Independent Component Analysis

PCA finds a new orthogonal basis that best preserves variance — a purely second-order-statistics criterion. Independent component analysis (ICA) asks a genuinely different question, motivated by the "cocktail-party problem": given $n$ microphones each recording an overlapping mixture of $n$ simultaneous speakers, can the original, statistically independent speech signals be recovered from only the mixed recordings? ICA answers yes — but only under a specific, checkable condition on the sources that PCA never needs to worry about.