Nonlinear Independent Component Analysis Research Articles

Towards interpretable Cryo-EM: disentangling latent spaces of molecular conformations.

Molecules are essential building blocks of life and their different conformations (i.e., shapes) crucially determine the functional role that they play in living organisms. Cryogenic Electron Microscopy (cryo-EM) allows for acquisition of large image datasets of individual molecules. Recent advances in computational cryo-EM have made it possible to learn latent variable models of conformation landscapes. However, interpreting these latent spaces remains a challenge as their individual dimensions are often arbitrary. The key message of our work is that this interpretation challenge can be viewed as an Independent Component Analysis (ICA) problem where we seek models that have the property of identifiability. That means, they have an essentially unique solution, representing a conformational latent space that separates the different degrees of freedom a molecule is equipped with in nature. Thus, we aim to advance the computational field of cryo-EM beyond visualizations as we connect it with the theoretical framework of (nonlinear) ICA and discuss the need for identifiable models, improved metrics, and benchmarks. Moving forward, we propose future directions for enhancing the disentanglement of latent spaces in cryo-EM, refining evaluation metrics and exploring techniques that leverage physics-based decoders of biomolecular systems. Moreover, we discuss how future technological developments in time-resolved single particle imaging may enable the application of nonlinear ICA models that can discover the true conformation changes of molecules in nature. The pursuit of interpretable conformational latent spaces will empower researchers to unravel complex biological processes and facilitate targeted interventions. This has significant implications for drug discovery and structural biology more broadly. More generally, latent variable models are deployed widely across many scientific disciplines. Thus, the argument we present in this work has much broader applications in AI for science if we want to move from impressive nonlinear neural network models to mathematically grounded methods that can help us learn something new about nature.

Unsupervised representation learning of spontaneous MEG data with nonlinear ICA

Resting-state magnetoencephalography (MEG) data show complex but structured spatiotemporal patterns. However, the neurophysiological basis of these signal patterns is not fully known and the underlying signal sources are mixed in MEG measurements. Here, we developed a method based on the nonlinear independent component analysis (ICA), a generative model trainable with unsupervised learning, to learn representations from resting-state MEG data. After being trained with a large dataset from the Cam-CAN repository, the model has learned to represent and generate patterns of spontaneous cortical activity using latent nonlinear components, which reflects principal cortical patterns with specific spectral modes. When applied to the downstream classification task of audio-visual MEG, the nonlinear ICA model achieves competitive performance with deep neural networks despite limited access to labels. We further validate the generalizability of the model across different datasets by applying it to an independent neurofeedback dataset for decoding the subject's attentional states, providing a real-time feature extraction and decoding mindfulness and thought-inducing tasks with an accuracy of around 70% at the individual level, which is much higher than obtained by linear ICA or other baseline methods. Our results demonstrate that nonlinear ICA is a valuable addition to existing tools, particularly suited for unsupervised representation learning of spontaneous MEG activity which can then be applied to specific goals or tasks when labelled data are scarce.

Nonlinear independent component analysis for discrete-time and continuous-time signals

We study the classical problem of recovering a multidimensional source signal from observations of nonlinear mixtures of this signal. We show that this recovery is possible (up to a permutation and monotone scaling of the source’s original component signals) if the mixture is due to a sufficiently differentiable and invertible but otherwise arbitrarily nonlinear function and the component signals of the source are statistically independent with ‘nondegenerate’ second-order statistics. The latter assumption requires the source signal to meet one of three regularity conditions which essentially ensure that the source is sufficiently far away from the nonrecoverable extremes of being deterministic or constant in time. These assumptions, which cover many popular time series models and stochastic processes, allow us to reformulate the initial problem of nonlinear blind source separation as a simple-to-state problem of optimisation-based function approximation. We propose to solve this approximation problem by minimizing a novel type of objective function that efficiently quantifies the mutual statistical dependence between multiple stochastic processes via cumulant-like statistics. This yields a scalable and direct new method for nonlinear Independent Component Analysis with widely applicable theoretical guarantees and for which our experiments indicate good performance.

