The Spatial LASSO With Applications to Unmixing Hyperspectral Biomedical Images

Hyperspectral imaging (HSI) is a spectroscopic method that uses densely sampled measurements along the electromagnetic spectrum to identify the unique molecular composition of an object. Traditionally HSI has been associated with remote sensing-type applications, but recently has found increased use in biomedicine, from investigations at the cellular to the tissue level. One of the main challenges in the analysis of HSI is estimating the proportions, also called abundance fractions of each of the molecular signatures. While there is great promise for HSI in the area of biomedicine, large variability in the measurements and artifacts related to the instrumentation has slow adoption into more widespread practice. In this article, we propose a novel regularization and variable selection method called the spatial LASSO (SPLASSO). The SPLASSO incorporates spatial information via a graph Laplacian-based penalty to help improve the model estimation process for multivariate response data. We show the strong performance of this approach on a benchmark HSI dataset with considerable improvement in predictive accuracy over the standard LASSO. Supplementary materials for this article are available online.     

Apparent power-law distributions in animal movements can arise from intraspecific interactions

Lévy flights have gained prominence for analysis of animal movement. In a Lévy flight, step-lengths are drawn from a heavy-tailed distribution such as a power law (PL), and a large number of empirical demonstrations have been published. Others, however, have suggested that animal movement is ill fit by PL distributions or contend a state-switching process better explains apparent Lévy flight movement patterns. We used a mix of direct behavioural observations and GPS tracking to understand step-length patterns in females of two related butterflies. We initially found movement in one species (Euphydryas editha taylori) was best fit by a bounded PL, evidence of a Lévy flight, while the other (Euphydryas phaeton) was best fit by an exponential distribution. Subsequent analyses introduced additional candidate models and used behavioural observations to sort steps based on intraspecific interactions (interactions were rare in E. phaeton but common in E. e. taylori). These analyses showed a mixed-exponential is favoured over the bounded PL for E. e. taylori and that when step-lengths were sorted into states based on the influence of harassing conspecific males, both states were best fit by simple exponential distributions. The direct behavioural observations allowed us to infer the underlying behavioural mechanism is a state-switching process driven by intraspecific interactions rather than a Lévy flight.