Spatial snow water equivalent estimation for mountainous areas using wireless-sensor networks and remote-sensing products

We developed an approach to estimate snow water equivalent (SWE) through interpolation of spatially representative point measurements using a k-nearest neighbors (k-NN) algorithm and historical spatial SWE data. It accurately reproduced measured SWE, using different data sources for training and evaluation. In the central-Sierra American River basin, we used a k-NN algorithm to interpolate data from continuous snow-depth measurements in 10 sensor clusters by fusing them with 14 years of daily 500-m resolution SWE-reconstruction maps. Accurate SWE estimation over the melt season shows the potential for providing daily, near real-time distributed snowmelt estimates. Further south, in the Merced-Tuolumne basins, we evaluated the potential of k-NN approach to improve real-time SWE estimates. Lacking dense ground-measurement networks, we simulated k-NN interpolation of sensor data using selected pixels of a bi-weekly Lidar-derived snow water equivalent product. k-NN extrapolations underestimate the Lidar-derived SWE, with a maximum bias of −10 cm at elevations below 3000 m and +15 cm above 3000 m. This bias was reduced by using a Gaussian-process regression model to spatially distribute residuals. Using as few as 10 scenes of Lidar-derived SWE from 2014 as training data in the k-NN to estimate the 2016 spatial SWE, both RMSEs and MAEs were reduced from around 20–25 cm to 10–15 cm comparing to using SWE reconstructions as training data. We found that the spatial accuracy of the historical data is more important for learning the spatial distribution of SWE than the number of historical scenes available. Blending continuous spatially representative ground-based sensors with a historical library of SWE reconstructions over the same basin can provide real-time spatial SWE maps that accurately represents Lidar-measured snow depth; and the estimates can be improved by using historical Lidar scans instead of SWE reconstructions

Découverte automatique de structures musicales en temps réel par la géométrie de l'information

National audienceThis master's thesis aims at exploring the challenge of automatically retrieving musical structures within an audio file. Our main contribution is to formulate this well-studied problem in the frame- work of computational information geometry, an emerging field at the frontier between statistics, differential geometry, and data mining. In this framework, we unify the fundamental tasks of event segmentation and similarity computing in a single sequential scheme for structure discovery. Furthermore, we propose an original metric on temporal segments, which combines several criteria of geometrical comparability : divergence between centroids, as well as inclusion and intersection ratios of corresponding information balls.Ce rapport de fin de stage vise à explorer la découverte automatique de structures musicales dans un fichier audio. Notre contribution principale est de formuler ce problème dans le cadre de la géométrie de l'information computationnelle, une disci- pline émergente mêlant statistiques, géométrie différentielle, et fouille de données. Nous y rassemblons la segmentation en évènements mu- sicaux et le calcul de leurs similarités en un seul schéma séquentiel de structuration. De plus, nous proposons une métrique originale entre segments temporels, qui combine plusieurs critères de ressemblance géométrique : divergence entre centroïdes, mais aussi rapports d'inclusion et d'intersection entre les boules informationnelles associées

Efficient Bregman Range Search

We develop an algorithm for efficient range search when the notion of dissimilarity is given by a Bregman divergence. The range search task is to return all points in a potentially large database that are within some specified distance of a query. It arises in many learning algorithms such as locally-weighted regression, kernel density estimation, neighborhood graph-based algorithms, and in tasks like outlier detection and information retrieval. In metric spaces, efficient range search-like algorithms based on spatial data structures have been deployed on a variety of statistical tasks. Here we describe an algorithm for range search for an arbitrary Bregman divergence. This broad class of dissimilarity measures includes the relative entropy, Mahalanobis distance, Itakura-Saito divergence, and a variety of matrix divergences. Metric methods cannot be directly applied since Bregman divergences do not in general satisfy the triangle inequality. We derive geometric properties of Bregman divergences that yield an efficient algorithm for range search based on a recently proposed space decomposition for Bregman divergences.