A review of disentangled representation learning for visual data processing and analysis

表示学习是机器学习研究的核心问题之一。机器学习算法的输入表征从过去主流的手工特征过渡到现在面向多媒体数据的潜在表示，使算法性能获得了巨大提升。然而，视觉数据的表示通常是高度耦合的，即输入数据的所有信息成分被编码进同一个特征空间，从而互相影响且难以区分，使得表示的可解释性不高。解耦表示学习旨在学习一种低维的可解释性抽象表示，可以识别并分离出隐藏在高维观测数据中的不同潜在变化因素。通过解耦表示学习，可以捕获到单个变化因素信息并通过相对应的潜在子空间进行控制，因此解耦表示更具有可解释性。解耦表征可用于提高样本效率和对无关干扰因素的容忍度，为数据中的复杂变化提供一种鲁棒性表示，提取的语义信息对识别分类、域适应等人工智能下游任务具有重要意义。本文首先介绍并分析解耦表示的研究现状及其因果机制，总结解耦表示的3个重要性质。然后，将解耦表示学习算法分为4类，并从数学描述、类型特点及适用范围3个方面进行归纳及对比。随后，分类总结了现有解耦表示工作中常用的损失函数、数据集及客观评估指标。最后，总结了解耦表示学习在实际问题中的各类应用，并对其未来发展进行了探讨。;Representation learning is essential for machine learning technique nowadays. The transition of input representations have been developing intensively in algorithm performance benefited from the growth of hand-crafted features to the representation for multi-media data. However，the representations of visual data are often highly entangled. The interpretation challenges are to be faced because all information components are encoded into the same feature space. Disentangled representation learning（DRL）aims to learn a low-dimensional interpretable abstract representation that can sort the multiple factors of variation out in high-dimensional observations. In the disentangled representation，we can capture and manipulate the information of a single factor of variation through the corresponding latent subspace，which makes it more interpretable. DRL can improve sample efficiency and tolerance to the nuisance variables and offer robust representation of complex variations. Their semantic information is extracted and beneficial for artificial intelligence（AI）downstream tasks like recognition，classification and domain adaptation. Our summary is focused on brief introduction to the definition， research development and applications of DRL. Some of independent component analysis（ICA）-nonlinear DRL researches are covered as well since the DRL is similar to the identifiability issue of nonlinear independent component analysis（nonlinear ICA）. The cause and effects mechanism of DRL as high-dimensional ground truth data is generated by a set of unobserved changing factors（generating factors）. The DRL can be used to model the factors of variation in terms of latent representation，and the observed data generation process is restored. We summarize the key elements that a well-defined disentangled representation should be qualified into three aspects，which are 1）modularity，2）compactness，and 3）explicitness. First，explicitness consists of the two sub-requirements of completeness and informativeness. Then，current DRL types are categorized into 1）dimension-wise disentanglement，2）semantic-based disentanglement，3）hierarchical disentanglement，and 4） nonlinear ICA four types in terms of its formulation，characteristics，and scope of application. Dimension-wise disentanglement is assumed that the generative factors are solely and each dimension of latent vector can be separated and mapped，which is suitable for learning the disentangled representation of simple synthetic visual data. Semantic-based disentanglement is hypnotized that some semantic information is solely as well. The generative factors are group-disentangled in terms of specific semantics and they are mapped to different latent spaces，which is suitable for complicated ground truth data. Hierarchical disentanglement is based on the assumption that there is a correlation between generative factors at different levels of abstraction. The generative factors are disentangled by group from the bottom up and they can be mapped to latent space of different semantic abstraction levels to form a hierarchical disentangled representation. Nonlinear ICA provides an identifiable method for observed data-mixed disentangling unknown generative factors through a nonlinear reversible generator. For the motivation of loss functions，the loss functions can be commonly used in disentangled representation learning，which are grouped into three categories：1）modularity constraint：a single latent variable-constrained in the disentangled representation to capture only a single or a single group of factors of variation，and it promotes the separation of factors of variation mutually；2）explicitness constraint：current latent variable of the latent representation is activated to encode the ground truth of the corresponding generating factor effectively，and the entire latent representation contains complete information about all generative factors；and 3）multi-purpose constraint：lossrelated can optimize multiple disentangled representation，including modularity，compactness，and explicitness of the disentangled representation at the same time. The model-relevant can combine multiple loss constraint terms to form the final hybrid objective function. We compare the scope of application and limitations of each type of loss functions and summarize the classical disentangled representation works using the hybrid objective function further.

