ICA vs NNMF...An Overview

Many a times u must have heared the term "BLIND" while describing a convolution problem or speech / beam synthesis. The above methods deal with this problem; for starters these two are statistical and mathematical techniques, having numerous applications...actually u will be just amazed to know some of these.

The above techniques r used to reveal hidden factors that underly sets of random variables, signals, data etc.

Lets make them more interesting by first citing the application of these:

APPLICATIONS:

• Power system: We can suppress the effect of harmonics in the power system, by separating the harmonics from the sinusoidal current.
• Telecommunication: We can suppress the interference in the spread spectrum communication. It’s also used for Array processing, i.e. in Blind beamforming applications. Also in airports when the radar receives signals from more than 1 planes this methods can be used to separate the interfering signals from the antenna "look ahead" signal space.
• Speech processing: In cock-tail party problems, from the mixture of speech signals we can separate the speech signal of the individuals
• Finance / Econometrics It is a tempting alternative to try this techniques on financial data. There are many situations in that application domain in which parallel time series are available, such as currency exchange rates or daily returns of stocks, that may have some common underlying factors
• Bio-Medical science:The EEG (electroencephalogram) data consists of mixture of different components of brain activity. These can reveal interesting information on brain activity by giving access to its independent components. It can be also used for MEG data,recovering the faint child heart beat when he is still in mothers womb
• Digital image processing: Like other applications, from the mixture of digital images the individual component can be separated. ICA and NNMF also finds application in feature extraction techniques.

ICA (Independent Component Analysis)

This is a method 2 separate two or more statistically independent ( covariance=0) signals from there mixtures. The mixtures should be linear(however its also possible to separate nonlinear mixtures), having no time lag and the mixing variables should be independent of the signals.
It uses the property "Nonguassianity for independence" While the measures of nongaussianity are Kurtosis, Negentropy (superior to previous one).

NNMF (Nonnegative Matrix Factorization)

As the name specifies this method is used to factorize a matrix into 2 factors(matrices) with the constraint that all three matrices must be non-negetive, i.e., all elements must be equal to or greater than zero.

The whole process involves images of the matrix and optimizing the residue to obtain the best result.

Comparision:

INDEPENDENT COMPONENT ANALYSIS			NON-NEGATIVE MATRIX FACTORIZATION
FASTER, especially with FastICA technique, which is achieved by imposing nonlinearities in the data ACCURACY, not that accurate as that can be achieved by NNMF. ASSUMPTIONS, one important assumption in ICA technique is that the signals should be statistically independent. Hence it is difficult to use this tech. for reverberation suppression.			SLOWER as compared to previous method. As the iteration steps involve numerous images and residues. More accurate, and higher degrees of accuracy can be achieved No such assumption is necessary. So this can be very beneficial when accuracy is the main criterion sacrificing speed of computation

However as most of the signals in real world are Gaussian and independent in nature (it may sound contrasting but its true) ICA technique cannot be neglected. So it all depends on the application we were using them and speed-accuracy trade-off.