# Independent Component Analysis

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As is usually the case in deep learning, this problem has no simple analytic solution, and to make matters worse, the orthonormality constraint makes it slightly more difficult to optimize for the objective using gradient descent - every iteration of gradient descent must be followed by a step that maps the new basis back to the space of orthonormal bases (hence enforcing the constraint). | As is usually the case in deep learning, this problem has no simple analytic solution, and to make matters worse, the orthonormality constraint makes it slightly more difficult to optimize for the objective using gradient descent - every iteration of gradient descent must be followed by a step that maps the new basis back to the space of orthonormal bases (hence enforcing the constraint). | ||

- | In practice, optimizing for the objective function while enforcing the orthonormality constraint (as described in [[Independent Component Analysis#Orthonormal ICA | Orthonormal ICA]] section below) is feasible but slow. Hence, the use of orthonormal ICA is limited to situations where it is important to obtain an orthonormal basis ([[TODO]]: what situations) | + | In practice, optimizing for the objective function while enforcing the orthonormality constraint (as described in [[Independent Component Analysis#Orthonormal ICA | Orthonormal ICA]] section below) is feasible but slow. Hence, the use of orthonormal ICA is limited to situations where it is important to obtain an orthonormal basis ([[TODO]]: what situations) . |

== Orthonormal ICA == | == Orthonormal ICA == |