Independent component analysis: Jacobi-like diagonalization of optimized composite-order cumulants

2009 ◽  
Vol 465 (2105) ◽  
pp. 1393-1411 ◽  
Author(s):  
Shafayat Abrar ◽  
Asoke Kumar Nandi
Keyword(s):  
Independent Component Analysis ◽  
Fourth Order ◽  
A Priori ◽  
Component Analysis ◽  
Independent Component ◽  
Simultaneous Diagonalization ◽  
Statistical Knowledge ◽  
Common Framework ◽  
Ica Algorithm ◽  
Number Of Authors

In the field of blind source separation, Jacobi-like diagonalization-based approaches constitute an important tool for independent component analysis (ICA). Recently, simultaneous diagonalization of cumulant matrices of third- and fourth-order has been studied by a number of authors. In this work, we present an optimal parametrized composition of these cumulants that puts two classical contrasts, namely, the cumulant-based ICA and the weighted fourth-order contrast in a common framework. It is shown that the optimal weight parameter depends on the a priori statistical knowledge of the original mixing sources. Following the same spirit of the ICA algorithm, we derive the analytical solution for the case of two sources. Finally, a number of computer simulations have been performed to illustrate the behaviour of the Jacobi-like iterations for the maximization of the proposed parametrized contrast.

Study of the synthesis mechanism of 4-amino-3,5-dimethyl pyrazole by fibre optic in-line FT-IR spectroscopy combined with independent component analysis

2014 ◽  
Vol 6 (12) ◽  
pp. 4305-4311 ◽  
Author(s):  
Jiguang Li ◽  
Jun Gao ◽  
Hua Li ◽  
Xiaofeng Yang ◽  
Yu Liu
Keyword(s):  
Ir Spectroscopy ◽  
Independent Component Analysis ◽  
Component Analysis ◽  
Independent Component ◽  
Fibre Optic ◽  
Synthesis Mechanism ◽  
Ft Ir ◽  
Ica Algorithm ◽  
Ft Ir Spectroscopy

The synthesis mechanism of 4-amino-3,5-dimethyl pyrazole was investigated using in-line FT-IR spectroscopy combined with a Fast-ICA algorithm.

scholarly journals Orthogonal Approach to Independent Component Analysis Using Quaternionic Factorization

2020 ◽  
Author(s):  
Adam Borowicz
Keyword(s):  
Independent Component Analysis ◽  
Additive Noise ◽  
Component Analysis ◽  
Independent Component ◽  
Actual Distribution ◽  
Rotation Matrices ◽  
Fastica Algorithm ◽  
Non Gaussian ◽  
Ica Algorithm ◽  
Source Signals

Abstract Independent component analysis (ICA) is a popular technique for demixing multi-channel data. The performance of typical ICA algorithm strongly depends on many factors such as the presence of additive noise, the actual distribution of source signals, and the estimated number of non-Gaussian components. Often a linear mixing model is assumed and the source signals are extracted by proceeding data whitening followed by a sequence of plane (Jacobi) rotations. In this article, we develop a four-unit, symmetric algorithm, based on the quaternionic factorization of the rotation matrices and the Newton-Raphson iterative scheme. Unlike conventional rotational techniques such as the JADE algorithm, our method exploits 4 x 4 rotation matrices and uses negentropy approximation as a contrast function. Consequently, the proposed method can be adapted to a given data distribution (e.g. super-Gaussians) by selecting the appropriate non-linear function that approximates the negentropy. Compared to the widely used, symmetric FastICA algorithm, the proposed method does not require an orthogonalization step and offers better numerical stability in the presence of multiple Gaussian sources.

