Joint alignment of a collection of functions is the process of independently transforming the functions so that they appear more similar to each other. Typically, such unsupervised alignment algorithms fail when presented with complex data sets arisi
ng from multiple modalities or make restrictive assumptions about the form of the functions or transformations, limiting their generality. We present a transformed Bayesian infinite mixture model that can simultaneously align and cluster a data set. Our model and associated learning scheme offer two key advantages: the optimal number of clusters is determined in a data-driven fashion through the use of a Dirichlet process prior, and it can accommodate any transformation function parameterized by a continuous parameter vector. As a result, it is applicable to a wide range of data types, and transformation functions. We present positive results on synthetic two-dimensional data, on a set of one-dimensional curves, and on various image data sets, showing large improvements over previous work. We discuss several variations of the model and conclude with directions for future work.
We use single-spin resonant spectroscopy to study the spin structure in the orbital excited-state of a diamond nitrogen-vacancy center at room temperature. We find that the excited state spin levels have a zero-field splitting that is approximately h
alf of the value of the ground state levels, a g-factor similar to the ground state value, and a hyperfine splitting ~20x larger than in the ground state. In addition, the width of the resonances reflects the electronic lifetime in the excited state. We also show that the spin-splitting can significantly differ between NV centers, likely due to the effects of local strain, which provides a pathway to control over the spin Hamiltonian and may be useful for quantum information processing.
