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This work 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.