Map Construction and Comparison
|
|
|
- Walter Fitzgerald
- 5 years ago
- Views:
Transcription
1 Map Construction and Comparison Using Local Structure Brittany Terese Fasy, Tulane University joint work with M. Ahmed and C. Wenk 6 February 2014 SAMSI Workshop B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
2 Introduction B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
3 Introduction B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
4 Examples Introduction B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
5 Examples Introduction Road networks: B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
6 Examples Introduction Road networks: GPS trajectories of cars. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
7 Introduction Examples Road networks: GPS trajectories of cars. Hiking paths: B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
8 Introduction Examples Road networks: GPS trajectories of cars. Hiking paths: GPS paths of people. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
9 Introduction Examples Road networks: GPS trajectories of cars. Hiking paths: GPS paths of people. Migration paths: B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
10 Introduction Examples Road networks: GPS trajectories of cars. Hiking paths: GPS paths of people. Migration paths: GPS on animals. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
11 Introduction Examples Road networks: GPS trajectories of cars. Hiking paths: GPS paths of people. Migration paths: GPS on animals. Fillaments of galaxies: B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
12 Introduction Examples Road networks: GPS trajectories of cars. Hiking paths: GPS paths of people. Migration paths: GPS on animals. Fillaments of galaxies: point cloud data. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
13 Introduction Examples Road networks: GPS trajectories of cars. Hiking paths: GPS paths of people. Migration paths: GPS on animals. Fillaments of galaxies: point cloud data. Biological systems: B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
14 Introduction Examples Road networks: GPS trajectories of cars. Hiking paths: GPS paths of people. Migration paths: GPS on animals. Fillaments of galaxies: point cloud data. Biological systems: Marron s brain vessels. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
15 Introduction Examples Road networks: GPS trajectories of cars. Hiking paths: GPS paths of people. Migration paths: GPS on animals. Fillaments of galaxies: point cloud data. Biological systems: Marron s brain vessels. Hurricane paths: B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
16 Introduction Examples Road networks: GPS trajectories of cars. Hiking paths: GPS paths of people. Migration paths: GPS on animals. Fillaments of galaxies: point cloud data. Biological systems: Marron s brain vessels. Hurricane paths: historical paths. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
17 Introduction Examples Road networks: GPS trajectories of cars. Hiking paths: GPS paths of people. Migration paths: GPS on animals. Fillaments of galaxies: point cloud data. Biological systems: Marron s brain vessels. Hurricane paths: historical paths. Networks: B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
18 Introduction Examples Road networks: GPS trajectories of cars. Hiking paths: GPS paths of people. Migration paths: GPS on animals. Fillaments of galaxies: point cloud data. Biological systems: Marron s brain vessels. Hurricane paths: historical paths. Networks: path-constrained trajectories. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
19 Part I Part I: Map Construction B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
20 Part I Road Network Representation Definition (Road Network) A road network G = (V, E) is an embedded 1-complex. Edges E represent the roads or streets and the vertices V represent the intersections. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
21 Part I Road Network Representation Definition (Road Network) A road network G = (V, E) is an embedded 1-complex. Edges E represent the roads or streets and the vertices V represent the intersections. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
22 Part I The Data GPS Trajectories street-path: p : I G noise: ε: I R 2 Definition (Link Length) The Link Lengh of a path is the number of edges in the path. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
23 Part I The Data GPS Trajectories street-path: p : I G noise: ε: I R 2 trajectory: ˆp = p + ε Definition (Link Length) The Link Lengh of a path is the number of edges in the path. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
24 Part I Trajectory Data Athens Trajectories from School Bus Data B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
25 Part I The Reconstruction Problem Problem Statement Given a set of (constrained) trajectories, extract the underlying geometric graph structure, in particular: Intersections (Vertices of degree > 2) Streets (Edges: PL paths between vertices) B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
26 Part I Existing Reconstructing Algorithms [ACCGGM-12] M. Aanjaneya, F. Chazal, D. Chen, M. Glisse, L. Guibas, and D. Morozov. Metric Graph Reconstruction from Noisy Data, [BE-12a] J. Biagioni, J. Eriksson. Map Inference in the Face of Noise and Disparity. SIGSPATIAL, [KP-12] S. Karagiorgou and D. Pfoser. On Vehicle Tracking Data-Based Road Network Generation. SIGSPATIAL, [AW-12] M. Ahmed, C. Wenk. Constructing Street Networks from GPS Trajectories. European Symp. on Algorithms, [OTHER] There were too many algorithms to cite here... B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
27 Part I Incremental Fréchet Matching [AW] Assumptions 1 A1: d F (p, ˆp) ε 2 for all trajectories ˆp. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
