 |
Therefore, independent component analysis can be considered as a problem of searching for the direction with the maximum non-Gaussianity.
In other words, in independent component analysis with non-Gaussianity, the algorithm to update the weight matrix 𝑾 is important,
A quantitative measure of the non-Gaussianity of the random variable is needed.
Let us denote a random variable as y.
In this study, we apply negentropy as a measure of non-Gaussianity.
However, since the computation of negentropy is complicated by the need to estimate the probability density function, we use a non-quadratic function g, which can be expressed by the approximation equation 4-1
where E represents the expected value calculation, Equation 4-2 is used for the non-quadratic function g, and 𝑣 is a Gaussian variable with y standardized to mean 0 and variance 1.
From the above, when maximizing negentropy, the fastest algorithm, fast independent component analysis (fast ICA), can be obtained by using an immovable point with excellent convergence characteristics.
Therefore, the algorithm for updating the weight matrix using the fixed point algorithm can be expressed as in Equation 5. |
IEEE/ICACT20230070 Slide.07
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