Multimodal Soft Nonnegative Matrix Co-Factorization for Convolutive Source Separation

Abstract

International audienceIn this paper, the problem of convolutive source separation via multimodal soft Nonnegative Matrix Co-Factorization (NMCF) is addressed. Different aspects of a phenomenon may be recorded by sensors of different types (e.g., audio and video of human speech), and each of these recorded signals is called a modality. Since the underlying phenomenon of the modalities is the same, they have some similarities. Especially, they usually have similar time changes. It means that changes in one of them usually correspond to changes in the other one. So their active or inactive periods are usually similar. Assuming this similarity, it is expected that the activation coefficient matrices of their Nonnegative Matrix Factorization (NMF) have a similar form. In this paper, the similarity of the activation coefficient matrices between the modalities is considered for co-factorization. This similarity is used for separation procedure in a soft manner by using penalty terms. This results in more flexibility in the separation procedure. Simulation results and comparison with state-of-the-art algorithms show the effectiveness of the proposed algorithm

Phonocardiogram Signal Denoising Based on Nonnegative Matrix Factorization and Adaptive Contour Representation Computation

“…The key idea of denoising techniques based on NMF lies in that information of a single natural phenomenon can be acquired using different devices, called modalities [19], [20]. For instance, ECG corresponds to the recording of the electrical activity of the heart, while PCG to heart sounds.…”

Quasi-Periodic Non-Negative Matrix Factorization for Phonocardiographic Signals Denoising

“…To minimize (8), an alternating MM algorithm is used to derive multiplicative updates that ensure the non-negativity of the estimated W (i) (resp. H (i) ) given H (i) (resp.…”

“…W (i) ). To this end, auxiliary functions L(•|•) (where• stands for the current estimation) of each term in (8) are expressed in Appendix. Vanishing the derivative of the overall auxiliary function of (8) leads to the update equations:…”

“…PCG denoising has been investigated by many approaches of interest, such as adaptive filtering [1], Kalman filtering [2], wavelets [3], Empirical Modal Decomposition (EMD) [4] or Non-negative Matrix Factorization (NMF) [5], [6]. Among these methods, the NMF [7], [8] is particularly adapted to take into account the quasi-periodic property of physiological signals, since the algorithm applied to spectrograms is wellsuited to identify events with particular spectrum and temporal regularity, such as quasi-periodicity [9]. Indeed, the NMF method decomposes a signal in k components, by approximating an observation matrix X ∈ R m×n + of positive or zero coefficients by a product of two matrices with non-negative values W ∈ R m×k + and H ∈ R k×n + : X = V + N where V = W H and N is the residual error from the approximation.…”

Capacity and Limits of Multimodal Remote Sensing: Theoretical Aspects and Automatic Information Theory-Based Image Selection

“…It is expected that multimodal remote sensing enhances the understanding of Earth's surface physical phenomena. Nonetheless, it has been proved, either in remote sensing [4], [5] or in other data science research fields [3], [10], that processing more data and records does not always result in detailed information extraction because of nonidealities, mismatches and estimation imperfections [5], [11], [12]. This effect is even more evident in a multimodal analysis set-up, as the differences in temporal, spatial, spectral, and radiometric resolutions might affect the correct alignment, labelling and reference of the records to be processed [1]- [3], [5], [8], [9].…”