Probabilistic Simplex Component Analysis via Variational Auto-Encoding

Simplex component analysis (SCA) aims to estimate the vertices of the convex hull where data samples reside in. SCA finds various applications in signal processing, e.g., hyperspectral unmixing and noisy label learning. Recent works proposed to tackle SCA from a probabilistic viewpoint using variational inference (VI) tools, which fends against noise more effectively relative to the deterministic counterparts. However, the computational efficiency of VI for SCA hinges on the use of the Dirichlet variational posterior. Such variational posterior appears to lack expressiveness—making the SCA performance limited if the true posterior is complex. This work proposes to employ a logistic-normal variational posterior, which exhibits enhanced expressive power. To circumvent the computational bottleneck, a neural representation-based inference algorithm is proposed—which exploits a connection between the logistic-normal distribution and variational auto-encoding. Numerical experiments using simulated and semi-real data are conducted to showcase the effectiveness of our algorithm design.