Nonparametric Independent Component Analysis Research Articles

A non-parametric Bayesian joint model for latent individual molecular profiles and survival in oncology.

The development of prognostic molecular signatures considering the inter-patient heterogeneity is a key challenge for the precision medicine. We propose a joint model of this heterogeneity and the patient survival, assuming that tumor expression results from a mixture of a subset of independent signatures. We deconvolute the omics data using a non-parametric independent component analysis with a double sparseness structure for the source and the weight matrices, corresponding to the gene-component and individual-component associations, respectively. In a simulation study, our approach identified the correct number of components and reconstructed with high accuracy the weight ([Formula: see text]0.85) and the source ([Formula: see text]0.75) matrices sparseness. The selection rate of components with high-to-moderate prognostic impacts was close to 95%, while the weak impacts were selected with a frequency close to the observed false positive rate ([Formula: see text]25%). When applied to the expression of 1063 genes from 614 breast cancer patients, our model identified 15 components, including six associated to patient survival, and related to three known prognostic pathways in early breast cancer (i.e. immune system, proliferation, and stromal invasion). The proposed algorithm provides a new insight into the individual molecular heterogeneity that is associated with patient prognosis to better understand the complex tumor mechanisms.

Two pairwise iterative schemes for high dimensional blind source separation

In this paper, we address the problem of scalability to higher dimensional space in blind source separation (BSS), where the number of sources is greater than two. Herein, we propose two schemes of pairwise non-parametric independent component analysis (ICA) algorithms based on Convex Cauchy–Schwarz Divergence (CCS–DIV) for high dimensional problem in BSS. We extend the pairwise method to the scenario of more than two sources, two improved ICA algorithms are developed. Moreover, we employ adaptive sampling technique that samples the signal into small time blocks to evaluate the integration of the CCS–DIV and reduce the computational complexity. The two presented methods enable fast and efficient demixing of sources in real-world high dimensional source applications. Finally, we demonstrate with simulations including a wide variety of source distributions, showing that our presented methods outperform many of the presently known methods in terms of performance and computational complexity.

Performance comparison of MeRMaId-ICA and Np-ICA in composite abdominal electrocardiogram separation

Blind source separation strives to disintegrate a multivariate composite non-invasive abdominal electrocardiogram signal into independent non-Gaussian signals such as maternal and foetal electrocardiograms. This paper proffers two separation algorithms especially for foetal electrocardiogram (FECG) extraction as it has a great role in diagnosing the foetal heart deformities namely minimum Renyi's mutual information called MeRMaId algorithm and non-parametric independent component analysis (Np-ICA) algorithm. Both the algorithms are experimentally evaluated on synthetic and real abdominal data. Performance juxtaposition of these two algorithms is done by scrutinising the signal to noise ratio at assorted noise levels and signal to interference ratio at assorted amplitude levels, and computing correlation coefficient (ρ) of the original and the estimated maternal and foetal electrocardiograms.

Performance comparison of new nonparametric independent component analysis algorithm for different entropic indexes

Most independent component analysis (ICA) algorithms use mutual information (MI) measures based on Shannon entropy as a cost function, but Shannon entropy is not the only measure in the literature. In this paper, instead of Shannon entropy, Tsallis entropy is used and a novel ICA algorithm, which uses kernel density estimation (KDE) for estimation of source distributions, is proposed. KDE is directly evaluated from the original data samples, so it solves the important problem in ICA: how to choose nonlinear functions as the probability density function (pdf) estimation of the sources.

Convex Divergence ICA for Blind Source Separation

Independent component analysis (ICA) is vital for unsupervised learning and blind source separation (BSS). The ICA unsupervised learning procedure attempts to demix the observation vectors and identify the salient features or mixture sources. This work presents a novel contrast function for evaluating the dependence among sources. A convex divergence measure is developed by applying the convex functions to the Jensen's inequality. Adjustable with a convexity parameter, this inequality-based divergence measure has a wide range of the steepest descents to reach its minimum value. A convex divergence ICA (C-ICA) is constructed and a nonparametric C-ICA algorithm is derived with different convexity parameters where the non-Gaussianity of source signals is characterized by the Parzen window-based distribution. Experimental results indicate that the specialized C-ICA significantly reduces the number of learning epochs during estimation of the demixing matrix. The convergence speed is improved by using the scaled natural gradient algorithm. Experiments on the BSS of instantaneous, noisy and convolutive mixtures of speech and music signals further demonstrate the superiority of the proposed C-ICA to JADE, Fast-ICA, and the nonparametric ICA based on mutual information.