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>

Exploratory Analysis of Fossil-Fuel CO2 Emissions Time Series Using Independent Component Analysis

2011 ◽  
pp. 1520-1538
Author(s):  
Sargam Parmar ◽  
Bhuvan Unhelkar
Keyword(s):  
Time Series ◽  
Independent Component Analysis ◽  
Co2 Emissions ◽  
Fossil Fuel ◽  
Multivariate Time Series ◽  
Component Analysis ◽  
Linear Mapping ◽  
Independent Component ◽  
Carbon Dioxide Co2 ◽  
Ica Algorithm

Carbon dioxide (CO2) is one of the most important gases in the atmosphere, and is necessary for sustaining life on Earth. However, it is also a major greenhouse gas out of the six that contribute to global warming and climate change. During the last decade technologists, economists and sociologists are taking substantial interest in studying the impact of greenhouse phenomenon. Scientists are trying to find solutions to reduce CO2 emissions by changes in structure of energy production and consumption. Every attempt is being made to use new models and methods to estimate measure and monitor greenhouse gases in the future. Independent Component Analysis (ICA) is a method for automatically identifying a set of underlying factors in a given data set. This chapter describes the use of the ICA algorithm in Environmentally Intelligent (EI) applications. EI applications have a wide ranging responsibilities including collection, analysis and reporting of environmental data related to the organization. ICA algorithm opens up the opportunity to improve the quality of data being analyzed by these EI applications. ICA finds application in several fields of interest and it is a tempting alternative to try ICA on multivariate time series such as a CO2 emission from fossil fuel for the period 1950 to 2006. This chapter describes the linear mapping of the observed multivariate time series into a new space of statistically independent components (ICs) that might reveal driving mechanisms for CO2 emissions that may otherwise remain hidden.

What are the Driving Factors behind the Fluctuation of Crude Oil Prices? : An Independent Component Analysis

2014 ◽  
Vol 1073-1076 ◽  
pp. 2508-2511
Author(s):  
Hui Ping Li ◽  
Li Wei Fan ◽  
Peng Zhou
Keyword(s):  
Independent Component Analysis ◽  
Crude Oil ◽  
Oil Prices ◽  
Component Analysis ◽  
Driving Factors ◽  
Independent Component ◽  
Spot Prices ◽  
Independent Components ◽  
Crude Oil Prices ◽  
Ica Algorithm

This study adopted independent component analysis (ICA) to explore the underlying driving factors affect the international crude oil prices. Three original benchmark crude oil spot prices were first preprocessed to become normalized form by centering and whitening. Three independent components were then estimated by Fast-ICA algorithm. We find that the three independent components vary differently in their fluctuation amplitude and indicate clearly different hidden factors consisting of dominant long-term trend, medium-term extreme events influence, as well as frequent short-term irregular events such as weather and speculation. It shows that ICA is a powerful tool in finding out common hidden driving factors of international parallel crude oil prices.

scholarly journals Minimax Mutual Information Approach for Independent Component Analysis

2004 ◽  
Vol 16 (6) ◽  
pp. 1235-1252 ◽  
Author(s):  
Deniz Erdogmus ◽  
Kenneth E. Hild ◽  
Yadunandana N. Rao ◽  
José C. Príncipe
Keyword(s):  
Mutual Information ◽  
Independent Component Analysis ◽  
Maximum Entropy ◽  
Component Analysis ◽  
Performance Measure ◽  
Higher Order ◽  
Independent Component ◽  
Maximization Problem ◽  
Maximum Output ◽  
Ica Algorithm

Minimum output mutual information is regarded as a natural criterion for independent component analysis (ICA) and is used as the performance measure in many ICA algorithms. Two common approaches in information-theoretic ICA algorithms are minimum mutual information and maximum output entropy approaches. In the former approach, we substitute some form of probability density function (pdf) estimate into the mutual information expression, and in the latter we incorporate the source pdf assumption in the algorithm through the use of nonlinearities matched to the corresponding cumulative density functions (cdf). Alternative solutions to ICA use higher-order cumulant-based optimization criteria, which are related to either one of these approaches through truncated series approximations for densities. In this article, we propose a new ICA algorithm motivated by the maximum entropy principle (for estimating signal distributions). The optimality criterion is the minimum output mutual information, where the estimated pdfs are from the exponential family and are approximate solutions to a constrained entropy maximization problem. This approach yields an upper bound for the actual mutual information of the output signals—hence, the name minimax mutual information ICA algorithm. In addition, we demonstrate that for a specific selection of the constraint functions in the maximum entropy density estimation procedure, the algorithm relates strongly to ICA methods using higher-order cumulants.

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