  Dictionary learning algorithms have been successfully used for both
reconstructive and discriminative tasks, where an input signal is represented
with a sparse linear combination of dictionary atoms. While these methods are
mostly developed for single-modality scenarios, recent studies have
demonstrated the advantages of feature-level fusion based on the joint sparse
representation of the multimodal inputs. In this paper, we propose a multimodal
task-driven dictionary learning algorithm under the joint sparsity constraint
(prior) to enforce collaborations among multiple homogeneous/heterogeneous
sources of information. In this task-driven formulation, the multimodal
dictionaries are learned simultaneously with their corresponding classifiers.
The resulting multimodal dictionaries can generate discriminative latent
features (sparse codes) from the data that are optimized for a given task such
as binary or multiclass classification. Moreover, we present an extension of
the proposed formulation using a mixed joint and independent sparsity prior
which facilitates more flexible fusion of the modalities at feature level. The
efficacy of the proposed algorithms for multimodal classification is
illustrated on four different applications -- multimodal face recognition,
multi-view face recognition, multi-view action recognition, and multimodal
biometric recognition. It is also shown that, compared to the counterpart
reconstructive-based dictionary learning algorithms, the task-driven
formulations are more computationally efficient in the sense that they can be
equipped with more compact dictionaries and still achieve superior performance.
