Dependent component analysis (DCA) is a

blind signal separation Blind may refer to: * The state of blindness, being unable to see * A window blind, a covering for a window Blind may also refer to: Arts, entertainment, and media Films * ''Blind'' (2007 film), a Dutch drama by Tamar van den Dop * ''Blind' ...

(BSS) method and an extension of

Independent component analysis In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and that the subcomponents a ...

(ICA). ICA is the separating of mixed signals to individual signals without knowing anything about source signals. DCA is used to separate mixed signals into individual sets of signals that are dependent on signals within their own set, without knowing anything about the original signals. DCA can be ICA if all sets of signals only contain a single signal within their own set.

Mathematical representation

For simplicity, assume all individual sets of signals are the same size, k, and total N sets. Building off the basic equations of BSS (seen below) instead of independent source signals, one has independent sets of signals, s(t) = (,...,)^T, which are mixed by

coefficient In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression (including variables such as , and ). When the coefficients are themselves ...

s A= _ij�R^mxkN that produce a set of mixed signals, x(t)=(x₁(t),...,x_m(t))^T. The signals can be multidimensional.

x(t) = A*s(t)

The following equation BSS separates the set of mixed signals, x(t), by finding and using coefficients, B= _ij�R^kNxm, to separate and get the set of

approximation An approximation is anything that is intentionally similar but not exactly equal to something else. Etymology and usage The word ''approximation'' is derived from Latin ''approximatus'', from ''proximus'' meaning ''very near'' and the prefix '' ...

of the original signals, y(t)=(,...,)^T.

y(t) = B*x(t)

Methods

Sub-Band Decomposition ICA (SDICA) is based on the fact that

wideband In communications, a system is wideband when the message bandwidth significantly exceeds the coherence bandwidth of the channel. Some communication links have such a high data rate that they are forced to use a wide bandwidth; other links may h ...

source signals are dependent, but that other subbands are independent. It uses an

adaptive filter An adaptive filter is a system with a linear filter that has a transfer function controlled by variable parameters and a means to adjust those parameters according to an optimization algorithm. Because of the complexity of the optimization algor ...

by choosing subbands using a minimum of

mutual information In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the " amount of information" (in units such as ...

(MI) to separate mixed signals. After finding subband signals, ICA can be used to reconstruct, based on subband signals, by using ICA. Below is a formula to find MI based on

entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...

, where H is entropy.

\widehat(y)=\sum_^N\widehat H(y_n)- \widehat H(y)

\widehat(y_n)=-\frac\sum_^Tlog\widehat P_(y_n(t))

\widehat(y)=-\frac\sum_^Tlog\widehat P_(y_n(t))

References

{{Reflist Signal processing