Multimodal latent variable analysis

Abstract

Consider a set of multiple, multimodal sensors capturing a complex system or a physical phenomenon of interest. Our primary goal is to distinguish the underlying sources of variability manifested in the measured data. The first step in our analysis is to find the common source of variability present in all sensor measurements. We base our work on a recent paper, which tackles this problem with alternating diffusion (AD). In this work, we suggest to further the analysis by extracting the sensor-specific variables in addition to the common source. We propose an algorithm, which we analyze theoretically, and then demonstrate on three different applications: a synthetic example, a toy problem, and the task of fetal ECG extraction.

Efficient Fetal-Maternal ECG Signal Separation from Two Channel Maternal Abdominal ECG via Diffusion-Based Channel Selection

“…The main ingredient in is the diffusion geometry. Since we have more than one aECG channel, we could consider modern diffusion-based manifold learning techniques to extract information common in two channels, like the alternating diffusion (Papyan and Talmon, 2016 ; Talmon and Wu, 2016 ; Lederman and Talmon, in press ). The non-stationary nature of the fECG signal, which often presents itself as a time-varying frequency, might jeopardize the diffusion-based approach.…”

Nonlinear Filtering With Variable Bandwidth Exponential Kernels

“…Such kernel construction has been often used in the past decade for analysis of dynamical systems [16], image processing [29], non-linear independent component analysis [21], and other applications [25]. Quadratic form distances have also been used with alternating diffusion kernels in multisensor applications [20]. Other approaches for informed metric construction based on prior information about the problem at hand have been proposed in [30], [31], [32].…”

“…This is the underlying idea behind directed diffusions [11], selftuning kernels [14], and other kernels with a data-driven distance metric [15] which are successfully applied to many applications in the past decade. These applications include multiscale analysis of dynamical systems [16], [17], [18], multimodal data analysis [19], [20], and non-linear independent component analysis [21].…”