Approach and Applications of Constrained ICA

Abstract

Abstract-This paper presents the technique of constrained independent component analysis (cICA) and demonstrates two applications, less-complete ICA, and ICA with reference (ICA-R). The cICA is proposed as a general framework to incorporate additional requirements and prior information in the form of constraints into the ICA contrast function. The adaptive solutions using the Newton-like learning are proposed to solve the constrained optimization problem. The applications illustrate the versatility of the cICA by separating subspaces of independent components according to density types and extracting a set of desired sources when rough templates are available. The experiments using face images and functional MR images demonstrate the usage and efficacy of the cICA.Index Terms-Constrained optimization, ICA with reference (ICA-R), independent component analysis (ICA), less-complete ICA.

Monte Carlo Algorithm for Least Dependent Non-Negative Mixture Decomposition

“…This gives rise to constraints which are not easily taken into account in typical ICA algorithms that heavily rely on linear algebra [8,9]. This would not be problematic by itself -in other applications signals are often non-negative, too.…”

Smooth Signal Extraction From Instantaneous Mixtures

“…The non-Gaussianity cost function is defined [5] ( 5) where is a non-quadratic function, and is a zero-mean unitnorm Gaussian variable. The smoothness criterion is defined by the following cost function: (6) Defining , the above equation is written as follows: (7) In addition, we have to ensure that we are only performing rotation and not any scaling deformation. Therefore, we impose the following unit-norm constraint to the estimated components : (8) Consequently, the inequality constrained optimization problem is the following: (9) subject to (10)…”

“…To solve this equality constrained optimization problem, the method of Lagrange multipliers is employed. The objective is to formulate an approximate Newton-type method, following a derivation similar to the original FastICA algorithm [5], [6]. As traditionally performed by these methods, the unit-norm constraint (11) is enforced by projection of the estimated on the unit-sphere in each iteration (12); therefore, it is not considered in the optimization cost function (12)…”

“…Hence, the update for the th component should always be orthogonal to the space spanned by the vectors (19) where . The proposed method resembles constrained ICA, proposed in [6]. The difference is that the inequality constraint is treated as a ZTP problem that results in a simpler approach and seems to be stable.…”

“…However, adding a constraint to the estimation criterion can identify the desired components with some additional computational overhead but without separating and testing all present independent components, especially when is large. The concept of constrained ICA has been previously introduced in [6], however, in the concept of global search for independent components that resemble several reference signals. In [1], the extraction of components with temporal periodic structure is introduced assuming a priori knowledge of the sources' autocorrelation function.…”