Measure Transportation and Statistical Decision Theory

Unlike the real line, the real space, in dimension d ≥ 2, is not canonically ordered. As a consequence, extending to a multivariate context fundamental univariate statistical tools such as quantiles, signs, and ranks is anything but obvious. Tentative definitions have been proposed in the literature but do not enjoy the basic properties (e.g., distribution-freeness of ranks, their independence with respect to the order statistic, their independence with respect to signs) they are expected to satisfy. Based on measure transportation ideas, new concepts of distribution and quantile functions, ranks, and signs have been proposed recently that, unlike previous attempts, do satisfy these properties. These ranks, signs, and quantiles have been used, quite successfully, in several inference problems and have triggered, in a short span of time, a number of applications: fully distribution-free testing for multiple-output regression, MANOVA, and VAR models; R-estimation for VARMA parameters; distribution-free testing for vector independence; multiple-output quantile regression; nonlinear independent component analysis; and so on.

Enhancing Linear Independent Component Analysis: Comparison of Various Metaheuristic Methods

Various methods have been exploited in the blind source separation problems, especially in cocktail party problems. The most commonly used method is the independent component analysis (ICA). Many linear and nonlinear ICA methods, such as the radial basis functions (RBF) and self-organizing map (SOM) methods utilise neural networks and genetic algorithms as optimisation methods. For the contrast function, most of the traditional methods, especially the neural networks, use the gradient descent as an objective function for the ICA method. Most of these methods trap in local minima and consume numerous computation requirements. Three metaheuristic optimisation methods, namely particle, quantum particle, and glowworm swarm optimisation methods are introduced in this study to enhance the existing ICA methods. The proposed methods exhibit better results in separation than those in the traditional methods according to the following separation quality measurements: signal-to-noise ratio, signal-to-interference ratio, log-likelihood ratio, perceptual evaluation speech quality and computation time. These methods effectively achieved an independent identical distribution condition when the sampling frequency of the signals is 8 kHz.

Neural Networks Principal Component Analysis for estimating the generative multifactor model of returns under a statistical approach to the Arbitrage Pricing Theory. Evidence from the Mexican Stock Exchange

A nonlinear principal component analysis (NLPCA) represents an extension of the standard principal component analysis (PCA) that overcomes the limitation of the PCA’s assumption about the linearity of the model. The NLPCA belongs to the family of nonlinear versions of dimension reduction or the extraction techniques of underlying features, including nonlinear factor analysis and nonlinear independent component analysis, where the principal components are generalized from straight lines to curves. The NLPCA can be achieved via an artificial neural network specification where the PCA classic model is generalized to a nonlinear mode, namely, Neural Networks Principal Component Analysis (NNPCA). In order to extract a set of nonlinear underlying systematic risk factors, we estimate the generative multifactor model of returns in a statistical version of the Arbitrage Pricing Theory (APT), in the context of the Mexican Stock Exchange. We used an auto-associative multilayer perceptron neural network or autoencoder, where the ‘bottleneck’ layer represented the nonlinear principal components, or in our context, the scores of the underlying factors of systematic risk. This neural network represents a powerful technique capable of performing a nonlinear transformation of the observed variables into the nonlinear principal components, and to execute a nonlinear mapping that reproduces the original variables. We propose a network architecture capable of generating a loading matrix that enables us to make a first approach to the interpretation of the extracted latent risk factors. In addition, we used a two stage methodology for the econometric contrast of the APT involving first, a simultaneous estimation of the system of equations via Seemingly Unrelated Regression (SUR), and secondly, a cross-section estimation via Ordinary Least Squared corrected by heteroskedasticity and autocorrelation by means of the Newey-West heteroskedasticity and autocorrelation consistent covariances estimates (HEC). The evidence found shows that the reproductions of the observed returns using the estimated components via NNPCA are suitable in almost all cases; nevertheless, the results in an econometric contrast lead us to a partial acceptance of the APT in the samples and periods studied.