28 Part I Assumption A1 Trajectories are Close to Paths Definition (Fréchet Distance) d F (p, ˆp) = inf α max t d (p(t), ˆp(α(t))). Assumption A1 d F (p, ˆp) ε 2 for all trajectories ˆp. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
29 Part I Incremental Fréchet Matching [AW] Assumptions 1 A1: d F (p, ˆp) ε 2 for all trajectories ˆp. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
30 Part I Incremental Fréchet Matching [AW] Assumptions 1 A1: d F (p, ˆp) ε 2 for all trajectories ˆp. 2 A2: If two paths in G come close enough, they intersect. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
31 Part I Assumption A2 Close Paths Intersect Assumption A2 If two paths in G come close enough, they intersect. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
32 Part I Assumption A2 Close Paths Intersect Assumption A2 If two paths in G come close enough, they intersect. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
33 Part I Incremental Fréchet Matching [AW] Assumptions 1 A1: d F (p, ˆp) ε 2 for all trajectories ˆp. 2 A2: If two paths in G come close enough, they intersect. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
34 Part I Incremental Fréchet Matching [AW] Assumptions 1 A1: d F (p, ˆp) ε 2 for all trajectories ˆp. 2 A2: If two paths in G come close enough, they intersect. 3 A3: For each street s and a ball B far enough away from the endpoints of s, s B is two points. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
35 Part I Assumption A3 Roads Are Nice Assumption A3 For each street s and a ball B far enough away from the endpoints of s, s B is two points. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
36 Part I Incremental Fréchet Matching [AW] Assumptions 1 A1: d F (p, ˆp) ε 2 for all trajectories ˆp. 2 A2: If two paths in G come close enough, they intersect. 3 A3: For each street s and a ball B far enough away from the endpoints of s, s B is two points. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
37 Part I Incremental Fréchet Algorithm [AW] For each trajectory t: 1 Find the portion of the map closest to t. 2 Add edges if necessary. 3 Simplify: B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
38 Part I Incremental Fréchet Algorithm [AW] For each trajectory t: 1 Find the portion of the map closest to t. 2 Add edges if necessary. 3 Simplify: B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
39 Part I Computing the Fréchet Distance The Free Space Diagram B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
40 Part I Computing the Fréchet Distance The Free Space Diagram B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
41 Part I Computing the Fréchet Distance The Free Space Diagram B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
42 Part I Computing the Fréchet Distance The Free Space Diagram B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
43 Part I Computing the Fréchet Distance The Free Space Diagram O(mn log(mn)) using parametric search [AG-95]. O(mn log 2 (mn)) randomized approach [CW-10]. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
44 Finding Closest Match... Partial Fréchet Distance Part I Let grey region have weight 1 and white region weight 0. Find the shortest path from one end to the other under this metric. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
45 Finding Closest Match... Partial Fréchet Distance Part I Let grey region have weight 1 and white region weight 0. Find the shortest path from one end to the other under this metric. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
46 Best Match in Graph [BBW-09] Part I B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
47 Best Match in Graph [BBW-09] Part I B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
48 Best Match in Graph [BBW-09] Part I B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
49 Best Match in Graph [BBW-09] Part I B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
50 Part I Incremental Fréchet Algorithm [AW] For each trajectory t: 1 Find the portion of the map closest to t. 2 Add edges if necessary. 3 Simplify: B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
51 Adding Edges Part I B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
52 Adding Edges Part I B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
53 Part I Incremental Fréchet Algorithm [AW] For each trajectory t: 1 Find the portion of the map closest to t. 2 Add edges if necessary. 3 Simplify: B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
54 Part I Incremental Fréchet Algorithm [AW] For each trajectory t: 1 Find the portion of the map closest to t. 2 Add edges if necessary. 3 Simplify: Min-link curve simplification algorithm. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
55 Part I Dataset 1: Berlin 27,188 GPS trajectories from school buses. D = 5.2km x 6.1km. Trajectories have 7 observations on average. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
56 Dataset 1: Berlin Part I B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
57 Dataset 1: Berlin Part I B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
58 Dataset 1: Berlin Part I B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
59 Dataset 1: Berlin Part I B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
60 Part I Dataset 2: Chicago GPS trajectories from university buses. D = 7 km x 4.5 km Trajectories: samples (avg km). B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
61 Dataset 2: Chicago Part I B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
62 Dataset 2: Chicago Part I B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
63 Dataset 2: Chicago Part I B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
64 Dataset 2: Chicago Part I B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
65 Dataset 2: Chicago Part I B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
66 Part II Part II: Map Comparison B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
