Probabilistic Simplex Component Analysis

This study presents PRISM, a probabilistic simplex component analysis approach to identifying the vertices of data-circumscribing from data. The problem has rich variety applications, most notable being hyperspectral unmixing in remote sensing and non-negative matrix factorization machine learning. PRISM uses simple model, namely, uniform data distribution additive Gaussian noise, it carries out inference by maximum likelihood. model is sound sense that are provably identifiable under some assumptions, suggests can be effective combating noise when number points large. strong, but hidden, relationships with volume minimization, powerful geometric for same problem. We these fundamental aspects, we also consider algorithmic schemes based on importance sampling variational inference. In particular, scheme shown resemble special regularizer, which draws an interesting connection approach. Numerical results provided demonstrate potential PRISM.