Independent component analysis method

The scalp recordings were obtained from multi-channels system, model Medtronic in ChoRay hospital. With collected data, we read it in Madab. Then, we use the independent component analysis method to obtain independent components. The eorrected EEG signals... 

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]. 

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 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... 

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... 

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). 

S. Tong, A. Bezerianos, J. Paul, Y. Zhu, and N. Tbakor, Removal of ECO interference from the EEG recordings in animals using independent component analysis, /. Neurosci. Methods 108 11-17 (2001). 

Delorme A, Makeig S. EEGLAB an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis. J Neurosci Methods 2004 134(1) 9-21. 

Y. Ning, et oL, "Independent Component Analysis and Time-Frequency Method for Noisy EEG Signal Analysis," in Signal Processing, 2006 8th International Conference on, 2006. 

Dominic Langlois, Sylvain Chattier, and Dominique Gosselin, An Introduction to Independent Component Analysis InfoMax and Fas-tlCA algorithms. Tutorials in Quantitative Methods for Psychology 2010, Vol. 6(1), p. 31-38. 

SneUings A, Anderson D, Aldridge J (2006) Improved signal and reduced noise in neural recordings from closespaced electrode arrays using independent component analysis as a preprocessor. J Neurosci Methods 150(2) 254-264, Jan. 2006. 

Bouveresse DJR, Moya-Gonzalez A, Ammari F, Rutledge DN. Two novel methods for the determination of the number of components in independent components analysis models. Chemometr Intell Lab 2012 112 24-32. 

The above equation is called independent component analysis or ICA. The problem is to determine both the matrix A and the independent components s, knowing only the measured variables x. The only assumption the methods take is that the components Sj are independent. It has also been proved that the... 

Used in conjunction with infrared, NMR, UV and visible spectral data, mass spectrometry is an extremely valuable aid in the identification and structural analysis of organic compounds, and, independently, as a method of determining relative molecular mass (RMM). The analysis of mixtures can be accomplished by coupling the technique to GC (p. 114). This was formerly done by using sets of simultaneous equations and matrix calculations based on mass spectra of the pure components. It is well suited to gas... 

The authors wanted to select indicators that specifically tap melancholic depression. To evaluate this construct, a principal components analysis of the joint pool of K-SADS and BDI items was performed. Two independent statistical tests suggested a two-component solution, but the resulting components appeared to reflect method factors, rather than substantive factors. Specifically, all of the BDI items loaded on the first component (except for three items that did not load on either component) and nearly all of the K-SADS items loaded on the second component. In fact, the first component correlated. 98 with the BDI and the second component correlated. 93 with the K-SADS. Ambrosini et al., however, concluded that the first component reflected depression severity and the second component reflected melancholic depression. This interpretation was somewhat at odds with the data. Specifically, the second component included some K-SADS items that did not tap symptoms of melancholia (e.g., irritability and anger) and did not include some BDI items that measure symptoms of melancholia (e.g., loss of appetite). 

This fact leads to the concept of total variance, a parameter corresponding to the sum of variances arising from different components of the variation. Analysis of variance represents a statistical means for partitioning the total variance into individual components. This method attempts to analyze variation by assigning portions of the variance to each set of independent variables. In general, the experimenter will not or cannot include all the variables influencing the response in an experiment, and random variation in the response is observed even... 

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