Algorithms for Spectral Decomposition with Applications

There are two main approaches that can be taken to extract relevant features from these high-dimensional data streams. The first set of approaches relies on extracting features using a physics-based paradigm where the underlying physical mechanism that generates the spectra is used to infer the most important features in the data stream.

We focus on a complementary methodology that uses a data-driven technique that is informed by the underlying physics but also has the ability to adapt to unmodeled system attributes and dynamics. We discuss the following four algorithms: Spectral Decomposition Algorithm (SDA), Non-Negative Matrix Factorization (NMF), Independent Component Analysis (ICA) and Principal Components Analysis (PCA) and compare their performance on a spectral emulator which we use to generate artificial data with known statistical properties.