67 Different Approaches Part II [BE-12b] J. Biagioni, J. Eriksson. James Biagioni and Jakob Eriksson. Inferring Road Maps from GPS Traces: Survey and Comparative Evaluation. In 91st Annual Meeting of the Transportation Research Board, [AFHW-14] M. Ahmed, B. Fasy, K. Hickmann, C. Wenk. Path-Based Distance for Street Map Comparison. Arxiv. [AFW-14] M. Ahmed, B. Fasy, C. Wenk. Local Homology Based Distance Between Maps. In Submission. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
68 Path-Based Methods Part II B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
69 Path-Based Methods Part II B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
70 Path-Based Methods Part II B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
71 Path-Based Methods Part II B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
72 Path-Based Methods Part II B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
73 Part II Local Topology Approach [AFW] We will use the embedding and the local homology to create a local distance signature. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
74 Local Distance Signature Finding the Local Persistence Diagram Part II D R 2 is the compact domain. G 1 D is the road network. r > 0 is the scale. x D. LG 1 (x, 0) = (G 1 B r (x))/ B r (x) B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
75 Local Distance Signature Finding the Local Persistence Diagram Part II D R 2 is the compact domain. G 1 D is the road network. r > 0 is the scale. x D. LG 1 (x, ε) = (G 1 ε B r (x))/ B r (x) B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
76 Local Distance Signature Finding the Local Persistence Diagram Part II D R 2 is the compact domain. G 1 D is the road network. r > 0 is the scale. x D. LG 1 (x, 2ε) = (G 1 2ε B r (x))/ B r (x) B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
77 Local Distance Signature Finding the Local Persistence Diagram Part II LG 1 (x, 0) = (G 1 B r (x))/ B r (x) B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
78 Local Distance Signature Computing the Local Distance Part II (death-birth)/ (birth+death)/2 25 lhd(x, r) := W (Dgm 1 (LG 1 (x, r)), Dgm 1 (LG 2 (x, r))) B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
79 Local Distance Signature Computing the Local Distance Part II (death-birth)/ (birth+death)/2 25 lhd(x, r) := W (Dgm 1 (LG 1 (x, r)), Dgm 1 (LG 2 (x, r))) B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
80 Part II Local Topology Based Distance Definition (Local Homology Distance) d LH (G 1, G 2 ) = 1 D D lhd(x, r) dx B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
81 Part II Local Topology Based Distance Definition (Local Homology Distance) d LH (G 1, G 2 ) = 1 D r1 r 0 D lhd(x, r) dx dr B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
82 Part II Local Topology Based Distance Definition (Local Homology Distance) d LH (G 1, G 2 ) = 1 D r1 ω r r 0 D lhd(x, r) dx dr B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
83 Part II Local Topology Based Distance Definition (Local Homology Distance) d LH (G 1, G 2 ) = 1 D r1 ω r r 0 D lhd(x, r) dx dr Variants 1 D is a rectangular domain. 2 D = (G 1 G 2 ) + B δ 3 r 0 = r 1 (fixed radius) 4 r 0 = 0 = metric B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
84 Part II Local Topology Based Distance Definition (Local Homology Distance) d LH (G 1, G 2 ) = 1 D r1 ω r r 0 D lhd(x, r) dx dr Variants 1 D is a rectangular domain. 2 D = (G 1 G 2 ) + B δ 3 r 0 = r 1 (fixed radius) 4 r 0 = 0 = metric B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
85 Part II Dataset 3: Athens GPS trajectories from school buses. D = 2.6 km x 6 km Two reconstruction algorithms: [BE-12a] and [KP-12]. Trajectories: samples B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
86 Dataset 3: Athens Part II B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
87 Dataset 3: Athens Part II B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
88 Dataset 3: Athens Part II Thanks Fabrizio and Jisu! B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
89 Part II Results Athens: Comparing Two Different Reconstructions B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
90 Part II Results Athens: Comparing Two Different Reconstructions B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
91 Part II The Bootstrap... When the Ground Truth is Unknown The Bootstrap n input trajectories S n. Compute Ĝ = Ĝ(S n). B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
92 Part II The Bootstrap... When the Ground Truth is Unknown The Bootstrap n input trajectories S n. Compute Ĝ = Ĝ(S n). Find subsample Sn. Compute Ĝ = Ĝ(S n). B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
93 Part II The Bootstrap... When the Ground Truth is Unknown The Bootstrap n input trajectories S n. Compute Ĝ = Ĝ(S n). Find subsample S n. Compute Ĝ = Ĝ(S n). Repeat B times, obtaining Ĝ 1,... Ĝ B. Let T j = d LH (Ĝ, Ĝ j ). B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
94 Part II The Bootstrap... When the Ground Truth is Unknown The Bootstrap n input trajectories S n. Z α = inf{z : 1 B B I (T j > z) α} 1 Compute Ĝ = Ĝ(S n). Find subsample S n. Compute Ĝ = Ĝ(S n). Repeat B times, obtaining Ĝ 1,... Ĝ B. Let T j = d LH (Ĝ, Ĝ j ). B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
95 Part II The Bootstrap... When the Ground Truth is Unknown The Bootstrap n input trajectories S n. Z α = inf{z : 1 B B I (T j > z) α} 1 Compute Ĝ = Ĝ(S n). Find subsample S n. Compute Ĝ = Ĝ(S n). Repeat B times, obtaining Ĝ 1,... Ĝ B. Let T j = d LH (Ĝ, Ĝ j ). B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
96 Part II Ongoing Apply this to different construction algorithms versus the ground truth to rank algorithms. Implementation of distance measure. Improve theoretical guarantees. Input Model: other noise models? Output Model: road category, direction, intersection regions,... B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
