An example application of ICA is to solve the "Cocktail Party Problem." This problem states we have multiple people talking at a party, but alas the party is very crowded. We try to record the happenings of the party with a microphone, but so many people are talking that no one is understood. However, if we record the party with multiple microphones, can we reconstruct individual voices. Ignoring delays due to distance to the microphones, ICA can solve this problem.
For every signal coming recorded, the ICA method assumes that this signal is composed of a linear combination of source signals. Thus, ICA is an example of “Blind Source Separation,” which is to say: if we know nothing other than the recorded mixtures, can we recover the original signals?
It turns out that we can separate the original signals if the original signals are statistically independent, an assumption of ICA. This usually turns out to mean that all but one of the original signals need be non-Gaussian. In the paradigm that is ICA we are thus solving the linear system:
where x is the recorded signals, s is the assumed original signals, and A is the mixing matrix. Ultimately, we are looking for the inverse of A, namely W which transforms the mixed signals into independent components:
For more specific information regarding the whitening process and the algorithms behind this process, check out this ICA tutorial for the complete info.
So how does this relate to biomedical engineering? Well first and foremost it has been applied successfully to the problem of EEG signals that are highly contaminated with artifactual noise. In our work, we evaluated "independent modes of variation" of bone models using the fastICA algorithm. This produced some interesting results, which are shown below:
In this work I was attempting to discover if there is any anatomical meaning that is captured in the independent components. The population of bone models consisted of 35 femurs and whitening was performed using the first 5-7 principal components. The population was assumed to be a mixture of 7 original "signals" (or in our nomeclature, primary anatomical variations). As such this method fails, the indpendent components are just that: independent. The effect here is that unlike PCA, the independent components are decorrelated with themselves. This means that effectively the proximal portions of the bone move in a completely different way in each of the 7 modes, and this movement is completely different than variations on the distal end.