Variations on Coherence

In this chapter, we illustrate the use of coherence and its generalizations to other application domains, namely, compressed sensing, multiset CCA, kernel methods, and time-frequency modeling. The concept of coherence in compressed sensing and matrix completion is made clear by the restricted isometry property and the concept of coherence index, which are discussed in the chapter. We also consider in this chapter multiview learning, in which the aim is to extract a low-dimensional latent subspace from a series of views of a common information source. The basic tool for fusing data from different sources is multiset canonical correlation analysis (MCCA). Coherence is a measure that can be extended to any reproducing kernel Hilbert space (RKHS). We present in the chapter two kernel methods in which coherence between pairs of nonlinearly transformed vectors plays a prominent role: the kernelized versions of CCA (KCCA) and the LMS adaptive filtering algorithm (KLMS). The chapter concludes with a discussion of a complex time-frequency distribution based on the coherence between a time series and its Fourier transform.