Independent components analysis

Canonical correlation analysis identifies and quantifies the associations between two sets of variables [126]. Canonical correlation analysis is conducted by using canonical variates. Consider n observations of two random vectors X and y of dimensions p and q forming data sets Xpxn and Y xn with 

For coefficient vectors a and b form the linear combinations u = a X and V = b Y. Then, for the first pair u, v the the maximum correlation 

Canonical variates will be used in the formulation of subspace state-space models in Section 4.5. 

Independent Component Analysis (ICA) is a signal processing method for transforming multivariate data into statistically independent components expressed as linear combinations of observed variables [91, 119, 134]. Consider a process with m zero-mean variables x = (xi X2 XmY The 

The signs, powers and orders of independent components (IC) can not be estimated. 

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The hypothesis of a normal distribution is a strong limitation that should be always kept in mind when PCA is used. In electronic nose experiments, samples are usually extracted from more than one class, and it is not always that the totality of measurements results in a normally distributed data set. Nonetheless, PCA is frequently used to analyze electronic nose data. Due to the high correlation normally shown by electronic nose sensors, PCA allows a visual display of electronic nose data in either 2D or 3D plots. Higher order methods were proposed and studied to solve pattern recognition problems in other application fields. It is worth mentioning here the Independent Component Analysis (ICA) that has been applied successfully in image and sound analysis problems [18]. Recently ICA was also applied to process electronic nose data results as a powerful pre-processor of data [19]. 

Hyvarinen, A., Karhunen, J., and Oja, E. (2001) Independent component analysis. John Wiley Sons, New York. 

Foy, B.R. and Theiler, J., Scene analysis and detection in thermal infrared remote sensing using independent component analysis. Independent Component Analyses, Wavelets, Unsupervised Smart Sensors, and Neural Networks 11, Proceedings of SPIE vol. 5439, 131-139(2004)... 

Similarly to PCA, other methods exist that represent the image raw data in a space of smaller dimensionality, aiming to retain all relevant information. Some of these project the image in a small space according to different criteria, such as statistical independence in independent component analysis (ICA) [33], or are based on properties linked to data topology [34]. 

Independent component analysis (ICA) is proposed as an alternative to PCA for MSPM. Various studies indicate that ICA-based MSPM tools are more successful for non-Gaussian data [162]. Several papers have been published recently to illustrate the strengths and limitations of ICA for MSPM [137, 138, 163, 164]. 

M Girolami. Self-Organizing Neural Networks Independent Component Analysis and Blind Source Separation. Springer-Verlag, London, UK, 1991. 

M Kano, S Hasebe, I Hashimoto, and H Ohno. Evolution of multivariate statistical process control Independent component analysis and external analysis. Comput. Chem. Engg., 28(6-7) 1157-1166, 2004. 

J-M Lee, SJ Qin, and I-B Lee. Fault detection and diagnosis of multivariate processes based on modified independent components analysis. AIChE J., 2006. Submitted. 

J-M Lee, CK Yoo, and I-B Lee. Statistical process monitoring with independent components analysis. J. Process Control, 14 467-485, 2004. 

An in-depth review of statistical methods for metabonomic data analysis is beyond the scope of this chapter. Briefly, there are a few main approaches to data analysis. Examples of multivariate data analyses include the so-called unsupervised analyses such as PCA, independent component analysis (ICA), and hierarchical clustering analysis (HCA), while partial least square differential analysis (PLS-DA) is... 

Calamante, E, M. Morup, L.K. Hansen, Defining a local arterial input function for perfusion MRI using independent component analysis. Magn Reson Med, 2004. 52(4) p. 789-97. 

Linear transformation of the original variables can lead to suitable representations of original multivariate data. As is shown above, MPCA method makes this transform pointing towards directions of maximum variance. In Independent Component Analysis (ICA) the goal is finding components (or directions) as independent as possible. This linear decomposition of one random vector (multivariate data) x follows the expression ... 

Xueguang, S., Wei, W., Zhenyu, H., Wensheng, C. A new regression method based on independent component analysis. Talanta 69, 676-680 (2006)... 

The factorial methods in this chapter are also called second-order transformations, because only two moments, mean and covariance, are needed to describe the Gaussian distribution of the variables. Other second-order transformations are FA, independent component analysis (ICA), and multivariate curve resolution (MCR). 

Example 5.7 Independent Component Analysis (ICA) of Data from Three Sensor Signals... 

A. Delorme and S. Makeig. EEGLAB an open source toolbox for analysis of single-trial dynamics including independent component analysis. /. Neurosci. Meth., 134 9 21,2004. 

A. Snellings, D.J. Anderson, and J.W. Aldridge, Use of multichannel recording electrodes and independent component analysis for target localization in deep brain structures. Proceedings of the 1st International IEEE EMBS Conference on Neural Engineering, Capri Island, Italy, 305-308 (2003). 

Archibald, R., Datskos, R, Devault, G., Lamberti, V., Lavrik, N., Noid, D., Sepaniak, M., and Dutta, P. 2007. Independent component analysis of nanomechanical responses of cantilever arrays. Anal Chim Acta 584,101-105. 

Lin, C.-T., Wu, R.-C., Liang, S.-E, Chao, W.-H., Chen, Y.-J., and Jung, T.-P. 2005. EEG-based drowsiness estimation for safety driving using independent component analysis. IEEE Trans. Circuits Systems 52 2726-2738. 

S. Balasubramanian, S. Panigrahi, C.M. Logue, C. Doetkott, M. MarcheUo, J.S. Sherwood, Independent component analysis-processed electronic nose data for predicting SalmoneUa typhimurium populations in contaminated beef. Food Control 19(3), 236-246 (2008)... 

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