Consider the following picture representing the experimental data sequence obtained by two 1D-sensors (each point of the sequence is plotted on XY plane according to the respective sensor reading):
It's visually obvious that two modes have been registered. Let's assume that generally those two modes interfere, so there's no easy possibility to separate them by isolating certain sequence segments. I try the classic principal component analysis by finding the covariance matrix, then finding the set of eigenvalues and corresponding eigenvectors:
White box dimensions represents the magnitude if the eigenvalues, box orientation represents the direction of eigenvectors.
It's clear that PCA first component deviates slightly from the high-magnitude mode direction, while the second component deviates greatly due to skewness of the lower-magnitude mode original direction.
It is known that PCA, being based on eigenvectors, results in orthogonal basis of primary components.
Is there other elegant methods (or PCA-derived methods) to obtain the non-orthogonal basis of primary skewed components?