Blind Source Separation over Space

利用空间非平稳性的非线性盲源分离

Nonlinear blind source separation exploiting spatial nonstationarity

针对现有空间盲源分离算法仅支持线性解混的问题，本文将可识别变分自编码器拓展至空间数据，提出配套解释方法，并验证其在仿真、地球化学数据集及多变量预测预处理中的有效性。

Model-Independent Analytic Nonlinear Blind Source Separation

Consider a time series of measurements of the state of an evolving system, x(t), where x has two or more components. This paper shows how to perform nonlinear blind source separation; i.e., how to determine if these signals are equal to linear or nonlinear mixtures of the state variables of two or more statistically independent subsystems. First, the local distributions of measurement velocities are processed in order to derive vectors at each point in x-space. If the data are separable, each of these vectors must be directed along a subspace of x-space that is traversed by varying the state v…

Identifiability for Blind Source Separation of Multiple Finite Alphabet Linear Mixtures

We give under weak assumptions a complete combinatorial characterization of identifiability for linear mixtures of finite alphabet sources, with unknown mixing weights and unknown source signals, but known alphabet. This is based on a detailed treatment of the case of a single linear mixture. Notably, our identifiability analysis applies also to the case of unknown number of sources. We provide sufficient and necessary conditions for identifiability and give a simple sufficient criterion together with an explicit construction to determine the weights and the source signals for deterministic da…

Multiscale Blind Source Separation

We provide a new methodology for statistical recovery of single linear mixtures of piecewise constant signals (sources) with unknown mixing weights and change points in a multiscale fashion. We show exact recovery within an $ε$-neighborhood of the mixture when the sources take only values in a known finite alphabet. Based on this we provide the SLAM (Separates Linear Alphabet Mixtures) estimators for the mixing weights and sources. For Gaussian error, we obtain uniform confidence sets and optimal rates (up to log-factors) for all quantities. SLAM is efficiently computed as a nonconvex optimiza…

Correction to: "Blind maximum likelihood separation of a linear-quadratic mixture"

An error occurred in the computation of a gradient in our paper entitled "Blind maximum likelihood separation of a linear-quadratic mixture", presented in ICA'2004. The equations (20) in Appendix and (17) in the text were not correct. The current paper presents the correct version of these equations.

Nonlinear Blind Source Separation Using Sensor-Independent Signal Representations

Consider a time series of signal measurements $x(t)$, having components $x_k \mbox{ for } k = 1,2, \ldots ,N$. This paper shows how to determine if these signals are equal to linear or nonlinear mixtures of the state variables of two or more statistically-independent subsystems. First, the local distribution of measurement velocities ($\dot{x}$) is processed in order to derive $N$ local vectors at each $x$. If the data are separable, each of these vectors is directed along a subspace traversed by varying the state variable of one subsystem, while all other subsystems are kept constant. Because…