的表征。此外，这些描述符会根据疾病进行交互，这可能会使它们的计算分析产生偏差。在本文中，我们旨在通过无监督流形学习来表征这种相互作用。我们建议使用多流形学习的稀疏版本来对齐编码每个描述符的潜在空间，并根据每对样本对对齐的强度进行加权。虽然这个框架到目前为止只适用于链接来自同一个流形的不同数据集，

我们将我们的方法与线性和非线性嵌入策略进行基准测试，其中通过多核学习融合流形，通过扩散图独立嵌入每个描述符，以及基于成对对应的严格对齐。我们首先在来自 0D 心脏模型的合成数据集上评估了这些方法，其中描述符之间的交互受到完全控制。然后，我们将它们转移到从 3D 超声心动图获得的 310 名受试者（100 名健康和 210 名右心室疾病患者）的右心室网格中，其中形状和变形之间的联系是了解疾病的关键。我们的实验强调了联合考虑形状和变形描述符的相关性，并且对于我们的应用来说，流形对齐比融合更可取。