Nonlinear Blind Source Separation and Fault Feature Extraction Method for Mining Machine Diagnosis

Mining machines are strongly nonlinear systems, and their transmission vibration signals are nonlinear mixtures of different kinds of vibration sources. In addition, vibration signals measured by the accelerometer are contaminated by noise. As a result, it is inefficient and ineffective for the blind source separation (BSS) algorithm to separate the critical independent sources associated with the transmission fault vibrations. For this reason, a new method based on wavelet de-noising and nonlinear independent component analysis (ICA) is presented in this paper to tackle the nonlinear BSS problem with additive noise. The wavelet de-noising approach was first employed to eliminate the influence of the additive noise in the BSS procedure. Then, the radial basis function (RBF) neural network combined with the linear ICA was applied to the de-noised vibration signals. Vibration sources involved with the machine faults were separated. Subsequently, wavelet package decomposition (WPD) was used to extract distinct fault features from the source signals. Lastly, an RBF classifier was used to recognize the fault patterns. Field data acquired from a mining machine was used to evaluate and validate the proposed diagnostic method. The experimental analysis results show that critical fault vibration source component can be separated by the proposed method, and the fault detection rate is superior to the linear ICA based approaches.

3D reconstruction of cracks propagation in mechanical workpieces analyzing non-stationary acoustic mixtures

Abstract Cracks are one of the main causes of solid bodies weakening and are a hidden threat for mechanical systems. Acoustic emission is an indicator of cracks initiation and propagation and is widely exploited for the localization of cracks in non- or weakly-transparent environments. The present study enriches the functionality of multiple existing algorithms in crack localization using acoustics. The novelty is in the reconstruction of the complex geometry of the crack path and tracking its propagation in time, whereas existing methods focus only on the localization of the crack without any information about its geometry. The algorithm uses sparse acoustic signal representations as relative energies of the narrow frequency bands, extracted with the M-band wavelet transform. Non-linear independent component analysis is applied to de-mix the recorded acoustic signals into a number of separate acoustic patterns. Furthermore, a triangulation, using the time delay arrivals, is applied for each of such patterns separately, thus extracting multiple individual emittance sources. The algorithm was tested using synthetic data that replayed various scenarios of crack propagation together with different detector arrays configurations and its behavior was analyzed. Additional verification with real-time data was carried out by analyzing signals from crack propagation in glass along a known programmed path. The acoustic data was recorded with four fiber Bragg gratings. In both cases, the algorithmic framework showed a high efficiency in recovering the geometrical configuration of the crack.

