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Manifold learning: Laplacian Eigenmaps

Aug 26, 2012

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Overview. Isomap and LLELocal geometry derived from k-nearest neighborsrequire dense data points on the manifold for good estimationIsomapGlobal approachPreserve the Geodesic distanceLLELocal approachPreserve linear combination weights. Outline of lecture. Laplacian EigenmapsProblem defini

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Manifold learning: Laplacian Eigenmaps

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1. Manifold learning: Laplacian Eigenmaps

Laplacian Determinacy – A Certain Mistake

Laplacian Determinacy – A Certain Mistake. Pierre Simon Laplace - 1776: “An intelligence that knows all of the relations of the entities of the universe at one instant could state their positions, motions, and general effects any instant in the past of future. .

216 views • 1 slides

Laplacian Surface Editing

Laplacian Surface Editing. Olga Sorkine Daniel Cohen-Or Yaron Lipman Tel Aviv University Marc Alexa TU Darmstadt Christian R össl Hans-Peter Seidel Max-Planck Institut für Informatik. Differential coordinates. Intrinsic surface representation

1.34k views • 42 slides

Manifold Learning Using Geodesic Entropic Graphs

Manifold Learning Using Geodesic Entropic Graphs. Research supported in part by: ARO-DARPA MURI DAAD19-02-1-0262. Alfred O. Hero and Jose Costa Dept. EECS, Dept Biomed. Eng., Dept. Statistics University of Michigan - Ann Arbor hero@eecs.umich.edu http://www.eecs.umich.edu/~hero.

569 views • 20 slides

Fast image deconvolution using Hyper-Laplacian Prior

Fast image deconvolution using Hyper-Laplacian Prior . Dilip Krishnan Rob Fergus New york University Presented by Zhengming Xing. Outline. Introduction Algorithm Experiment result. introduction. Hyper-Laplacian Prior speed. algorithm.

477 views • 14 slides

Manifold Learning Via Homology

Manifold Learning Via Homology. Presenter: Ronen Talmon Topological Methods in Electrical Engineering and Networks January 19, 2011. Sources.

594 views • 36 slides

Compressing the Laplacian Pyramid

Compressing the Laplacian Pyramid. Georgios Georgiadis Hamidreza Khazaei March 9, 2010 EE 398A – Image and Video Compression. Introduction. Multiresolution representation of images is widely used e.g. Laplacian Pyramid (LP)

429 views • 11 slides

Lecture 13-14 Face Recognition – Subspace/Manifold Learning

EE4-62 MLCV. Lecture 13-14 Face Recognition – Subspace/Manifold Learning . Tae-Kyun Kim. EE4-62 MLCV. Face Recognition Applications. Applications include Automatic face tagging at commercial weblogs Face image retrieval in MPEG7 (our solution is MPEG7 standard)

712 views • 41 slides

Lecture 13-14 Face Recognition – Subspace/Manifold Learning

EE4-62 MLCV. Lecture 13-14 Face Recognition – Subspace/Manifold Learning . Tae-Kyun Kim. EE4-62 MLCV. Face Image Tagging and Retrieval. Face tagging at commercial weblogs Key issues User interaction for face tags Representation of a long- time accumulated data

618 views • 40 slides

 = 1.0 k = 1.26

Laplacian of Gaussian approximation.  = 1.0 k = 1.26. LoG approximation (G k - G  ) LoG. Laplacian of Gaussian approximation. Image pyramid (10 octaves). subsampling. Original image. -. =. First “octave”: 4 successive blurred image 3 corresponding DoG.

234 views • 5 slides

CHAPTER 20 LAPLACE EQUATION

CHAPTER 20 LAPLACE EQUATION. Team 6: Bhanu Kuncharam Tony Rochav Wei Lu. 20.1 Introduction. Remembering from chapter 16, the Laplacian operator (in Cartesian coordinates ): There are two types of Laplacian equations, Homogeneous

4.08k views • 71 slides

What can Manifold Enable?

What can Manifold Enable?. Manifold enables cross-disciplinary evaluations Applications   Power   Thermal   Cooling Multi-scale simulation  cycle-level to functional Tradeoff studies. Performance. Large Graphs. Energy/Power. Reliability. www.commons.wikimedia.org. imaging1.com.

258 views • 11 slides

Advanced Machine Learning &amp; Perception

Advanced Machine Learning &amp; Perception. Instructor: Tony Jebara. Topic 12. Manifold Learning (Unsupervised) Beyond Principal Components Analysis (PCA) Multidimensional Scaling (MDS) Generative Topographic Map (GTM) Locally Linear Embedding (LLE) Convex Invariance Learning (CoIL)

324 views • 17 slides

Dimensionality Reduction

Dimensionality Reduction. Haiqin Yang. Outline. Dimensionality reduction vs. manifold learning Principal Component Analysis (PCA) Kernel PCA Locally Linear Embedding (LLE) Laplacian Eigenmaps (LEM) Multidimensional Scaling (MDS) Isomap Semidefinite Embedding (SDE) Unified Framework.

