Optimization of Kurtosis in the Extend-Infomax Blind Signal Separation Algorithm

A kurtosis optimization method is proposed to improve the blind separated signal qualities based on the extend-infomax algorithm. The kurtosis of the hypothetical source signal was optimized based on the probability density function of sub-Gaussian signals. Obtained parameters after kurtosis optimization were then utilized to validate the effectiveness of the algorithm, which showed that the running time of the algorithm was significantly reduced, and the qualities of the separated signals were enhanced. Methods. Using kurtosis as a control variable, a one-way analysis of variance (ANOVA) was carried out on the algorithm’s performance metrics, the number of iterations, and the signal-to-noise ratio of the separated signal. Results. The results showed that there were significant differences in the above metrics under different kurtosis levels. The curves of average metric values indicate that, with the increase in kurtosis of the hypothetical source signal, the performance of the algorithm was improved.

Tractable Relaxations of Composite Functions

In this paper, we introduce new relaxations for the hypograph of composite functions assuming that the outer function is supermodular and concave extendable. Relying on a recently introduced relaxation framework, we devise a separation algorithm for the graph of the outer function over P, where P is a special polytope to capture the structure of each inner function using its finitely many bounded estimators. The separation algorithm takes [Formula: see text] time, where d is the number of inner functions and n is the number of estimators for each inner function. Consequently, we derive large classes of inequalities that tighten prevalent factorable programming relaxations. We also generalize a decomposition result and devise techniques to simultaneously separate hypographs of various supermodular, concave-extendable functions using facet-defining inequalities. Assuming that the outer function is convex in each argument, we characterize the limiting relaxation obtained with infinitely many estimators as the solution of an optimal transport problem. When the outer function is also supermodular, we obtain an explicit integral formula for this relaxation.