Successive Projection Algorithm Robust to Outliers
This is an incremental improvement for applications like hyperspectral unmixing and document classification, addressing specific drawbacks of an existing algorithm.
The paper tackles the lack of robustness to outliers and data fitting in the successive projection algorithm (SPA) for separable nonnegative matrix factorization, proposing Robust SPA (RSPA) that maintains provable robustness in low-noise settings and improves index selection based on reconstruction error, with effectiveness demonstrated on synthetic data and hyperspectral images.
The successive projection algorithm (SPA) is a fast algorithm to tackle separable nonnegative matrix factorization (NMF). Given a nonnegative data matrix $X$, SPA identifies an index set $\mathcal{K}$ such that there exists a nonnegative matrix $H$ with $X \approx X(:,\mathcal{K})H$. SPA has been successfully used as a pure-pixel search algorithm in hyperspectral unmixing and for anchor word selection in document classification. Moreover, SPA is provably robust in low-noise settings. The main drawbacks of SPA are that it is not robust to outliers and does not take the data fitting term into account when selecting the indices in $\mathcal{K}$. In this paper, we propose a new SPA variant, dubbed Robust SPA (RSPA), that is robust to outliers while still being provably robust in low-noise settings, and that takes into account the reconstruction error for selecting the indices in $\mathcal{K}$. We illustrate the effectiveness of RSPA on synthetic data sets and hyperspectral images.