This paper addresses the problem of blind source separation and, presents a fixed-point nonlinear principal component analysis (NPCA) algorithm. It is a block-wise batch algorithm and gives an alternative perspective ...
详细信息
This paper addresses the problem of blind source separation and, presents a fixed-point nonlinear principal component analysis (NPCA) algorithm. It is a block-wise batch algorithm and gives an alternative perspective on existing adaptive online NPCA algorithms. Utilizing new activation functions that automatically satisfy a stability condition, the proposed algorithm can separate mixed signals with sub- and super-Gaussian source distributions. The efficiency is confirmed by extensive computer simulations on man-made sources as well as practical speech signals. (c) 2005 Elsevier B.V. All rights reserved.
This article presents and examines a new algorithm for solving a score equation for the maximum likelihood estimate in certain problems of practical interest. The method circumvents the need to compute second-order de...
详细信息
This article presents and examines a new algorithm for solving a score equation for the maximum likelihood estimate in certain problems of practical interest. The method circumvents the need to compute second-order derivatives of the full likelihood function. It exploits the structure of certain models that yield a natural decomposition of a very complicated likelihood function. In this decomposition, the first part is a log-likelihood from a simply analyzed model, and the second part is used to update estimates from the first part. Convergence properties of this iterative (fixed-point) algorithm are examined, and asymptotics are derived for estimators obtained using only a finite number of iterations. Illustrative examples considered in the article include multivariate Gaussian copula models, nonnormal random-effects models, generalized linear mixed models, and state-space models. Properties of the algorithm and of estimators are evaluated in simulation studies on a bivariate copula model and a nonnormal linear random-effects model.
Real-time functional magnetic resonance imaging fMRI) enables one to monitor a subject's brain activity during an ongoing session. The availability of online information about brain activity is essential for devel...
详细信息
Real-time functional magnetic resonance imaging fMRI) enables one to monitor a subject's brain activity during an ongoing session. The availability of online information about brain activity is essential for developing and refining interactive fMRI paradigms in research and clinical trials and for neurofeedback applications. Data analysis for real-time fMRI has traditionally been based on hypothesis-driven processing methods. Off-line data analysis, conversely, may be usefully complemented by data-driven approaches, such as independent component analysis (ICA), which can identify brain activity without a priori temporal assumptions on brain activity. However, ICA is commonly considered a time-consuming procedure and thus unsuitable to process the high flux of fMRI data while they are acquired. Here, by specific choices regarding the implementation, we exported the ICA framework and implemented it into real-time fMRI data analysis. We show that, reducing the ICA input to a few points within a time-series in a sliding-window approach, computational times become compatible with real-time settings. Our technique produced accurate dynamic readouts of brain activity as well as a precise spatiotemporal history of quasistationary patterns in the form of cumulative activation maps and time courses. Results from real and simulated motor activation data show comparable performances for the proposed ICA implementation and standard linear regression analysis applied either in a sliding-window or in a cumulative mode. Furthermore, we demonstrate the possibility of monitoring transient or unexpected neural activities and suggest that real-time ICA may provide the fMRI researcher with a better understanding and control of subjects' behaviors and performances. (C) 2003 Elsevier Inc. All rights reserved.
The goal of this letter is to shed new light on a wavelet-based denoising method developed by Hadjileontiadis et al, which is derived from an iterative denoising algorithm by Coifman and Wickerhauser. The underlying a...
详细信息
The goal of this letter is to shed new light on a wavelet-based denoising method developed by Hadjileontiadis et al, which is derived from an iterative denoising algorithm by Coifman and Wickerhauser. The underlying algorithm is revisited and interpreted as a fixed-point algorithm. This allows to derive a new version of the algorithm largely increasing computational efficiency.
Independent component analysis (ICA) has been successfully employed to decompose functional MRI (fMRI) time-series into sets of activation maps and associated time-courses. Several ICA algorithms have been proposed in...
