Robust Subspace Recovery (RoSuRe) algorithm was recently introduced as a principled and numerically efficient algorithm that unfolds underlying Unions of Subspaces (UoS) structure, present in the data. The union of Subspaces (UoS) is capable of identifying more complex trends in data sets than simple linear models. We build on and extend RoSuRe to prospect the structure of different data modalities individually. We propose a novel multi-modal data fusion approach based on group sparsity which we refer to as Robust Group Subspace Recovery (RoGSuRe). Relying on a bi-sparsity pursuit paradigm and non-smooth optimization techniques, the introduced framework learns a new joint representation of the time series from different data modalities, respecting an underlying UoS model. We subsequently integrate the obtained structures to form a unified subspace structure. The proposed approach exploits the structural dependencies between the different modalities data to cluster the associated target objects. The resulting fusion of the unlabeled sensors' data from experiments on audio and magnetic data has shown that our method is competitive with other state of the art subspace clustering methods. The resulting UoS structure is employed to classify newly observed data points, highlighting the abstraction capacity of the proposed method.

中文翻译：

---

鲁棒组子空间恢复：多模态数据融合的新方法


鲁棒子空间恢复 (RoSuRe) 算法最近被引入，作为一种原理性且数值高效的算法，可展开数据中存在的底层子空间并集 (UoS) 结构。子空间并集 (UoS) 能够识别数据集中比简单线性模型更复杂的趋势。我们以 RoSuRe 为基础并对其进行扩展，以分别探索不同数据模式的结构。我们提出了一种基于组稀疏性的新型多模态数据融合方法，我们将其称为鲁棒组子空间恢复（RoGSuRe）。依靠双稀疏追求范式和非平滑优化技术，所引入的框架从不同的数据模态中学习时间序列的新联合表示，尊重底层的 UoS 模型。我们随后整合所获得的结构以形成统一的子空间结构。所提出的方法利用不同模态数据之间的结构依赖性来对关联的目标对象进行聚类。来自音频和磁数据实验的未标记传感器数据的最终融合表明，我们的方法与其他最先进的子空间聚类方法具有竞争力。由此产生的 UoS 结构用于对新观察到的数据点进行分类，突出了所提出方法的抽象能力。