513 views • 25 slides

Manifold Lab 1

Manifold Lab 1. Setting the environment Compiling/running programs. Summary. Setting manifold environment How to compile/run manifold programs Compiling/running HelloWorld program. Copy needed manifold files and some examples to your directory.

237 views • 5 slides

Manifold Learning Techniques: So which is the best?

Manifold Learning Techniques: So which is the best?. Todd Wittman Math 8600: Geometric Data Analysis Instructor: Gilad Lerman Spring 2005. Manifold Learning for Dimensionality Reduction.

706 views • 46 slides

Andrew Nealen TU Berlin Takeo Igarashi The University of Tokyo / PRESTO JST Olga Sorkine

Laplacian Mesh Optimization. Andrew Nealen TU Berlin Takeo Igarashi The University of Tokyo / PRESTO JST Olga Sorkine Marc Alexa TU Berlin. What is it ?. Overview. Motivation Problem formulation Laplacian mesh processing basics Laplacian mesh optimization framework Applications

574 views • 38 slides

Manifold Learning – from Brain Visualization to Advanced Image Processing

IMT. IMT. Intrinsic and Extrinsic means. Geodesics. Manifolds. Image Processing. Manifold Learning – from Brain Visualization to Advanced Image Processing. Manifold Learning. Diffusion Weighted MRI. Tensors. Visualization. Machine Learning. Anders Brun, PhD student

666 views • 41 slides

Manifold-Enhanced Compressive Measurement

Manifold-Enhanced Compressive Measurement. Richard Baraniuk Aswin Sankaranarayanan Chinmay Hegde. Research Highlight. 500:1. In an image classification task , exploiting manifold signal prior improves resilience to noise by 500:1 (27dB). CoM System Architecture. Why CM Works.

458 views • 35 slides

AMS TIM &amp; General Meeting TRD Integration Status Report

AMS TIM &amp; General Meeting TRD Integration Status Report. Th. Kirn I. Phys. Institute B, RWTH Aachen Houston, 23rd October 2007. TRD: Manifold and Tower Gas Tubing. TRD: Manifold and Tower Gas Tubing. TRD: Manifold and Tower Gas Tubing. TRD: Manifold and Tower Gas Tubing: Gas Tightness.

288 views • 17 slides

Manifold learning: MDS and Isomap

Manifold learning: MDS and Isomap. Manifold learning. A manifold is a topological space which is locally Euclidean. Manifold learning. A global geometric framework for nonlinear dimensionality reduction Tenenbaum JB, de Silva V., and Langford JC Science, 290: 2319–2323, 2000

847 views • 28 slides

§3.1 Laplace’s equation

§3.1 Laplace’s equation. Christopher Crawford PHY 311 2014-02-19. Outline. Overview Summary of Ch. 2 Intro to Ch. 3, Ch. 4 Laplacian – cur vature (X-ray) operator PDE’s in physics with Laplacian Laplacian in 1-d, 2-d, 3-d

452 views • 12 slides

LS1 Project

LS1 Project. Weld in dowel holes to move head over bores. Index and install new dowel hole. Remove seat rings for larger valves. Port cylinder head. Cut manifold in half for offset of heads. Flow head and manifold. With manifold cut in half, that makes porting easier. A second view.

278 views • 17 slides

More Related

Manifold learning: Laplacian Eigenmaps

Manifold learning: Laplacian Eigenmaps

Presentation Transcript

Laplacian Determinacy – A Certain Mistake

Laplacian Surface Editing

Manifold Learning Using Geodesic Entropic Graphs

Fast image deconvolution using Hyper-Laplacian Prior

Manifold Learning Via Homology

Compressing the Laplacian Pyramid

Lecture 13-14 Face Recognition – Subspace/Manifold Learning

Lecture 13-14 Face Recognition – Subspace/Manifold Learning

 = 1.0 k = 1.26

CHAPTER 20 LAPLACE EQUATION

What can Manifold Enable?

Advanced Machine Learning &amp;amp; Perception

Dimensionality Reduction

Manifold Lab 1

Manifold Learning Techniques: So which is the best?

Andrew Nealen TU Berlin Takeo Igarashi The University of Tokyo / PRESTO JST Olga Sorkine

Manifold Learning – from Brain Visualization to Advanced Image Processing

Manifold-Enhanced Compressive Measurement

AMS TIM &amp;amp; General Meeting TRD Integration Status Report

Manifold learning: MDS and Isomap

§3.1 Laplace’s equation

LS1 Project

Advanced Machine Learning & Perception

AMS TIM & General Meeting TRD Integration Status Report