Principal component Analysis, Principal Components Analysis, PCA) is a kind of Analysis, simplify the technology of data sets.Principal component analysis is often used to reduce the dimensions of the data sets, while keeping the characteristic of the largest contribution to the variance of a data set.This is by retaining low order principal component, ignore higher-order principal component.Principal component analysis (pca) is a statistical method of dimension reduction, it is by using a orthogonal transformation, the original random vector that are relevant to the component into its component is not related to the new random vector, this appears to be the original random vector on the algebra of covariance matrix transformation into a diagonal matrix, on the geometry of the original coordinate transformation into a new orthogonal coordinate system, make it points to sample points to spread the most open p orthogonal direction, and then to multidimensional variable system dimension, make it to a high precision system is transformed into low dimensional variables, then through constructing the proper value function, further the low-dimensional systems into one dimension. The principle of principal component analysis is to try to into a new set of the original variables were independent of each other a few variables, at the same time, according to the actual need to take out a few less the sum of the variables as much as possible to reflect the original statistical methods of information called principal component analysis (or called principal component analysis, also is a kind of mathematical processing dimension reduction method.Independent Component Analysis (Independent Component Analysis, ICA) and Independent Component Analysis is a method of using statistics principle to compute.It is a linear transformation, the transformation or the data signal is separated into independent non-gaussian statistics linear combination of the signal source.At present more popular ICA algorithm and Infomax algorithm (information maximization), FastICA algorithm (fixed-point algorithm, Fixed - point, fast ICA algorithm), classification method is mainly based on different methods to calculate the separation matrix W. To calculate the maximum likelihood estimation, hypothesis and between is independent, yet for speech signal or other time continuous dependence characteristics (such as temperature), the hypothesis cannot be established.But in enough data, assuming independent influence on the effect is not big, if disrupted the sample in advance at the same time, rising and run the stochastic gradient algorithm, then can accelerate the convergence speed. This paper analyses the FastICA algorithm, independent component analysis of an improved learning algorithm of gradient, hereinafter referred to as orthogonal information maximization algorithm (OrthogonalIn fomax, O RTH - Infomax) this algorithm combines Infomax algorithm and the advantages of Fixed - Point algorithm.From two aspects of speech signal and the fMRI signal to compare the three algorithms..In terms of speech signal separation accuracy, Orth - Infomax separation algorithm has the best accuracy.For real fMRI data, Orth - Infomax algorithm has the best dynamic accuracy estimate brain activation time.Corresponding to the voice and data of the experimental results and the experimental results of fMRI data. In many ICA algorithm, fixed point algorithm (also called FastlCA) for its quick convergence rate, good separation effect is widely used in signal processing field.The algorithm can estimate the statistically independent of each other from the observed signals, mixed by unknown factors, the original signal.The ICA is the main application of the feature extraction, physiological data signal blind source separation, analysis, speech signal processing, image processing, face recognition, etc. Keywords: principal component analysis, independent component analysis, the maximum likelihood estimation, FastICA algorithm, the application of ICA
