08_ICA - Unmixing fMRI with Independent Component Analysis...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE MARCH/APRIL 2006 79 FUNCTIONAL MAGNETIC RESONANCE IMAGING Unmixing fMRI with Independent Component Analysis Using ICA to Characterize High-Dimensional fMRI Data in a Concise Manner. BY VINCE D. CALHOUN AND TÜLAY ADALI ©DIGITAL STOCK 0739-5175/06/$20.00©2006IEEE hat an antithetical mind!—tenderness, rough- ness—delicacy, coarseness—sentiment, sensual- ity—soaring and groveling, dirt and deity—all mixed up in that one compound of inspired clay! —Lord Byron Independent component analysis (ICA) is a statistical method used to discover hidden factors (sources or features) from a set of measurements or observed data such that the sources are maximally independent. Typically, it assumes a generative model where observations are assumed to be linear mixtures of independent sources, and unlike principal component analy- sis (PCA), which uncorrelates the data, ICA works with high- er-order statistics to achieve independence. An intuitive example of ICA can be given by a scatter-plot of two independent signals s 1 and s 2 . Figure 1(a) shows a plot of the two independent signals ( s 1 , s 2 ) in a scatter plot. Figure 1(b) and (c) shows the projections for PCA and ICA, respectively, for a linear mixture of s 1 and s 2 . PCA finds the orthogonal vectors u 1 , u 2 but does not find independent vectors. In con- trast, ICA is able to find the independent vectors a 1 , a 2 of the linear mixed signals ( s 1 , s 2 ) and is thus able to restore the orig- inal sources. A typical ICA model assumes that the source signals are not observable, are statistically independent, and are non- Gaussian, with an unknown but linear mixing process. Consider an observed M- dimensional random vector denoted by x = ( x 1 ,... x M ) T , which is generated by the ICA model: x = As ,( 1 ) where s = [ s 1 , s 2 s N ] T is an N- dimensional vector whose elements are assumed independent sources and A M × N is an unknown mixing matrix. Typically M > = N , so A is usually of full rank. The goal of ICA is to estimate an unmixing matrix W N × M such that y [defined in (2)] is a good approxima- tion to the true sources: s . y = Wx ( 2 ) ICA is hence an approach to solving the blind source separation problem, which traditionally addresses the solu- tion of the cocktail party problem in which several people are speaking simultaneously in the same room. The prob- lem is to separate the voices of the different speakers by using recordings of several microphones in the room [2]. The basic ICA model for blind source separation is shown in Figure 2. Popular approaches for performing ICA include maximiza- tion of information transfer, which is equivalent to maximum likelihood estimation, maximization of non-Gaussianity, mutual information minimization, and tensorial methods. The most commonly used ICA algorithms are Infomax [3], FastICA [4], and joint approximate diagonalization of eigen- matrices (JADE) [5]. The original Infomax algorithm for blind separation by [3] is better suited to estimation of super- Gaussian sources. To overcome this limitation, techniques
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/10/2010 for the course TBE 2300 taught by Professor Cudeback during the Spring '10 term at Webber.

Page1 / 12

08_ICA - Unmixing fMRI with Independent Component Analysis...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online