详细信息
Independent component analysis (ICA) has been successfully employed to decompose functional MRI (fMRI) time-series into sets of activation maps and associated time-courses. Several ICA algorithms have been proposed in the neural network literature. Applied to fMRI, these algorithms might lead to different spatial or temporal readouts of brain activation. We compared the two ICA algorithms that have been used so far for spatial ICA (sICA) of fMRI time-series: the Infomax (Bell and Sejnowski [1995]: Neural Comput 7:1004-1034) and the fixed-point (Hyvarinen [1999]: Adv Neural Inf Proc Syst 10:273-279) algorithms. We evaluated the Infomax- and fixedpoint-based sICA decompositions of simulated motor, and real motor and visual activation fMRI time-series using an ensemble of measures. Log-likelihood (McKeown et al. [1998]: Hum Brain Mapp 6:160-188) was used as a measure of how significantly the estimated independent sources fit the statistical structure of the data;receiver operating characteristics (ROC) and linear correlation analyses were used to evaluate the algorithms' accuracy of estimating the spatial layout and the temporal dynamics of simulated and real activations;cluster sizing calculations and an estimation of a residual gaussian noise term within the components were used to examine the anatomic structure of ICA components and for the assessment of noise reduction capabilities. Whereas both algorithms produced highly accurate results, the fixed-point outperformed the Infomax in terms of spatial and temporal accuracy as long as inferential statistics were employed as benchmarks. Conversely, the Infomax sICA was superior in terms of global estimation of the ICA model and noise reduction capabilities. Because of its adaptive nature, the Infomax approach appears to be better suited to investigate activation phenomena that are not predictable or adequately modelled by inferential techniques. (C) 2002 Wiley-Liss, Inc.
Independent component analysis (ICA) has been shown as a promising tool for the analysis of functional magnetic resonance imaging (fMRI) time series. Each of these studies, however, used a general-purpose algorithm fo...
详细信息
Independent component analysis (ICA) has been shown as a promising tool for the analysis of functional magnetic resonance imaging (fMRI) time series. Each of these studies, however, used a general-purpose algorithm for performing ICA and the computational efficiency and accuracy of elicited neuronal activations have not been discussed in much detail. We have previously proposed a direct search method for improving computational efficiency. The method, which is based on independent component-cross correlation-sequential epoch (ICS) analysis, utilizes a form of the fixed-point ICA algorithm and considerably reduces the time required for extracting desired components. At the same time, it is shown that the accuracy of detecting physiologically meaningful components is much improved by tailoring the contrast function used in the algorithm. In this study, further improvement was made to this direct search method by integrating an optimal contrast function. Functional resolution of activation maps could be controlled with a suitable selection of the contrast function derived from prior knowledge of the spatial patterns of physiologically desired components. A simple skewness-weighted contrast function was verified to extract sufficiently precise activation maps from the fMRI time series acquired using a 3.0 Tesla MRI system. (C) 2001 Wiley-Liss, Inc.
The paper discusses an approach to comparative statics in the large by making use of a homotopy continuation method. This is based on the path-following approach presented by the author which is in turn due to the fix...
详细信息
The paper discusses an approach to comparative statics in the large by making use of a homotopy continuation method. This is based on the path-following approach presented by the author which is in turn due to the fixed-point algorithm explored by Garcia and Zangwill. We investigate from a global viewpoint the Hicksian laws of comparative statics for the Hicksian case which is a key to the first Hicksian law at least locally, and obtain the first Hicksian law in the large. Global results for the dominant diagonal case and the G1-Metzlerian case are also obtained.
This paper shows that the generalized Newton algorithm [GN(r)], developed by Kalaba and Tishler (Ref. 1), can be described as a fixed-point algorithm. In addition to specifying sufficient conditions for convergence of...
详细信息
This paper shows that the generalized Newton algorithm [GN(r)], developed by Kalaba and Tishler (Ref. 1), can be described as a fixed-point algorithm. In addition to specifying sufficient conditions for convergence of the GN(r), we show that, forr=1, 2, 3, its rate of convergence increases with the order of the derivatives which are used.
For certain functionsf fromR n toR n , the Eaves—Saigal algorithm computes a path inR n × (0, 1] which converges ...
详细信息
For certain functionsf fromR
n
toR
n
, the Eaves—Saigal algorithm computes a path inR
n
× (0, 1] which converges to a zero off. In this case, it is shown that even whenf is of classC
∞ and has a unique zero, the converging path may retrogress infinitely many times.
暂无评论