Non-linear ICA Analysis of Resting-State fMRI in Mild Cognitive Impairment

Compared to linear independent component analysis (ICA), non-linear ICA is more suitable for the decomposition of mixed components. Existing studies of functional magnetic resonance imaging (fMRI) data by using linear ICA assume that the brain's mixed signals, which are caused by the activity of brain, are formed through the linear combination of source signals. But the application of the non-linear combination of source signals is more suitable for the mixed signals of brain. For this reason, we investigated statistical differences in resting state networks (RSNs) on 32 healthy controls (HC) and 38 mild cognitive impairment (MCI) patients using post-nonlinear ICA. Post-nonlinear ICA is one of the non-linear ICA methods. Firstly, the fMRI data of all subjects was preprocessed. The second step was to extract independent components (ICs) of fMRI data of all subjects. In the third step, we calculated the correlation coefficient between ICs and RSN templates, and selected ICs of the largest spatial correlation coefficient. The ICs represent the corresponding RSNs. After finding out the eight RSNs of MCI group and HC group, one sample t-tests were performed. Finally, in order to compare the differences of RSNs between MCI and HC groups, the two-sample t-tests were carried out. We found that the functional connectivity (FC) of RSNs in MCI patients was abnormal. Compared with HC, MCI patients showed the increased and decreased FC in default mode network (DMN), central executive network (CEN), dorsal attention network (DAN), somato-motor network (SMN), visual network(VN), MCI patients displayed the specifically decreased FC in auditory network (AN), self-referential network (SRN). The FC of core network (CN) did not reveal significant group difference. The results indicate that the abnormal FC in RSNs is selective in MCI patients.

Deep Independence Network Analysis of Structural Brain Imaging: Application to Schizophrenia.

Linear independent component analysis (ICA) is a standard signal processing technique that has been extensively used on neuroimaging data to detect brain networks with coherent brain activity (functional MRI) or covarying structural patterns (structural MRI). However, its formulation assumes that the measured brain signals are generated by a linear mixture of the underlying brain networks and this assumption limits its ability to detect the inherent nonlinear nature of brain interactions. In this paper, we introduce nonlinear independent component estimation (NICE) to structural MRI data to detect abnormal patterns of gray matter concentration in schizophrenia patients. For this biomedical application, we further addressed the issue of model regularization of nonlinear ICA by performing dimensionality reduction prior to NICE, together with an appropriate control of the complexity of the model and the usage of a proper approximation of the probability distribution functions of the estimated components. We show that our results are consistent with previous findings in the literature, but we also demonstrate that the incorporation of nonlinear associations in the data enables the detection of spatial patterns that are not identified by linear ICA. Specifically, we show networks including basal ganglia, cerebellum and thalamus that show significant differences in patients versus controls, some of which show distinct nonlinear patterns.

Performance evaluation of analog circuit using improved LSSVR subject to data information uncertainty

This paper demystifies the proposed analog circuit performance evaluation methods based on improved LSSVR (ILSSVR) by examining the arithmetic speed and the evaluation reliability online. The ILSSVR performance evaluation scheme has the robustness for the signal information uncertainty, which may be deduced by nonlinear feature, time varying feature and contain faults value about industrial field data information. More specially, the self-update via incremental and reduced interaction is employed to detect the interests both on history data information and the updated data information, and the features extraction nonlinear independent component analysis (NICA) is proposed, then the number of the feature data is controlled and desired time consumed is guaranteed. In addition, the multi-kernel and weighted idea have also been employed to interfuse quite flexibility to the bandwidths of kernel online. The proposed analog circuit performance evaluation scheme ILSSVR is evaluated for two filter circuit: leapfrog filter circuit and self-adapting filter circuit. And the effectiveness is illustrated through a numerical example.

Improvement of BCI Performance Through Nonlinear Independent Component Analysis Extraction

Electroencephalogram (EEG) recordings provide an important means of brain-computer communication, but their classification accuracy and transfer rate are limited by unexpected signal variations due to artifacts and noises. In this paper, a nonlinear independent component analysis (NICA) extraction method for brain signal based EEG-P300 are proposed. The performance of the proposed method is investigated through a comparison of well known extraction methods (i.e., AAR, JADE, and SOBI algorithms). Finally, the promising results reported here reflect the considerable potential of EEG for the continuous classification of mental states.

