Robust Independent Component Analysis via Minimum Divergence Estimation

Independent component analysis (ICA) has been shown to be useful in many applications. However, most ICA methods are sensitive to data contamination and outliers. In this article we introduce a general minimum U-divergence framework for ICA, which covers some standard ICA methods as special cases. Within the U-family we further focus on the gamma-divergence due to its desirable property of super robustness, which gives the proposed method gamma-ICA. Statistical properties and technical conditions for the consistency of gamma-ICA are rigorously studied. In the limiting case, it leads to a necessary and sufficient condition for the consistency of MLE-ICA. This necessary and sufficient condition is weaker than the condition known in the literature. Since the parameter of interest in ICA is an orthogonal matrix, a geometrical algorithm based on gradient flows on special orthogonal group is introduced to implement gamma-ICA. Furthermore, a data-driven selection for the gamma value, which is critical to the achievement of gamma-ICA, is developed. The performance, especially the robustness, of gamma-ICA in comparison with standard ICA methods is demonstrated through experimental studies using simulated data and image data.Comment: 7 figure

New Negentropy Optimization Schemes for Blind Signal Extraction of Complex Valued Sources

Blind signal extraction, a hot issue in the field of communication signal processing, aims to retrieve the sources through the optimization of contrast functions. Many contrasts based on higher-order statistics such as kurtosis, usually behave sensitive to outliers. Thus, to achieve robust results, nonlinear functions are utilized as contrasts to approximate the negentropy criterion, which is also a classical metric for non-Gaussianity. However, existing methods generally have a high computational cost, hence leading us to address the problem of efficient optimization of contrast function. More precisely, we design a novel “reference-based” contrast function based on negentropy approximations, and then propose a new family of algorithms (Alg.1 and Alg.2) to maximize it. Simulations confirm the convergence of our method to a separating solution, which is also analyzed in theory. We also validate the theoretic complexity analysis that Alg.2 has a much lower computational cost than Alg.1 and existing optimization methods based on negentropy criterion. Finally, experiments for the separation of single sideband signals illustrate that our method has good prospects in real-world applications

Independent component analysis: algorithms and applications

A fundamental problem in neural network research, as well as in many other disciplines, is finding a suitable representation of multivariate data, i.e. random vectors. For reasons of computational and conceptual simplicity, the representation is often sought as a linear transformation of the original data. In other words, each component of the representation is a linear combination of the original variables. Well-known linear transformation methods include principal component analysis, factor analysis, and projection pursuit. Independent component analysis (ICA) is a recently developed method in which the goal is to find a linear representation of nongaussian data so that the components are statistically independent, or as independent as possible. Such a representation seems to capture the essential structure of the data in many applications, including feature extraction and signal separation. In this paper, we present the basic theory and applications of ICA, and our recent work on the subject

Improved Feature Extraction, Feature Selection, and Identification Techniques That Create a Fast Unsupervised Hyperspectral Target Detection Algorithm

This research extends the emerging field of hyperspectral image (HSI) target detectors that assume a global linear mixture model (LMM) of HSI and employ independent component analysis (ICA) to unmix HSI images. Via new techniques to fully automate feature extraction, feature selection, and target pixel identification, an autonomous global anomaly detector, AutoGAD, has been developed for potential employment in an operational environment for real-time processing of HSI targets. For dimensionality reduction (initial feature extraction prior to ICA), a geometric solution that effectively approximates the number of distinct spectral signals is presented. The solution is based on the theory of the shape of the eigenvalue curve of the covariance matrix of spectral data containing noise. For feature selection, previously a subjective definition called significant kurtosis change was used to denote the separation between targets classes and non-target classes. This research presents two new measures, potential target signal to noise ratio (PT SNR) and max pixel score which computed for each of the ICA features to create a new two dimensional feature space where the overlap between target and non-target classes is reduced compared to the one dimensional kurtosis value feature space. Finally, after target feature selection, adaptive noise filtering, but with an iterative approach, is applied to the signals. The effect is a reduction in the power of the noise while preserving the power of the target signal prior to target identification to reduce false positive detections. A zero-detection histogram method is applied to the smoothed signals to identify target locations to the user. MATLAB code for the AutoGAD algorithm is provided

Comparative Study of Performance of Particle Swarm Optimization and Fast Independent Component Analysis method in Cocktail Party Problem

هنالك الكثير من الطرق التي تستخدم لحل مشكلة فصل المصدر المحجوب، مثل طريقة تحليل المكونات المستقلة والتي اصبحت من اكثر الطرق استخداما. طريقة تحليل المكونات المستقلة تعتمد على واحدة من اثنتين من الخصائص: استقلالية العينة او non-Gaussianity. في هذا البحث استخدمت طريقة فصل المكونات المستقلة لحل مشكلة حفلة الكوكتيل. حيث تمت دراسة انجازية طريقتين: طريقة فصل المكونات السريعة وطريقة تحسين سرب الطيور ومقارنة النتائج بالاعتماد على بعض مقاييس الانجازية مثل (الموضوعي مثل  SNR و SDR (  و (ذاتي مثل single plotting  و playing ) . حيث طبقت الخوارزميتين على مصادر ذوي اشارتين وثلاث اشارات. وكنتيجة لعملية التقييم فأن خوازمية فصل المكونات السريعة اعطت نتائج اكثر دقة من خوارزمية تحسين سرب الطيور. حيث استخدمت اشارات للكلام بتردد 8 كيلو هرتز والتي حققت شروط كل من ال  i.i.d و well-condition والتي اختبرت على احاديث مختلفة لرجال ونساء وكذلك الموسيقى.     There are many methods used for solving the Blind Source Separation problem, such as Independent Component Analysis which became the most commonly used method. ICA methods depend on one of two properties: sample dependency or non-Gaussianity. In our study, the cocktail-party problem processed using ICA method. In this work, we studied the performance of two techniques with the independent component analysis is standard FastICA, and PSO; and compare the results of each algorithm with others according to some evaluation metrics (objective such as SNR and SDR ) and (subjective such as signals plotting and playing). The implement of these algorithms was to be made with two source signals and three source signals. As in the evaluation process, the PSO gives more accurate results than FastICA. Many input speech signals of 8 KHz sampling frequency, that achieve i.i.d. condition and well-condition were tested for different speeches for men and/or women, also music

Robust Independent Component Analysis viaMinimum γ-Divergence Estimation

Independent component analysis (ICA) has been shown to be useful in many applications. However, most ICA methods are sensitive to data contamination. In this article we introduce a general minimum U-divergence framework for ICA, which covers some standard ICA methods as special cases. Within the U-family we further focus on the γ-divergence due to its desirable property of super robustness for outliers, which gives the proposed method γ-ICA. Statistical properties and technical conditions for recovery consistency of γ-ICA are studied. In the limiting case, it improves the recovery condition of MLE-ICA known in the literature by giving necessary and sufficient condition. Since the parameter of interest in γ-ICA is an orthogonal matrix, a geometrical algorithm based on gradient flows on special orthogonal group is introduced. Furthermore, a data-driven selection for the γ value, which is critical to the achievement of γ-ICA, is developed. The performance, especially the robustness, of γ-ICA is demonstrated through experimental studies using simulated data and image data