Fractional component analysis (FCA) for mixed signals

This paper proposes fractional component analysis (FCA), whose goal is to decompose the observed signal into component signals and recover their fractions. The uniqueness of the idea in comparison with other similar methods is the concept of the virtual PDF (probability distribution function) that models signal mixing on the sensor. The paper derives the virtual PDF based on positivity constraint, unity constraint, and randomness assumption, and then builds it into the mixture density model. In order to learn parameters of this model from data using EM (Expectation-Maximization) algorithm, the key point is to derive the approximation of the virtual PDF using its cumulants. Finally the paper illustrates experimental results on synthetic data to show the unique decision boundary obtained from the method.