A typical example is the ``cocktail party problem''. (See a demo.) Given the signals from microphones recording speakers in the room (), one wants to recover the voice of each speaker. The problem can be formulated as

**Given**

or in matrix form

**Find**- the estimation
of the source variables
*the independent components*, - and the linear combination matrix .

- the estimation
of the source variables

Although this BSS problem seems severely under constrained, the independent component analysis (ICA) can find nearly unique solutions satisfying certain properties.

ICA can be compared with
*principal component analysis* (PCA)
for decorrelation. Given a set of variables , PCA finds a
matrix so that the components of
are
uncorrelated. Only under the special case when
are gaussian, are they also independent. In comparison, ICA is a more powerful
method in the senese that it satisfies a stronger requirement of finding
so that the components of
are independent
(and therefore are also necessarily uncorrelated).