Multimodal datasets, where measurements are obtained from multiple sensors, have become central to many scientific domains. In unsupervised settings, most representation learning methods focus on identifying shared latent structures, such as clusters or continuous processes that appear across modalities. However, some aspects of the data may be observed only through a single modality. For example, in computational biology, certain cell-subtypes may appear in genetic profiles but not in epigenetic markers. In this paper, we present DELVE, a spectral method for extracting modality-specific (differential) latent variables. Our approach constructs a graph for each modality and leverages differences in their connectivity patterns to design a graph filter that attenuates shared signals while preserving modality-specific components. We provide an asymptotic convergence analysis for our method under a product manifold model. To evaluate the performance of our method, we test its ability to recover differential latent structures in several synthetic and real datasets.

翻译：多模态数据集，即通过多个传感器获取测量数据的数据集，已成为许多科学领域的核心。在无监督设置下，大多数表示学习方法侧重于识别共享的潜在结构，例如跨模态出现的聚类或连续过程。然而，数据的某些方面可能仅通过单一模态被观测到。例如，在计算生物学中，某些细胞亚型可能出现在基因表达谱中，但不在表观遗传标记中。本文提出了DELVE，一种用于提取模态特定（差异）潜在变量的谱方法。我们的方法为每个模态构建一个图，并利用其连接模式的差异来设计一个图滤波器，该滤波器能衰减共享信号，同时保留模态特定的成分。我们在乘积流形模型下，为该方法提供了渐近收敛性分析。为了评估方法的性能，我们在多个合成和真实数据集上测试了其恢复差异潜在结构的能力。