5,270 research outputs found
Differential fast fixed-point algorithms for underdetermined instantaneous and convolutive partial blind source separation
This paper concerns underdetermined linear instantaneous and convolutive
blind source separation (BSS), i.e., the case when the number of observed mixed
signals is lower than the number of sources.We propose partial BSS methods,
which separate supposedly nonstationary sources of interest (while keeping
residual components for the other, supposedly stationary, "noise" sources).
These methods are based on the general differential BSS concept that we
introduced before. In the instantaneous case, the approach proposed in this
paper consists of a differential extension of the FastICA method (which does
not apply to underdetermined mixtures). In the convolutive case, we extend our
recent time-domain fast fixed-point C-FICA algorithm to underdetermined
mixtures. Both proposed approaches thus keep the attractive features of the
FastICA and C-FICA methods. Our approaches are based on differential sphering
processes, followed by the optimization of the differential nonnormalized
kurtosis that we introduce in this paper. Experimental tests show that these
differential algorithms are much more robust to noise sources than the standard
FastICA and C-FICA algorithms.Comment: this paper describes our differential FastICA-like algorithms for
linear instantaneous and convolutive underdetermined mixture
Underdetermined blind source separation based on Fuzzy C-Means and Semi-Nonnegative Matrix Factorization
Conventional blind source separation is based on over-determined with more sensors than sources but the underdetermined is a challenging case and more convenient to actual situation. Non-negative Matrix Factorization (NMF) has been widely applied to Blind Source Separation (BSS) problems. However, the separation results are sensitive to the initialization of parameters of NMF. Avoiding the subjectivity of choosing parameters, we used the Fuzzy C-Means (FCM) clustering technique to estimate the mixing matrix and to reduce the requirement for sparsity. Also, decreasing the constraints is regarded in this paper by using Semi-NMF. In this paper we propose a new two-step algorithm in order to solve the underdetermined blind source separation. We show how to combine the FCM clustering technique with the gradient-based NMF with the multi-layer technique. The simulation results show that our proposed algorithm can separate the source signals with high signal-to-noise ratio and quite low cost time compared with some algorithms
Fourier PCA and Robust Tensor Decomposition
Fourier PCA is Principal Component Analysis of a matrix obtained from higher
order derivatives of the logarithm of the Fourier transform of a
distribution.We make this method algorithmic by developing a tensor
decomposition method for a pair of tensors sharing the same vectors in rank-
decompositions. Our main application is the first provably polynomial-time
algorithm for underdetermined ICA, i.e., learning an matrix
from observations where is drawn from an unknown product
distribution with arbitrary non-Gaussian components. The number of component
distributions can be arbitrarily higher than the dimension and the
columns of only need to satisfy a natural and efficiently verifiable
nondegeneracy condition. As a second application, we give an alternative
algorithm for learning mixtures of spherical Gaussians with linearly
independent means. These results also hold in the presence of Gaussian noise.Comment: Extensively revised; details added; minor errors corrected;
exposition improve
A Unique "Nonnegative" Solution to an Underdetermined System: from Vectors to Matrices
This paper investigates the uniqueness of a nonnegative vector solution and
the uniqueness of a positive semidefinite matrix solution to underdetermined
linear systems. A vector solution is the unique solution to an underdetermined
linear system only if the measurement matrix has a row-span intersecting the
positive orthant. Focusing on two types of binary measurement matrices,
Bernoulli 0-1 matrices and adjacency matrices of general expander graphs, we
show that, in both cases, the support size of a unique nonnegative solution can
grow linearly, namely O(n), with the problem dimension n. We also provide
closed-form characterizations of the ratio of this support size to the signal
dimension. For the matrix case, we show that under a necessary and sufficient
condition for the linear compressed observations operator, there will be a
unique positive semidefinite matrix solution to the compressed linear
observations. We further show that a randomly generated Gaussian linear
compressed observations operator will satisfy this condition with
overwhelmingly high probability
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