Design of Smart Ion-Selective Electrode Arrays Based on Source Separation through Nonlinear Independent Component Analysis

The development of chemical sensor arrays based on Blind Source Separation (BSS) provides a promising solution to overcome the interference problem associated with Ion-Selective Electrodes (ISE). The main motivation behind this new approach is to ease the time-demanding calibration stage. While the first works on this problem only considered the case in which the ions under analysis have equal valences, the present work aims at developing a BSS technique that works when the ions have different charges. In this situation, the resulting mixing model belongs to a particular class of nonlinear systems that have never been studied in the BSS literature. In order to tackle this sort of mixing process, we adopted a recurrent network as separating system. Moreover, concerning the BSS learning strategy, we develop a mutual information minimization approach based on the notion of the differential of the mutual information. The method works requires a batch operation, and, thus, can be used to perform off-line analysis. The validity of our approach is supported by experiments where the mixing model parameters were extracted from actual data.

Hybridizing nonlinear independent component analysis and support vector regression with particle swarm optimization for stock index forecasting

One of the major activities of financial firms and private investors is to predict future prices of stocks. However, stock index prediction is regarded as a challenging task of the prediction problem since the stock market is a complex, chaotic and nonlinear dynamic system. As stock markets are highly dynamic and exhibit wide variation, it may be more realistic and practical that assumed the stock index data are a nonlinear mixture data. In this study, a hybrid stock index prediction model by utilizing nonlinear independent component analysis (NLICA), support vector regression (SVR) and particle swarm optimization (PSO) is proposed. In the proposed model, first, the NLICA is used to deal with the nonlinearity property of the stock index data. The proposed model utilizes NLICA to extract features from the observed stock index data. The features which can be used to represent underlying/hidden information of the data are then served as the inputs of SVR to build the stock index prediction model. Finally, PSO is applied to optimize the parameters of the SVR prediction model since the parameters of SVR must be carefully selected in establishing an effective and efficient SVR model. In order to evaluate the performance of the proposed approach, the closing indexes of the Taiwan stock exchange capitalization weighted stock index, Shanghai stock exchange composite index and Bombay stock exchange index are used as illustrative examples. Experimental results showed that the proposed hybrid stock index prediction method significantly outperforms the other six comparison models. It is an efficient and effective alternative for stock index forecasting.

Integration of nonlinear independent component analysis and support vector regression for stock price forecasting

Forecasting stock prices is a major activity of financial firms and private investors. In developing a stock price forecasting model, the first step is usually feature extraction. Nonlinear independent component analysis (NLICA), a novel feature extraction technique that assumes the observed mixtures are non-linear combinations of latent source signals, is used to find independent sources when observed data are mixtures of unknown sources, and prior knowledge of the mixing mechanisms is not available. In this paper, a stock price forecasting model which first uses NLICA as preprocessing to extract features from forecasting variables is developed. Then the features, called independent components (ICs), serve as the inputs of support vector regression (SVR) to build the forecasting model. The advantage of the proposed methodology is that the information hidden in the original data can be discovered by feature extraction. Therefore, NLICA can provide more valuable information for financial forecasting. Two datasets of major Asian stock markets—China and Japan, Shanghai Stock Exchange Composite (SSEC) and Nikkei 225 stock indexes, are used as illustrative examples. For comparison, the integration of traditional principal component analysis (PCA) with SVR (called PCA–SVR), linear ICA with SVR (called LICA–SVR) and single SVR approaches were applied to evaluate the prediction accuracy of the proposed approach. Empirical results show that the proposed method (NLICA–SVR) not only improves the prediction accuracy of the SVR approach but also outperforms the PCA–SVR, LICA–SVR and single SVR methods.

Parametrization of Linear Systems Using Diffusion Kernels

Modeling natural and artificial systems has played a key role in various applications and has long been a task that has drawn enormous efforts. In this work, instead of exploring predefined models, we aim to identify implicitly the system degrees of freedom. This approach circumvents the dependency of a specific predefined model for a specific task or system and enables a generic data-driven method to characterize a system based solely on its output observations. We claim that each system can be viewed as a black box controlled by several independent parameters. Moreover, we assume that the perceptual characterization of the system output is determined by these independent parameters. Consequently, by recovering the independent controlling parameters, we find in fact a generic model for the system. In this work, we propose a supervised algorithm to recover the controlling parameters of natural and artificial linear systems. The proposed algorithm relies on nonlinear independent component analysis using diffusion kernels and spectral analysis. Employment of the proposed algorithm on both synthetic and practical examples has shown accurate recovery of parameters.

