766 research outputs found
Bregman Voronoi Diagrams: Properties, Algorithms and Applications
The Voronoi diagram of a finite set of objects is a fundamental geometric
structure that subdivides the embedding space into regions, each region
consisting of the points that are closer to a given object than to the others.
We may define many variants of Voronoi diagrams depending on the class of
objects, the distance functions and the embedding space. In this paper, we
investigate a framework for defining and building Voronoi diagrams for a broad
class of distance functions called Bregman divergences. Bregman divergences
include not only the traditional (squared) Euclidean distance but also various
divergence measures based on entropic functions. Accordingly, Bregman Voronoi
diagrams allow to define information-theoretic Voronoi diagrams in statistical
parametric spaces based on the relative entropy of distributions. We define
several types of Bregman diagrams, establish correspondences between those
diagrams (using the Legendre transformation), and show how to compute them
efficiently. We also introduce extensions of these diagrams, e.g. k-order and
k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set
of points and their connexion with Bregman Voronoi diagrams. We show that these
triangulations capture many of the properties of the celebrated Delaunay
triangulation. Finally, we give some applications of Bregman Voronoi diagrams
which are of interest in the context of computational geometry and machine
learning.Comment: Extend the proceedings abstract of SODA 2007 (46 pages, 15 figures
Käyttäjien jäljittäminen ja kannusteiden hallinta älykkäissä liikennejärjestelmissä
A system for offering incentives for ecological modes of transport is presented. The main focus is on the verification of claims of having taken a trip on such a mode of transport. Three components are presented for the task of travel mode identification: A system to select features, a means to measure a GPS (Global Positioning System) trace's similarity to a bus route, and finally a machine-learning approach to the actual identification.
Feature selection is carried out by sorting the features according to statistical significance, and eliminating correlating features. The novel features considered are skewnesses, kurtoses, auto- and cross correlations, and spectral components of speed and acceleration. Of these, only spectral components are found to be particularly useful in classification.
Bus route similarity is measured by using a novel indexing structure called MBR-tree, short for "Multiple Bounding Rectangle", to find the most similar bus traces. The MBR-tree is an expansion of the R-tree for sequences of bounding rectangles, based on an estimation method for longest common subsequence that uses such sequences. A second option of decomposing traces to sequences of direction-distance-duration-triples and indexing them in an M-tree using edit distance with real penalty is considered but shown to perform poorly.
For machine learning, the methods considered are Bayes classification, random forest, and feedforward neural networks with and without autoencoders. Autoencoder neural networks are shown to perform perplexingly poorly, but the other methods perform close to the state-of-the-art.
Methods for obfuscating the user's location, and constructing secure electronic coupons, are also discussed
Perfect Sampling for Hard Spheres from Strong Spatial Mixing
We provide a perfect sampling algorithm for the hard-sphere model on subsets of R^d with expected running time linear in the volume under the assumption of strong spatial mixing. A large number of perfect and approximate sampling algorithms have been devised to sample from the hard-sphere model, and our perfect sampling algorithm is efficient for a range of parameters for which only efficient approximate samplers were previously known and is faster than these known approximate approaches. Our methods also extend to the more general setting of Gibbs point processes interacting via finite-range, repulsive potentials
Probabilistic spatial analysis in quantitative microscopy with uncertainty-aware cell detection using deep Bayesian regression
The investigation of biological systems with three-dimensional microscopy demands automatic cell identification methods that not only are accurate but also can imply the uncertainty in their predictions. The use of deep learning to regress density maps is a popular successful approach for extracting cell coordinates from local peaks in a postprocessing step, which then, however, hinders any meaningful probabilistic output. We propose a framework that can operate on large microscopy images and output probabilistic predictions (i) by integrating deep Bayesian learning for the regression of uncertainty-aware density maps, where peak detection algorithms generate cell proposals, and (ii) by learning a mapping from prediction proposals to a probabilistic space that accurately represents the chances of a successful prediction. Using these calibrated predictions, we propose a probabilistic spatial analysis with Monte Carlo sampling. We demonstrate this in a bone marrow dataset, where our proposed methods reveal spatial patterns that are otherwise undetectable
Lane and Road Marking Detection with a High Resolution Automotive Radar for Automated Driving
Die Automobilindustrie erlebt gerade einen beispiellosen Wandel, und die Fahrerassistenz und das automatisierte Fahren spielen dabei eine entscheidende Rolle. Automatisiertes Fahren System umfasst haupts\"achlich drei Schritte: Wahrnehmung und Modellierung der Umgebung, Fahrtrichtungsplanung, und Fahrzeugsteuerung. Mit einer guten Wahrnehmung und Modellierung der Umgebung kann ein Fahrzeug Funktionen wie intelligenter Tempomat, Notbremsassistent, Spurwechselassistent, usw. erfolgreich durchf\"uhren. F\"ur Fahrfunktionen, die die Fahrpuren erkennen m\"ussen, werden gegenw\"artig ausnahmslos Kamerasensoren eingesetzt. Bei wechselnden Lichtverh\"altnissen, unzureichender Beleuchtung oder bei Sichtbehinderungen z.B. durch Nebel k\"onnen Videokameras aber empfindlich gest\"ort werden. Um diese Nachteile auszugleichen, wird in dieser Doktorarbeit eine \glqq Radar\textendash taugliche\grqq{} Fahrbahnmakierungerkennung entwickelt, mit der das Fahrzeug die Fahrspuren bei allen Lichtverh\"altnissen erkennen kann. Dazu k\"onnen bereits im Fahrzeug verbaute Radare eingesetzt werden. Die heutigen Fahrbahnmarkierungen k\"onnen mit Kamerasensoren sehr gut erfasst werden. Wegen unzureichender R\"uckstreueigenschaften der existierenden Fahrbahnmarkierungen f\"ur Radarwellen werden diese vom Radar nicht erkannt. Um dies zu bewerkstelligen, werden in dieser Arbeit die R\"uckstreueigenschaften von verschiedenen Reflektortypen, sowohl durch Simulationen als auch mit praktischen Messungen, untersucht und ein Reflektortyp vorgeschlagen, der zur Verarbeitung in heutige Fahrbahnmakierungen oder sogar f\"ur direkten Verbau in der Fahrbahn geeignet ist. Ein weiterer Schwerpunkt dieser Doktorarbeit ist der Einsatz von K\"unstliche Intelligenz (KI), um die Fahrspuren auch mit Radar zu detektieren und zu klassifizieren. Die aufgenommenen Radardaten werden mittels semantischer Segmentierung analysiert und Fahrspurverl\"aufe sowie Freifl\"achenerkennung detektiert. Gleichzeitig wird das Potential von KI\textendash tauglichen Umgebungverstehen mit bildgebenden Radardaten aufgezeigt
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