  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.
