**1.2 Contributions**

Building on the work of Deep Subspace Clustering (DSC) [25], we propose a new and principled multi-modal fusion approach which accounts for a sensor' capacity to house private and unique information about some observed data as well as that information which is likely also captured and hence common to other sensors. This is accounted for in our robust fusion formulation for multi-modal sensor data. Unveiling the complex UoS of multi-modal data also requires us to account for scaling in our proposed formulation and solution, which in turn invokes the learning of multiple/deep scale Convolutional Neural Networks. Our proposed Multi-modal fusion approach, by virtue of each sensor information structure (i.e., private plus shared) seeks to enhance and robustify the subspace approximation of shared information for each of the sensors, thus yielding a parallel bank of UoS for each of the sensors. The robust Deep structure effectively achieves scaling while securing structured representation for unsupervised inference. We compare our approach to a well-known deep multimodal network [21] which was also based on [25].

In our proposed approach, we thus define the latent space in a way that safeguards the individual sensor private information which hence dedicates more degrees of freedom to each of the sensors. In contrast to the approach in [21]. In our evaluation, we use two recently released data sets each of which we partition into learning and validation subsets. The learned UoS structure for each of the data sets is then utilized to classify new observed data points, which illustrates the generalization power of the proposed approach. Different scenarios with corresponding additive noise to either the training set or the testing set, or both, were used to thoroughly investigate the robustness, and resilience of the clustering approach performance. Experimental results confirm a significant improvement for our Deep Robust Group Subspace Recovery network (DRoGSuRe) under numerous limiting scenarios and demonstrate robustness under these conditions.

The balance of the paper is organized as follows, in Section 2, we provide the problem formulation, background along with the derivation for our proposed approach, Deep Robust Group Subspace Recovery (DRoGSuRe). In Section 3, we describe the attributes of the proposed approach and contrast it to Deep Multimodal Subspace Clustering algorithm (DMSC). In Sections 4 and 5, we present a substantiative validation along with experimental results of our approach, while Section 6 provides concluding remarks.