97 Conclusion Summary Map Construction [AW-12] Constructing Street Networks from GPS Trajectories. Map Comparison [AFW-14] Local Homology Based Distance Between Maps. B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
98 More References Conclusion [AG-95] H. Alt, M. Godau. Computing the Frchet Distance Between Two Polygonal Curves. IJCGA, [BBW-09] K. Buchin, M. Buchin, Y. Wang. Exact Algorithms for Partial Curve Matching via the Fréchet Distance. SODA [CW-10] A. F. Cook IV, C. Wenk. Geodesic Frchet Distance Inside a Simple Polygon. ACM TALG 7(1), B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
99 Conclusion Thank You! Contact me: B. Fasy (Tulane) Map Construction and Comparison 6 Feb / 42
On Map Construction and Map Comparison
On Map Construction and Map Comparison Carola Wenk Department of Computer Science Tulane University Carola Wenk 1 GPS Trajectory Data Carola Wenk 2 GPS Trajectory Data & Roadmap Map Construction Carola
Constructing Street Networks from GPS Trajectories 1
Constructing Street Networks from GPS Trajectories 1 Mahmuda Ahmed 1 Carola Wenk 2 1 The University of Texas at San Antonio, USA 2 Tulane University, USA European Symposium on Algorithms, 2012 1 This work
Constructing Street-maps from GPS Trajectories
Constructing Street-maps from GPS Trajectories Mahmuda Ahmed, Carola Wenk The University of Texas @San Antonio Department of Computer Science Presented by Mahmuda Ahmed www.cs.utsa.edu/~mahmed Problem
Detection and approximation of linear structures in metric spaces
Stanford - July 12, 2012 MMDS 2012 Detection and approximation of linear structures in metric spaces Frédéric Chazal Geometrica group INRIA Saclay Joint work with M. Aanjaneya, D. Chen, M. Glisse, L. Guibas,
arxiv: v2 [cs.cg] 12 Jun 2014
![arxiv: v2 [cs.cg] 12 Jun 2014](/thumbs/86/94476179.jpg "arxiv: v2 [cs.cg] 12 Jun 2014")
Noname manuscript No. (will be inserted by the editor) A Comparison and Evaluation of Map Construction Algorithms Using Vehicle Tracking Data Mahmuda Ahmed Sophia Karagiorgou Dieter Pfoser Carola Wenk
Inferring Maps from GPS Data
Inferring Maps from GPS Data 1. Why infer maps from GPS traces? 2. Biagioni/Eriksson algorithm 3. Evaluation metrics 4. Similar approaches: satellite images, map update 5. Lab 4 1 2 3 OpenStreetMap Licensed
Model-Driven Matching and Segmentation of Trajectories
Model-Driven Matching and Segmentation of Trajectories Jiangwei Pan (Duke University) joint work with Swaminathan Sankararaman (Akamai Technologies) Pankaj K. Agarwal (Duke University) Thomas Mølhave (Scalable
Collaboration with: Dieter Pfoser, Computer Technology Institute, Athens, Greece Peter Wagner, German Aerospace Center, Berlin, Germany
Towards traffic-aware aware a routing using GPS vehicle trajectories Carola Wenk University of Texas at San Antonio carola@cs.utsa.edu Collaboration with: Dieter Pfoser, Computer Technology Institute,
arxiv: v1 [cs.cg] 21 Dec 2018
![arxiv: v1 [cs.cg] 21 Dec 2018](/thumbs/92/109550157.jpg "arxiv: v1 [cs.cg] 21 Dec 2018")
Distance Measures for Embedded Graphs arxiv:1812.09095v1 [cs.cg] 21 Dec 2018 Hugo A. Akitaya 1 Department of Computer Science, Tufts University, Medford, MA, USA hugo.alves_akitaya@tufts.edu Maike Buchin
Persistence stability for geometric complexes
Lake Tahoe - December, 8 2012 NIPS workshop on Algebraic Topology and Machine Learning Persistence stability for geometric complexes Frédéric Chazal Joint work with Vin de Silva and Steve Oudot (+ on-going
Statistical properties of topological information inferred from data
Saclay, July 8, 2014 DataSense Research day Statistical properties of topological information inferred from data Frédéric Chazal INRIA Saclay Joint works with B.T. Fasy (CMU), M. Glisse (INRIA), C. Labruère
Road Map Inference: A Segmentation and Grouping Framework
International Journal of Geo-Information Article Road Map Inference: A Segmentation and Grouping Framework Jia Qiu and Ruisheng Wang * Department of Geomatics Engineering, University of Calgary, 2500 University
Topological Measures of Similarity
(for curves on surfaces, mostly) Erin Wolf Chambers Saint Louis University erin.chambers@slu.edu Motivation: Measuring Similarity Between Curves How can we tell when two cycles or curves are similar to
Analyse Topologique des Données
Collège de France 31 mai 2017 Analyse Topologique des Données Frédéric Chazal DataShape team INRIA Saclay - Ile-de-France frederic.chazal@inria.fr Introduction [Shape database] [Galaxies data] [Scanned
Computational Topology in Reconstruction, Mesh Generation, and Data Analysis
Computational Topology in Reconstruction, Mesh Generation, and Data Analysis Tamal K. Dey Department of Computer Science and Engineering The Ohio State University Dey (2014) Computational Topology CCCG
Large-Scale Joint Map Matching of GPS Traces
Large-Scale Joint Map Matching of GPS Traces Yang Li Stanford University Stanford, CA, USA yangli1@stanford.edu Lin Zhang Tsinghua University Beijing, China linzhang@tsinghua.edu.cn Qixing Huang Stanford
Stability and Statistical properties of topological information inferred from metric data
Beijing, June 25, 2014 ICML workshop: Topological Methods for Machine Learning Stability and Statistical properties of topological information inferred from metric data Frédéric Chazal INRIA Saclay Introduction
Approximate Map Matching with respect to the Fréchet Distance
Approximate Map Matching with respect to the Fréchet Distance Daniel Chen Anne Driemel Leonidas J. Guibas Andy Nguyen Carola Wenk Abstract We extend recent results using curve simplification for approximating
Topological Inference via Meshing
Topological Inference via Meshing Benoit Hudson, Gary Miller, Steve Oudot and Don Sheehy SoCG 2010 Mesh Generation and Persistent Homology The Problem Input: Points in Euclidean space sampled from some
A Multicover Nerve for Geometric Inference. Don Sheehy INRIA Saclay, France
A Multicover Nerve for Geometric Inference Don Sheehy INRIA Saclay, France Computational geometers use topology to certify geometric constructions. Computational geometers use topology to certify geometric
