Biomedical Signal Processing Independent Component Analysis ICA Presentation

Biomedical Signal Processing Independent Component Analysis (ICA)

Presentation Outline • • • Definition of ICA Basic With Example Application Field of ICA Why ICA? ICA In Details ICA Model In Details ICA Algorithm Comparison ICA and PCA Limitations of ICA 2/21/2021 Md. Aminul Haque 2

What is ICA? ? • A statistical and computational technique for revealing hidden factors that underlie sets of random variables, measurements, or signals. ICA also known as Blind Signal Separation (BSS). 2/21/2021 Md. Aminul Haque 3

Example of ICA Observations (Mixtures) original signals ICA estimated signals 2/21/2021 Md. Aminul Haque 4

Application Field of ICA STATIC • Image denoising • Microarray data processing • Decomposing the spectra of galaxies • Face recognition • Facial expression recognition • Feature extraction • Clustering • Classification TEMPORAL • Medical signal processing – f. MRI, ECG, EEG • Brain Computer Interfaces • Modeling of the hippocampus, place cells • Modeling of the visual cortex • Time series analysis • Financial applications • Blind deconvolution Remark: Red colored fields are related to our subject Topic 2/21/2021 Md. Aminul Haque 5

Application Field of ICA (Cont. ) Applications of ICA to biomedical signals • EEG/ERP analysis (Makeig, Bell, Jung & Sejnowski, 1996) • ECG analysis (Cardoso 1998). • f. MRI analysis (Mc. Keown, Jung et al. 1998) 2/21/2021 Md. Aminul Haque 6

Why ICA? ? ? EEG brain scans measure the neuronal activity in various parts of the brain indirectly via electromagnetic signals recorded at sensors placed at various positions on the head. But All Signals of different positions is not our concern. • Factor analysis is a classical technique developed in statistical literature that aims at identifying these latent sources. • Independent component analysis (ICA) is a kind of factor analysis that can uniquely identify the latent variables. 2/21/2021 Md. Aminul Haque 7

Independent Component Analysis Goal: 8 2/21/2021 Md. Aminul Haque

ICA for EEG Signals • ICA can improve signal – effectively detect, separate and remove activity in EEG records from a wide variety of artifactual sources. • ICA weights help find location of sources. 2/21/2021 Md. Aminul Haque 9

ICA Model 2/21/2021 Md. Aminul Haque 10

ICA Initialization Latent variable model: 2/21/2021 Md. Aminul Haque 11

Example: ICA Model: 2/21/2021 Md. Aminul Haque 12

Independent Component Analysis PCA • Step 1: Center data: • Step 2: Whiten data: compute SVD of the centered data matrix – After whitening in the factor model, cov(x) = I, and A become orthogonal the covariance of x, We transform the observed X vector linearly so that we obtain a new vector which is white, i. e. its components are uncorrelated and their variances equal unity. In other words, the covariance matrix of equals the identity matrix: 2/21/2021 Md. Aminul Haque 13

ICA Model 2/21/2021 Md. Aminul Haque 14

ICA: Steps (Cont. ) Step 3: Find out orthogonal A and unit variance, non-Gaussian and independent S. The computational approaches are mostly based on information theoretic criterion. • Kullback-Leibler (KL) divergence • Negentropy Another different approach emerged recently is called “Product Density Approach” 2/21/2021 Md. Aminul Haque 15

ICA: Steps (Cont. ) Step 3: Find out orthogonal A and unit variance, non-Gaussian and independent S. The computational approaches are mostly based on information theoretic criterion. • Kullback-Leibler (KL) divergence • Negentropy Another different approach emerged recently is called “Product Density Approach” 2/21/2021 Md. Aminul Haque 16

ICA: KL Divergence Criterion • x is zero-mean and whitened • KL divergence measures “distance” between two probability densities – Find A such that KL(. ) is minimized: Joint density Independent density H is differential entropy: 2/21/2021 Md. Aminul Haque 17

ICA: KL Divergence Criterion… • Theorem for random variable transformation says: So, Hence, Minimize with respect to orthogonal A 2/21/2021 Md. Aminul Haque 18

ICA Model 2/21/2021 Md. Aminul Haque 19

ICA Algorithm (Fast ICA) • “Fixed-Point” Algorithm • Implementation – Fast ICA algorithm – Extensions • Algorithm Speed & Performance – Currently the fastest – Most Commonly Used 2/21/2021 Md. Aminul Haque 20

ICA Algorithm (Fast ICA) Iteration procedure for maximizing nongaussianity Step 1: choose an initial weight vector w Step 2: Let w+=E[xg(w. Tx)]-E[g’(w. Tx)]w (g: a non-quadratic function) Step 3: Let w=w+/||w+|| Step 4: if not converged, go back to Step 2 2/21/2021 Md. Aminul Haque 21

Compare ICA and PCA: Finds directions of maximal variance in gaussian data ICA: Finds directions of maximal independence in nongaussian data 2/21/2021 Md. Aminul Haque 22

Limitations of ICA • Scaling: ICA maximizes independence between signals (a 1, a 2, …. etc. ) • Signal Permutations: The mixing matrix and independent components are unknown. • Sensor Requirement: The number of separated signals cannot be larger than the number of inputs. Current research is being done to reduce this constraint. 2/21/2021 Md. Aminul Haque 23

Thanks for the Attention! 2/21/2021 Md. Aminul Haque 24