Fractional Component Analysis (FCA) for Mixed Signals

This paper proposes the fractional component analysis (FCA), whose goal is to decompose the observed signal into component signals and recover their fractions. The uniqueness of our idea in comparison with other similar methods is the concept of the virtual PDF (probability distribution function) that models signal mixing on the sensor. In this paper, we derive the virtual PDF based on positivity constraint, unity constraint, and randomness assumption, and we then build 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 we illustrate experimental results on synthetic data to show the unique decision boundary obtained from our method.