Collision detection for Point Clouds
Collision detection for Point Clouds Gabriel Zachmann Bonn University zach@cs.uni-bonn.de Motivation Modern acquisition techniques (laser scanners) lead to modern object representation Efficient rendering
Reconstruction of Filament Structure
Reconstruction of Filament Structure Ruqi HUANG INRIA-Geometrica Joint work with Frédéric CHAZAL and Jian SUN 27/10/2014 Outline 1 Problem Statement Characterization of Dataset Formulation 2 Our Approaches
An introduction to Topological Data Analysis through persistent homology: Intro and geometric inference
Sophia-Antipolis, January 2016 Winter School An introduction to Topological Data Analysis through persistent homology: Intro and geometric inference Frédéric Chazal INRIA Saclay - Ile-de-France frederic.chazal@inria.fr
Geometric Data. Goal: describe the structure of the geometry underlying the data, for interpretation or summary
Geometric Data - ma recherche s inscrit dans le contexte de l analyse exploratoire des donnees, dont l obj Input: point cloud equipped with a metric or (dis-)similarity measure data point image/patch,
Topological Inference via Meshing
Topological Inference via Meshing Don Sheehy Theory Lunch Joint work with Benoit Hudson, Gary Miller, and Steve Oudot Computer Scientists want to know the shape of data. Clustering Principal Component
Computing and Processing Correspondences with Functional Maps
Computing and Processing Correspondences with Functional Maps SIGGRAPH 2017 course Maks Ovsjanikov, Etienne Corman, Michael Bronstein, Emanuele Rodolà, Mirela Ben-Chen, Leonidas Guibas, Frederic Chazal,
Symposium on Theoretical Aspects of Computer Science 2008 (Bordeaux), pp
Symposium on Theoretical Aspects of Computer Science 2008 (Bordeaux), pp. 193-204 www.stacs-conf.org GEODESIC FRÉCHET DISTANCE INSIDE A SIMPLE POLYGON ATLAS F. COOK IV AND CAROLA WENK Department of Computer
Estimating Geometry and Topology from Voronoi Diagrams
Estimating Geometry and Topology from Voronoi Diagrams Tamal K. Dey The Ohio State University Tamal Dey OSU Chicago 07 p.1/44 Voronoi diagrams Tamal Dey OSU Chicago 07 p.2/44 Voronoi diagrams Tamal Dey
New Results on the Stability of Persistence Diagrams
New Results on the Stability of Persistence Diagrams Primoz Skraba Jozef Stefan Institute TAGS - Linking Topology to Algebraic Geometry and Statistics joint work with Katharine Turner and D. Yogeshwaran
Statistical topological data analysis using. Persistence landscapes
Motivation Persistence landscape Statistical topological data analysis using persistence landscapes Cleveland State University February 3, 2014 funded by AFOSR Motivation Persistence landscape Topological
Data Skeletonization via Reeb Graphs
Data Skeletonization via Reeb Graphs Xiaoyin Ge Issam Safa Mikhail Belkin Yusu Wang Abstract Recovering hidden structure from complex and noisy non-linear data is one of the most fundamental problems in
Open Problems Column Edited by William Gasarch
Open Problems Column Edited by William Gasarch 1 This Issues Column! This issue s Open Problem Column is by Brittany Terese Fasy and Bei Wang and is on Open Problems in Computational Topology; however,
Automatic Extraction of Road Networks from GPS Traces
Automatic Extraction of Road Networks from GPS Traces A road map inference method that generates road network from GPS traces through point segmentation and grouping. Jia Qiu, Department of Geomatics Engineering,
Applications of Geometric Spanner
Title: Name: Affil./Addr. 1: Affil./Addr. 2: Affil./Addr. 3: Keywords: SumOriWork: Applications of Geometric Spanner Networks Joachim Gudmundsson 1, Giri Narasimhan 2, Michiel Smid 3 School of Information
Topological Perspectives On Stratification Learning
Topological Perspectives On Stratification Learning Bei Wang School of Computing Scientific Computing and Imaging Institute (SCI) University of Utah www.sci.utah.edu/~beiwang August 9, 2018 Talk Overview
arxiv: v1 [cs.cg] 2 Mar 2018
![arxiv: v1 [cs.cg] 2 Mar 2018](/thumbs/94/118050065.jpg "arxiv: v1 [cs.cg] 2 Mar 2018")
A fast implementation of near neighbors queries for Fréchet distance (GIS Cup) Julian Baldus Karl Bringmann arxiv:1803.00806v1 [cs.cg] 2 Mar 2018 Abstract This paper describes an implementation of fast
R Package TDA for Statistical Inference on Topological Data Analysis and Lessons from its Maintenance
R Package TDA for Statistical Inference on Topological Data Analysis and Lessons from its Maintenance Jisu KIM Carnege Mellon University October 11, 2018 1 / 59 R Package TDA for Statistical Inference
Introduction to the R package TDA
Introduction to the R package TDA Brittany T. Fasy Computer Science Department,Tulane University Jisu Kim arxiv:1411.1830v2 [cs.ms] 29 Jan 2015 Abstract Department of Statistics, Carnegie Mellon University
Trajectory analysis. Ivan Kukanov
Trajectory analysis Ivan Kukanov Joensuu, 2014 Semantic Trajectory Mining for Location Prediction Josh Jia-Ching Ying Tz-Chiao Weng Vincent S. Tseng Taiwan Wang-Chien Lee Wang-Chien Lee USA Copyright 2011
Clustering algorithms and introduction to persistent homology
Foundations of Geometric Methods in Data Analysis 2017-18 Clustering algorithms and introduction to persistent homology Frédéric Chazal INRIA Saclay - Ile-de-France frederic.chazal@inria.fr Introduction
arxiv: v1 [cs.cg] 25 Jul 2013
![arxiv: v1 [cs.cg] 25 Jul 2013](/thumbs/76/73277084.jpg "arxiv: v1 [cs.cg] 25 Jul 2013")
APPLIED SIMILARITY PROBLEMS USING FRÉCHET DISTANCE arxiv:1307.6628v1 [cs.cg] 25 Jul 2013 by Kaveh Shahbaz A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the
Stratified Structure of Laplacian Eigenmaps Embedding
Stratified Structure of Laplacian Eigenmaps Embedding Abstract We construct a locality preserving weight matrix for Laplacian eigenmaps algorithm used in dimension reduction. Our point cloud data is sampled
What is Network Analyst?