Crack damage recognition of a reinforced concrete beam using acoustic emission and non-linear independent component analysis

Crack damage recognition of a reinforced concrete beam using acoustic emission and non-linear independent component analysis

Automatic motion compensation of free breathing acquired myocardial perfusion data by using independent component analysis

Images acquired during free breathing using first-pass gadolinium-enhanced myocardial perfusion magnetic resonance imaging (MRI) exhibit a quasiperiodic motion pattern that needs to be compensated for if a further automatic analysis of the perfusion is to be executed. In this work, we present a method to compensate this movement by combining independent component analysis (ICA) and image registration: First, we use ICA and a time-frequency analysis to identify the motion and separate it from the intensity change induced by the contrast agent. Then, synthetic reference images are created by recombining all the independent components but the one related to the motion. Therefore, the resulting image series does not exhibit motion and its images have intensities similar to those of their original counterparts. Motion compensation is then achieved by using a multi-pass image registration procedure. We tested our method on 39 image series acquired from 13 patients, covering the basal, mid and apical areas of the left heart ventricle and consisting of 58 perfusion images each. We validated our method by comparing manually tracked intensity profiles of the myocardial sections to automatically generated ones before and after registration of 13 patient data sets (39 distinct slices). We compared linear, non-linear, and combined ICA based registration approaches and previously published motion compensation schemes. Considering run-time and accuracy, a two-step ICA based motion compensation scheme that first optimizes a translation and then for non-linear transformation performed best and achieves registration of the whole series in 32±12s on a recent workstation. The proposed scheme improves the Pearsons correlation coefficient between manually and automatically obtained time-intensity curves from .84±.19 before registration to .96±.06 after registration.

Vibration Signal Processing for Gear Fault Diagnosis Based on Empirical Mode Decomposition and Nonlinear Blind Source Separation

Gear failures happen frequently in the gear mechanisms, and an unexpected serious gear fault may cause severe damage on the machinery. Hence, precise gear fault detection at the early stage is imperative to ensure the normal operation of the machinery. Independent component analysis (ICA) has been paid more and more attention for its powerful ability of separating the useful vibration source from the multi-sensor observations to enhance the fault feature extraction. This is the so called blind source separation (BSS) procedure. However, the popular ICA model may suffer from two limitations. One is the linear mixture assumption, and the other is the lack of sensor channels. Up to now, only limited research considered the nonlinear ICA model in the field of mechanic fault diagnosis, and techniques for the situation where the number of sensor channels is less than the number of independent sources for gear defect detection are scarce. In order to extract the useful source involved with the gear fault characteristics in single-channel vibration signal processing, this work presents a new method based on the empirical mode decomposition (EMD) and nonlinear ICA. The EMD was firstly employed to decompose the vibration signal into a number of intrinsic mode functions (IMFs), and then these IMFs were taken as the multi-channel observations. The post-nonlinear (PNL) ICA model based on the radial basis function (RBF) neural network was applied to the nonlinear BSS procedure on the IMFs. The experimental vibration data acquired from the gear fault test-bed were processed for the validation of the proposed method. The nonlinear ICA method has been compared with the linear ICA and non-ICA based approaches. The analysis results show that the sensitive characteristics of the gear meshing vibration can be separated from the single channel measurement by the proposed method, and the fault diagnosis precision can be enhanced significantly. The detection rate can be increased by 3.75% or better when the ICA based preprocessing is carried out, and the proposed nonlinear ICA outperforms the linear ICA detection model.