Performance evaluation of nonparametric ICA algorithm for fetal ECG extraction

Fetal electrocardiograms (FECG) contain important indications about the health and condition of the fetus. In this respect, it is crucial to apply a robust algorithm to ECG data for extraction of the FECG signal. Most of the independent component analysis (ICA) algorithms used for this purpose rely on simple statistical models. Such algorithms can fail to separate desired signals when the assumed statistical model is inaccurate. Statistical models can be estimated accurately using kernel density estimation methods. Therefore, the kernel density estimation method was used in this paper for building an ICA algorithm (nonparametric ICA: NpICA) and the algorithm was applied to abdominal recordings to separate the FECG signals, which had not been implemented before. Checking of the separation quality of the NpICA algorithm was applied to synthetic ECG signals and real multichannel ECG recordings obtained from a pregnant woman's skin. The test results showed that the NpICA algorithm outperformed other known ICA algorithms such as FastICA and JADE. The superior performance of the NpICA algorithm was especially evident in recordings with high signal length. This indicates that the NpICA method is more robust than other classical ICA algorithms for FECG extraction.

A general procedure for learning mixtures of independent component analyzers

This paper presents a new procedure for learning mixtures of independent component analyzers. The procedure includes non-parametric estimation of the source densities, supervised–unsupervised learning of the model parameters, incorporation of any independent component analysis (ICA) algorithm into the learning of the ICA mixtures, and estimation of residual dependencies after training for correction of the posterior probability of every class to the testing observation vector. We demonstrate the performance of the procedure in the classification of ICA mixtures of two, three, and four classes of synthetic data, and in the classification of defective materials, consisting of 3D finite element models and lab specimens, in non-destructive testing using the impact-echo technique. The application of the proposed posterior probability correction demonstrates an improvement in the classification accuracy. Semi-supervised learning shows that unlabeled data can degrade the performance of the classifier when they do not fit the generative model. Comparative results of the proposed method and standard ICA algorithms for blind source separation in one and multiple ICA data mixtures show the suitability of the non-parametric ICA mixture-based method for data modeling.

Nonparametric independent component analysis for detecting pressure fluctuation induced by roof corner vortex

The Nonparametric Independent Component Analysis (NICA) method is introduced to detect/infer the presence of roof corner vortex from experimentally measured wind pressure data. Different from the widely recognized Proper Orthogonal Decomposition (POD) method, which decomposes orthogonal pressure modes from the measurement, the NICA method is to separate the statistically independent pressure components/modes from the pressure data. Assuming that the measured wind pressures are caused by mixed wind flow phenomena, this paper attempts to decompose these independent flow induced pressure modes from the measured wind pressure data. Application of the NICA method to wind pressure data collected on the Texas Tech University (TTU) laboratory building justifies that the NICA method successfully separates/extracts from collected wind pressure data the pressure mode that is highly correlated with roof corner vortex. The corresponding time series coefficient of this mode is indicative of the presence of roof corner vortex.

Efficient Variant of Algorithm FastICA for Independent Component Analysis Attaining the CramÉr-Rao Lower Bound

FastICA is one of the most popular algorithms for independent component analysis (ICA), demixing a set of statistically independent sources that have been mixed linearly. A key question is how accurate the method is for finite data samples. We propose an improved version of the FastICA algorithm which is asymptotically efficient, i.e., its accuracy given by the residual error variance attains the Cramér-Rao lower bound (CRB). The error is thus as small as possible. This result is rigorously proven under the assumption that the probability distribution of the independent signal components belongs to the class of generalized Gaussian (GG) distributions with parameter alpha, denoted GG(alpha) for alpha > 2. We name the algorithm efficient FastICA (EFICA). Computational complexity of a Matlab implementation of the algorithm is shown to be only slightly (about three times) higher than that of the standard symmetric FastICA. Simulations corroborate these claims and show superior performance of the algorithm compared with algorithm JADE of Cardoso and Souloumiac and nonparametric ICA of Boscolo et al. on separating sources with distribution GG (alpha) with arbitrary alpha, as well as on sources with bimodal distribution, and a good performance in separating linearly mixed speech signals.