What is Network Analyst? Extension for analyzing transportation networks Four network solvers Route Closest Facility Service Area Uses Network Datasets Origin-Destination (OD) Cost Matrix Specialized layers
Random Simplicial Complexes
Random Simplicial Complexes Duke University CAT-School 2015 Oxford 10/9/2015 Part III Extensions & Applications Contents Morse Theory for the Distance Function Persistent Homology and Maximal Cycles Contents
Correctness. The Powercrust Algorithm for Surface Reconstruction. Correctness. Correctness. Delaunay Triangulation. Tools - Voronoi Diagram
Correctness The Powercrust Algorithm for Surface Reconstruction Nina Amenta Sunghee Choi Ravi Kolluri University of Texas at Austin Boundary of a solid Close to original surface Homeomorphic to original
Automatic Generation and Validation of Road Maps from GPS Trajectory Data Sets
Automatic Generation and Validation of Road Maps from GPS Trajectory Data Sets Hengfeng Li, Lars Kulik, Kotagiri Ramamohanarao Department of Computing and Information Systems The University of Melbourne
Knowledge-Based Trajectory Completion from Sparse GPS Samples
Knowledge-Based Trajectory Completion from Sparse GPS Samples Yang Li, Yangyan Li, Dimitrios Gunopulos 2, and Leonidas Guibas Stanford University, 2 University of Athens {yangli,yangyan,guibas}@stanford.edu,
Scanning Real World Objects without Worries 3D Reconstruction
Scanning Real World Objects without Worries 3D Reconstruction 1. Overview Feng Li 308262 Kuan Tian 308263 This document is written for the 3D reconstruction part in the course Scanning real world objects
Map Matching with Inverse Reinforcement Learning
Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence Map Matching with Inverse Reinforcement Learning Takayuki Osogami and Rudy Raymond IBM Research - Tokyo 5-6-52
A Geometric Perspective on Sparse Filtrations
CCCG 2015, Kingston, Ontario, August 10 12, 2015 A Geometric Perspective on Sparse Filtrations Nicholas J. Cavanna Mahmoodreza Jahanseir Donald R. Sheehy Abstract We present a geometric perspective on
Computing the Fréchet Distance Between Simple Polygons
Computing the Fréchet Distance Between Simple Polygons Kevin Buchin a,1, Maike Buchin a,1 and Carola Wenk b,2 a Institute of Computer Science, Freie Universität Berlin, Takustraße 9, D-14195 Berlin, Germany
Tutorial on the R package TDA
Tutorial on the R package TDA Jisu Kim Brittany T. Fasy, Jisu Kim, Fabrizio Lecci, Clément Maria, Vincent Rouvreau Abstract This tutorial gives an introduction to the R package TDA, which provides some
Computing the Fréchet Distance Between Folded Polygons 1
Computing the Fréchet Distance Between Folded Polygons 1 Atlas F. Cook IV 2, Anne Driemel 3, Sariel Har-Peled 4, Jessica Sherette 5, Carola Wenk 5 Abstract. We present the first results showing that the
Computational Geometry Learning
Computational Geometry Learning Jean-Daniel Boissonnat Frédéric Chazal Geometrica, INRIA http://www-sop.inria.fr/geometrica Lectures at MPRI MPRI Computational Geometry Learning Lectures at MPRI 1 / 14
Computational Statistics and Mathematics for Cyber Security
and Mathematics for Cyber Security David J. Marchette Sept, 0 Acknowledgment: This work funded in part by the NSWC In-House Laboratory Independent Research (ILIR) program. NSWCDD-PN--00 Topics NSWCDD-PN--00
Simulation of a mobile robot with a LRF in a 2D environment and map building
Simulation of a mobile robot with a LRF in a 2D environment and map building Teslić L. 1, Klančar G. 2, and Škrjanc I. 3 1 Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, 1000 Ljubljana,
Learning and Recognizing Visual Object Categories Without First Detecting Features
Learning and Recognizing Visual Object Categories Without First Detecting Features Daniel Huttenlocher 2007 Joint work with D. Crandall and P. Felzenszwalb Object Category Recognition Generic classes rather
Data Analysis, Persistent homology and Computational Morse-Novikov theory
Data Analysis, Persistent homology and Computational Morse-Novikov theory Dan Burghelea Department of mathematics Ohio State University, Columbuus, OH Bowling Green, November 2013 AMN theory (computational
Optimal Segmentation and Understanding of Motion Capture Data
Optimal Segmentation and Understanding of Motion Capture Data Xiang Huang, M.A.Sc Candidate Department of Electrical and Computer Engineering McMaster University Supervisor: Dr. Xiaolin Wu 7 Apr, 2005
Isotopic Fréchet Distance
CCCG 2011, Toronto ON, August 10 12, 2011 Isotopic Fréchet Distance Erin W. Chambers Tao Ju David Letscher Lu Liu Abstract We present a variant of the Fréchet distance (as well as geodesic and homotopic
Deliverable 2.1 Data Management I Deliverable lead contractor: CTI
Creating a Data Mart for Floating Car Data COOP-CT-2006-032823 Co-operative Research Projects, FP6 Deliverable 2.1 Data Management I Deliverable lead contractor: CTI Sotiris Brakatsoulas, CTI Dieter Pfoser,
Package TDA. December 9, 2017
Type Package Package TDA December 9, 2017 Title Statistical Tools for Topological Data Analysis Version 1.6 Date 2017-12-09 Author Brittany T. Fasy, Jisu Kim, Fabrizio Lecci, Clement Maria, Vincent Rouvreau.
