Yiyuan Tang

Letters: A fast fixed-point algorithm for complexity pursuit

Complexity pursuit is a recently developed algorithm using the gradient descent for separating interesting components from time series. It is an extension of projection pursuit to time series data and the method is closely related to blind separation of time-dependent source signals and independent component analysis (ICA). In this paper, a fixed-point algorithm for complexity pursuit is introduced. The fixed-point algorithm inherits the advantages of the well-known FastICA algorithm in ICA, which is very simple, converges fast, and does not need choose any learning step sizes.

A new fixed-point algorithm for independent component analysis

A new fixed-point algorithm for independent component analysis (ICA) is presented that is able blindly to separate mixed signals with sub- and super-Gaussian source distributions. The new fixed-point algorithm maximizes the likelihood of the ICA model under the constraint of decorrelation and uses the method of Lee et al. (Neural Comput. 11(2) (1999) 417) to switch between sub- and super-Gaussian regimes. The new fixed-point algorithm maximizes the likelihood very fast and reliably. The validity of this algorithm is confirmed by the simulations and experimental results

Blind source separation of more sources than mixtures using sparse mixture models

In this paper, blind source separation is discussed with more sources than mixtures. This blind separation technique assumes a linear mixing model and involves two steps: (1) learning the mixing matrix for the observed data using the sparse mixture model and (2) inferring the sources by solving a linear programming problem after the mixing matrix is estimated. Through the experiments of the speech signals, we demonstrate the efficacy of this proposed approach.

Blind source separation of more sources than mixtures using generalized exponential mixture models

Blind source separation is discussed with more sources than mixtures in this paper. The blind separation technique includes two steps. The first step is to estimate a mixing matrix, and the second is to estimate sources. If the sources are sparse, the mixing matrix can be estimated by using the generalized exponential mixture model. The generalized exponential mixture model is a powerful uniform framework to learn the mixing matrix for sparse sources. A gradient learning algorithm for the generalized exponential mixture model is derived. After estimating the mixing matrix, the sources can be obtained by using the maximum a posteriori approach. The speech-signal experiments demonstrate effectiveness of the proposed approach.

An EM algorithm for learning sparse and overcomplete representations

An expectation-maximization (EM) algorithm for learning sparse and overcomplete representations is presented in this paper. We show that the estimation of the conditional moments of the posterior distribution can be accomplished by maximum a posteriori estimation. The approximate conditional moments,enable the development of an EM algorithm for learning the overcomplete basis vectors and inferring the most probable basis coefficients

Expectation-Maximization approaches to independent component analysis

Expectation-Maximization (EM) algorithms for independent component analysis are presented in this paper. For super-Gaussian sources, a variational method is employed to develop an EM algorithm in closed form for learning the mixing matrix and inferring the independent components. For sub-Gaussian sources, a symmetrical form of the Pearson mixture model (Neural Comput. 11 (2) (1999) 417-441) is used as the prior, which also enables the development of an EM algorithm in fclosed form for parameter estimation.

A clustering approach for blind source separation with more sources than mixtures

In this paper, blind source separation is discussed with more sources than mixtures when the sources are sparse. The blind separation technique includes two steps. The first step is to estimate a mixing matrix, and the second is to estimate sources. The mixing matrix can be estimated by using a clustering approach which is described by the generalized exponential mixture model. The generalized exponential mixture model is a powerful uniform framework to learn the mixing matrix for sparse sources. After the mixing matrix is estimated, the sources can be obtained by solving a linear programming problem. The techniques we present here can be extended to the blind separation of more sources than mixtures with a Gaussian noise.