This paper provides an overview of the main challenges in multimodal data fusion across various disciplines and addresses two key issues: ''why we need data fusion'' and ''how we perform it.'' ABSTRACT | In various disciplines, information about the same phenomenon can be acquired from different types of detectors, at different conditions, in multiple experiments or subjects, among others. We use the term ''modality'' for each such acquisition framework. Due to the rich characteristics of natural phenomena, it is rare that a single modality provides complete knowledge of the phenomenon of interest. The increasing availability of several modalities reporting on the same system introduces new degrees of freedom, which raise questions beyond those related to exploiting each modality separately. As we argue, many of these questions, or ''challenges,'' are common to multiple domains. This paper deals with two key issues: ''why we need data fusion'' and ''how we perform it.''The first issue is motivated by numerous examples in science and technology, followed by a mathematical framework that showcases some of the benefits that data fusion provides. In order to address the second issue, ''diversity'' is introduced as a key concept, and a number of data-driven solutions based on matrix and tensor decompositions are discussed, emphasizing how they account for diversity across the data sets. The aim of this paper is to provide the reader, regardless of his or her community of origin, with a taste of the vastness of the field, the prospects, and the opportunities that it holds.

International audienceThis paper deals with a novel generalization of classical blind source separation (BSS) in two directions. First, relaxing the constraint that the latent sources must be statistically independent. This generalization is well-known and sometimes termed independent subspace analysis (ISA). Second, jointly analyzing several ISA problems, where the link is due to statistical dependence among corresponding sources in different mixtures. When the data are one-dimensional, i.e., multiple classical BSS problems, this model, known as independent vector analysis (IVA), has already been studied. In this paper, we combine IVA with ISA and term this new model joint independent subspace analysis (JISA). We provide full performance analysis of JISA, including closed-form expressions for minimal mean square error (MSE), Fisher information and Cramér-Rao lower bound, in the separation of Gaussian data. The derived MSE applies also for non-Gaussian data, when only second-order statistics are used. We generalize previously known results on IVA, including its ability to uniquely resolve instantaneous mixtures of real Gaussian stationary data, and having the same arbitrary permutation at all mixtures. Numerical experiments validate our theoretical results and show the gain with respect to two competing approaches that either use a finer block partition or a different norm

Independent component analysis (ICA) and blind source separation (BSS) deal with extracting a number of mutually independent elements from a set of observed linear mixtures. Motivated by various applications, this paper considers a more general and more flexible model: the sources can be partitioned into groups exhibiting dependence within a given group but independence between two different groups. We argue that this is tantamount to considering multidimensional components as opposed to the standard ICA case which is restricted to one-dimensional components. The core of the paper is devoted to the statistical analysis of the blind separation of multidimensional components based on second-order statistics, in a piecewise-stationary model. We develop the likelihood and the associated estimating equations for the Gaussian case. We obtain closed-form expressions for the Fisher information matrix and the Cramér-Rao bound of the de-mixing parameters, as well as the mean-square error (MSE) of the component estimates. The derived MSE is valid also for non-Gaussian data. Our analysis is verified through numerical experiments, and its performance is compared to classical ICA in various dependence scenarios, quantifying the gain in the accuracy of component recovery in presence of multidimensional components.

In this paper, we present a quasi-Newton (QN) algorithm for joint independent subspace analysis (JISA). JISA is a recently proposed generalization of independent vector analysis (IVA). JISA extends classical blind source separation (BSS) to jointly resolve several BSS problems by exploiting statistical dependence between latent sources across mixtures, as well as relaxing the assumption of statistical independence within each mixture. Algebraically, JISA based on second-order statistics amounts to coupled block diagonalization of a set of covariance and crosscovariance matrices, as well as block diagonalization of a single permuted covariance matrix. The proposed QN algorithm achieves asymptotically the minimal mean square error (MMSE) in the separation of multidimensional Gaussian components. Numerical experiments demonstrate convergence and source separation properties of the proposed algorithm.