A Multicover Nerve for Geometric Inference
A Multicover Nerve for Geometric Inference Donald R. Sheehy Abstract We show that filtering the barycentric decomposition of a Čech complex by the cardinality of the vertices captures precisely the topology
Networks in GIS. Geometric Network. Network Dataset. Utilities and rivers One-way flow. Traffic data 2-way flow Multi-modal data
Unit 6: Networks Networks in GIS Model the flow of resources Consist of a set of connected centers or junctions (ArcGIS) displayed as points. Junctions are connected by links, or edges (ArcGIS) displayed
Trajectory Clustering using a Variation of Fréchet Distance
Trajectory Clustering using a Variation of Fréchet Distance by Vafa Khoshaein Thesis submitted to the Faculty of Graduate and Postdoctoral Studies In partial fulfillment of the requirements For the MCS
A fast and robust algorithm to count topologically persistent holes in noisy clouds
A fast and robust algorithm to count topologically persistent holes in noisy clouds Vitaliy Kurlin Durham University Department of Mathematical Sciences, Durham, DH1 3LE, United Kingdom vitaliy.kurlin@gmail.com,
Fractional Cascading in Wireless. Jie Gao Computer Science Department Stony Brook University
Fractional Cascading in Wireless Sensor Networks Jie Gao Computer Science Department Stony Brook University 1 Sensor Networks Large number of small devices for environment monitoring 2 My recent work Lightweight,
Optimal transport and redistricting: numerical experiments and a few questions. Nestor Guillen University of Massachusetts
Optimal transport and redistricting: numerical experiments and a few questions Nestor Guillen University of Massachusetts From Rebecca Solnit s Hope in the dark (apropos of nothing in particular) To hope
Planning in Mobile Robotics
Planning in Mobile Robotics Part I. Miroslav Kulich Intelligent and Mobile Robotics Group Gerstner Laboratory for Intelligent Decision Making and Control Czech Technical University in Prague Tuesday 26/07/2011
DS504/CS586: Big Data Analytics Data Management Prof. Yanhua Li
Welcome to DS504/CS586: Big Data Analytics Data Management Prof. Yanhua Li Time: 6:00pm 8:50pm R Location: KH 116 Fall 2017 First Grading for Reading Assignment Weka v 6 weeks v https://weka.waikato.ac.nz/dataminingwithweka/preview
Curriculum Vitae Tim Ophelders last updated: September 12, 2018
Curriculum Vitae Tim Ophelders last updated: September 12, 2018 Personal Information Name Citizenship T. A. E. (Tim) Ophelders Dutch Work Address Email Department of Computational Mathematics, Science
Shape analysis through geometric distributions
Shape analysis through geometric distributions Nicolas Charon (CIS, Johns Hopkins University) joint work with B. Charlier (Université de Montpellier), I. Kaltenmark (CMLA), A. Trouvé, Hsi-Wei Hsieh (JHU)...
A roadmap for the computation of persistent homology
A roadmap for the computation of persistent homology Nina Otter Mathematical Institute, University of Oxford (joint with Mason A. Porter, Ulrike Tillmann, Peter Grindrod, Heather A. Harrington) 2nd School
Map Inference in the Face of Noise and Disparity
Map Inference in the Face of Noise and Disparity James Biagioni Dept. Computer Science University of Illinois at Chicago jbiagi1@uic.edu Jakob Eriksson Dept. Computer Science University of Illinois at
Mining Sub-trajectory Cliques to Find Frequent Routes (Technical Report)
Mining Sub-trajectory Cliques to Find Frequent Routes (Technical Report) Htoo Htet Aung, Long Guo and Kian-Lee Tan School of Computing, National University of Singapore Abstract. Knowledge of the routes
Markov Networks in Computer Vision. Sargur Srihari
Markov Networks in Computer Vision Sargur srihari@cedar.buffalo.edu 1 Markov Networks for Computer Vision Important application area for MNs 1. Image segmentation 2. Removal of blur/noise 3. Stereo reconstruction
Medial Scaffolds for 3D data modelling: status and challenges. Frederic Fol Leymarie
Medial Scaffolds for 3D data modelling: status and challenges Frederic Fol Leymarie Outline Background Method and some algorithmic details Applications Shape representation: From the Medial Axis to the
Polygonal representation of 3D urban terrain point-cloud data
Polygonal representation of 3D urban terrain point-cloud data part I Borislav Karaivanov The research is supported by ARO MURI 23 February 2011 USC 1 Description of problem Assumptions: unstructured 3D
Topological Data Analysis Workshop February 3-7, 2014
Topological Data Analysis Workshop February 3-7, 2014 SPEAKER TITLES/ABSTRACTS Yuliy Baryshnikov University of Illinois What is the Dimension of the Internet? The large-scale structure of the Internet
Smallest Intersecting Circle for a Set of Polygons
Smallest Intersecting Circle for a Set of Polygons Peter Otfried Joachim Christian Marc Esther René Michiel Antoine Alexander 31st August 2005 1 Introduction Motivated by automated label placement of groups
Observing Information: Applied Computational Topology.
