The cocktail party problem is a common problem in digital signal processing. It describes a scenario where a number of guests are in the same room at a cocktail party having simultaneous, mutually exclusive conversations. For our example, let's assume there are 5 speakers having mutually exclusive conversations. We want to record the conversations and play them at a later date.
If we place a single microphone in the middle of the room and record all of the conversations, we will hear distorted bits of different conversation when we play back the recording. We may be able to tease apart bits and pieces of the conversation from the speaker who was closest to the microphone; however, this is far from ideal and we can do much better. If we place five or more microphones in different parts of the room and record all of the conversations, then we can tease apart each conversation by analyzing the collective recordings.
This is done through Independent Componenet Analysis (ICA). ICA is a mathematical process that takes n linear equations as input and produces n linearly independent equations as output. Thus, if we take the five recordings, one from each mic, and process it through ICA, five independent speeches will be produced as output. These independent speeches correspond to the different conversations that were being recorded.
ICA is useful in EEG brain research because the EEG produces a cocktail party scenario. The brain has many componenets that may be "talking" at the same time, like the speakers at the party, and the EEG channels record voltage readings from the brain, like the microphones in the room. Thus, ICA allows us to seperate the data into independent equations that we believe correspond to different components in the brain.