An Extension to the Natural Gradient Algorithm for Robust Independent Component Analysis in the Presence of Outliers

2006 ◽  
Vol E89-A (9) ◽  
pp. 2429-2432
Author(s):  
M. TUFAIL
Keyword(s):  
Independent Component Analysis ◽  
Component Analysis ◽  
Independent Component ◽  
Gradient Algorithm ◽  
Natural Gradient

An ICA Algorithm Based on Symmetric and Asymmetric Generalized Gaussian Model

2011 ◽  
Vol 204-210 ◽  
pp. 470-475
Author(s):  
Feng Zhao ◽  
Yun Jie Zhang ◽  
Min Cai
Keyword(s):  
Independent Component Analysis ◽  
Gradient Method ◽  
Gaussian Model ◽  
Component Analysis ◽  
Independent Component ◽  
Blind Signal Separation ◽  
Natural Gradient ◽  
Analysis Model ◽  
Practical Applications ◽  
Source Signal

Maximum likelihood estimation is a very popular method to estimate the independent component analysis model because of good performance. Independent component analysis algorithm (the natural gradient method) based on this method is widely used in the field of blind signal separation. It potentially assumes that the source signal was symmetrical distribution, in fact in practical applications, source signals may be asymmetric. This article by distinguishing that the source signal is symmetrical or asymmetrical, proposes an improved natural gradient method based on symmetric generalized Gaussian model (People usually call generalized Gaussian model) and asymmetric generalized Gaussian model. The random mixed-signal simulation results show that the improved algorithm is better than the natural gradient separation method.

scholarly journals Blind Separation of Positive Sources by Globally Convergent Gradient Search

2004 ◽  
Vol 16 (9) ◽  
pp. 1811-1825 ◽  
Author(s):  
Erkki Oja ◽  
Mark Plumbley
Keyword(s):  
Independent Component Analysis ◽  
Cost Function ◽  
Gradient Flow ◽  
Component Analysis ◽  
Independent Component ◽  
Gradient Algorithm ◽  
Stiefel Manifold ◽  
Blind Separation ◽  
Solution Methods ◽  
Simplified Solution

The instantaneous noise-free linear mixing model in independent component analysis is largely a solved problem under the usual assumption of independent nongaussian sources and full column rank mixing matrix. However, with some prior information on the sources, like positivity, new analysis and perhaps simplified solution methods may yet become possible. In this letter, we consider the task of independent component analysis when the independent sources are known to be nonnegative and well grounded, which means that they have a nonzero pdf in the region of zero. It can be shown that in this case, the solution method is basically very simple: an orthogonal rotation of the whitened observation vector into nonnegative outputs will give a positive permutation of the original sources. We propose a cost function whose minimum coincides with nonnegativity and derive the gradient algorithm under the whitening constraint, under which the separating matrix is orthogonal. We further prove that in the Stiefel manifold of orthogonal matrices, the cost function is a Lyapunov function for the matrix gradient flow, implying global convergence. Thus, this algorithm is guaranteed to find the nonnegative well-grounded independent sources. The analysis is complemented by a numerical simulation, which illustrates the algorithm.

scholarly journals Tansformasi Lontar Babad Lombok Menuju Digitalisasi Berbasis Natural Gradient Flexible (NGF)

2021 ◽  
Vol 8 (2) ◽  
pp. 275
Author(s):  
Muhammad Tajuddin Anwar ◽  
Syahroni Hidayat ◽  
Ahmat Adil
Keyword(s):  
Independent Component Analysis ◽  
Component Analysis ◽  
Independent Component ◽  
Visual Perspective ◽  
Natural Gradient ◽  
Main Challenge ◽  
Highly Correlated ◽  
Ica Algorithm ◽  
Lombok Island