Observing Information: Applied Computational Topology. Bangor University, and NUI Galway April 21, 2008 What is the geometric information that can be gleaned from a data cloud? Some ideas either already
STRAW - An integrated mobility & traffic model for vehicular ad-hoc networks
STRAW - An integrated mobility & traffic model for vehicular ad-hoc networks David R. Choffnes & Fabián E. Bustamante Department of Computer Science, Northwestern University www.aqualab.cs.northwestern.edu
Automated transportation transfer detection using GPS enabled smartphones
2012 15th International IEEE Conference on Intelligent Transportation Systems Anchorage, Alaska, USA, September 16-19, 2012 Automated transportation transfer detection using GPS enabled smartphones Leon
Benchmarking Trajectory Matchers with SUMO
Benchmarking Trajectory Matchers with SUMO Dr. Jakob Erdmann Dr. Rüdiger Ebendt Institute of Transportation Systems German Aerospace Center 12489, Berlin Germany E-mail: Jakob.erdmann@dlr.de KEYWORDS Trajectory
Homology and Persistent Homology Bootcamp Notes 2017
Homology and Persistent Homology Bootcamp Notes Summer@ICERM 2017 Melissa McGuirl September 19, 2017 1 Preface This bootcamp is intended to be a review session for the material covered in Week 1 of Summer@ICERM
Simplicial Hyperbolic Surfaces
Simplicial Hyperbolic Surfaces Talk by Ken Bromberg August 21, 2007 1-Lipschitz Surfaces- In this lecture we will discuss geometrically meaningful ways of mapping a surface S into a hyperbolic manifold
3D Reconstruction from Scene Knowledge
Multiple-View Reconstruction from Scene Knowledge 3D Reconstruction from Scene Knowledge SYMMETRY & MULTIPLE-VIEW GEOMETRY Fundamental types of symmetry Equivalent views Symmetry based reconstruction MUTIPLE-VIEW
Geometric Learning and Topological Inference with Biobotic Networks: Convergence Analysis
1 Geometric Learning and opological Inference with Biobotic Networks: Convergence Analysis Alireza Dirafzoon 1, Alper Bozkurt 1, and Edgar Lobaton 1 arxiv:167.51v1 [cs.ro] 3 Jun 216 Abstract In this study,
Detect tracking behavior among trajectory data
Detect tracking behavior among trajectory data Jianqiu Xu, Jiangang Zhou Nanjing University of Aeronautics and Astronautics, China, jianqiu@nuaa.edu.cn, jiangangzhou@nuaa.edu.cn Abstract. Due to the continuing
Epipolar geometry-based ego-localization using an in-vehicle monocular camera
Epipolar geometry-based ego-localization using an in-vehicle monocular camera Haruya Kyutoku 1, Yasutomo Kawanishi 1, Daisuke Deguchi 1, Ichiro Ide 1, Hiroshi Murase 1 1 : Nagoya University, Japan E-mail:
Advanced Robotics Path Planning & Navigation
Advanced Robotics Path Planning & Navigation 1 Agenda Motivation Basic Definitions Configuration Space Global Planning Local Planning Obstacle Avoidance ROS Navigation Stack 2 Literature Choset, Lynch,
Stochastic Multiresolution Persistent Homology Kernel
Stochastic Multiresolution Persistent Homology Kernel Xiaojin Zhu, Ara Vartanian, Manish Bansal, Duy Nguyen, Luke Brandl Department of Computer Sciences, University of Wisconsin Madison 1210 W. Dayton
CrowdPath: A Framework for Next Generation Routing Services using Volunteered Geographic Information
CrowdPath: A Framework for Next Generation Routing Services using Volunteered Geographic Information Abdeltawab M. Hendawi, Eugene Sturm, Dev Oliver, Shashi Shekhar hendawi@cs.umn.edu, sturm049@umn.edu,
Subtrajectory Clustering: Models and Algorithms
Subtrajectory Clustering: Models and Algorithms Pankaj K. Agarwal Duke University pankaj@cs.duke.edu Abhinandan Nath Duke University abhinath@cs.duke.edu Kyle Fox The University of Texas at Dallas kyle.fox@utdallas.edu
arxiv: v1 [stat.ml] 29 Nov 2016
![arxiv: v1 [stat.ml] 29 Nov 2016](/thumbs/75/72309393.jpg "arxiv: v1 [stat.ml] 29 Nov 2016")
Probabilistic map-matching using particle filters Kira Kempinska 1, Toby Davies 1 and John Shawe-Taylor 2 arxiv:1611.09706v1 [stat.ml] 29 Nov 2016 1 Department of Security and Crime Science, University
CRF Based Point Cloud Segmentation Jonathan Nation
CRF Based Point Cloud Segmentation Jonathan Nation jsnation@stanford.edu 1. INTRODUCTION The goal of the project is to use the recently proposed fully connected conditional random field (CRF) model to
Package TDA. April 27, 2017
Type Package Package TDA April 27, 2017 Title Statistical Tools for Topological Data Analysis Version 1.5.1 Date 2017-04-27 Author Brittany T. Fasy, Jisu Kim, Fabrizio Lecci, Clement Maria, Vincent Rouvreau.
Statistical Inference for Topological Data Analysis
Statistical Inference for Topological Data Analysis PhD Thesis Proposal Fabrizio Lecci Department of Statistics Carnegie Mellon University Thesis Committe Jessi Cisewski Frederic Chazal Alessandro Rinaldo
DS504/CS586: Big Data Analytics Data Pre-processing and Cleaning Prof. Yanhua Li
Welcome to DS504/CS586: Big Data Analytics Data Pre-processing and Cleaning Prof. Yanhua Li Time: 6:00pm 8:50pm R Location: AK 232 Fall 2016 The Data Equation Oceans of Data Ocean Biodiversity Informatics,
for a Fleet of Driverless Vehicles
for a Fleet of Driverless Vehicles Olivier Mehani olivier.mehani@inria.fr La Route Automatisée A -Mines Paris/INRIA Rocquencourt- Joint Research Unit February 14, 2007 Eurocast 2007 Plan 1 2 3 Solution