<p class="Abstrak">Suku Sasak, yang tinggal di pulau Lombok Nusa Tenggara Barat, memiliki tradisi penulisan di daun lontar (<em>Borassus </em><em>Flabellifer</em>) kering, salah satunya adalah naskah Lontar Babad Lombok. Naskah Lontar Babad Lombok seiring berlalunya waktu, menjadi rapuh dan mudah patah sehingga memerlukan perawatan. Keadaan ini mendorongnya perlu dilakukan digitalisasi naskah lontar babad lombok sebagai bentuk pelestarian sehingga para generasi Milenial, khususnya di Lombok, dapat menikmati lontar babad lombok. Digitalisasi citra tersebut tantangan utama adalah tepi kabur teks dan perbedaan minimum antara teks dan bagian non-tekssebagai akibat dari proses perawatan. Oleh karena itu, dibutuhkan proses peningkatan kualitas citra hasil digitalisasi agar tulisan dapat lebih jelas terbaca. Salah satu metode yang terbukti mampu untuk memisahkan teks dari latar belakang yang sangat berkorelasi adalah <em>Natural Gradient Flexibel</em> (NGF) berbasiskan <em>Independent Component Analysis</em> (ICA), NGF-ICA. Penelitian ini bertujuan untuk melakukan peningkatan kualitas citra digitalisasi sebelum diumpankan pada database dan sistem informasi yang telah dibangun. Kualitas citra yang telah ditingkatkan diukur menggunakan metode MSE dan PSNR untuk tingkat kemiripannya, dan metode Entropi dan SSIM untuk informasi dan perspektif visual. Hasil penelitian menunjukkan bahwa penerapan algoritma NGF-ICA dapat memberikan citra keluaran dengan kualitas yang tinggi dengan nilai rata-rata MSE, PSNR, SSIM dan peningkatan Entropi sebesar 708, 19.95 db, 0.87 dan 0.45, secara berturut-turut.</p><p class="Abstrak"> </p><p><strong><em>Abstract</em></strong></p><p class="Abstract">Sasak tribe, who lives on Lombok Island, West Nusa Tenggara, has been writing manuscripts on dry palm leaves (Borassus Flabellifer) as a tradition, one of the manuscripts is Lontar Babad Lombok. As time pass by, the manuscript becomes brittle and breaks easily, therefore maintenances are required. this situation force the need to digitalize the manuscript as an act of preservation, hence the millennial generation, especially on Lombok Island, can enjoy the manuscript. the main challenge is the blurry edge of the text and the slight difference between the text and non-text part caused by the treatment process. Hence, it is needed to enhance the quality of the digitalize image to make the manuscript can be more clearly read. One of the proven methods that able to separate text from highly correlated backgrounds is Natural Gradient Flexibel (NGF) based on Independent Component Analysis (ICA), NGF-ICA. The aim of this study is to improve the quality of the digitized images before they fed into the database and information system that has been built. The enhanced image quality was measured, MSE and PSNR methods were used to measure the similarity level, and the Entropy and SSIM method were used to measure the information and visual perspective. The results show that the application of the NGF-ICA algorithm can generate high-quality output images with average values of MSE, PSNR, SSIM, and increasing Entropy by 708, 19.95 dB, 0.87, and 0.45, respectively.</p><p><strong><em><br /></em></strong></p>

Natural Gradient Learning for Over- and Under-Complete Bases in ICA

1999 ◽  
Vol 11 (8) ◽  
pp. 1875-1883 ◽  
Author(s):  
Shun-ichi Amari
Keyword(s):  
Independent Component Analysis ◽  
Blind Source Separation ◽  
Learning Algorithm ◽  
Component Analysis ◽  
Independent Component ◽  
New Technique ◽  
Natural Gradient ◽  
Stiefel Manifolds ◽  
A New Technique ◽  
Gradient Learning

Independent component analysis or blind source separation is a new technique of extracting independent signals from mixtures. It is applicable even when the number of independent sources is unknown and is larger or smaller than the number of observed mixture signals. This article extends the natural gradient learning algorithm to be applicable to these overcomplete and undercomplete cases. Here, the observed signals are assumed to be whitened by preprocessing, so that we use the natural Riemannian gradient in Stiefel manifolds.

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