Experimental Evaluation of Latent Variable Models. for Dimensionality Reduction


 Kerry Anthony
 2 years ago
 Views:
Transcription
1 Experimental Evaluation of Latent Variable Models for Dimensionality Reduction Miguel Á. CarreiraPerpiñán and Steve Renals a Dept. of Computer Science, University of Sheffield th IEEE Signal Processing Society Workshop on Neural Networks for Signal Processing (NNSP8) Aug. Sep., 8, Cambridge, UK a This work has been supported by a scholarship from the Spanish Ministry of Education and Science, by a ESPRIT Long Term Research Project SPRACH (77) and by an award from the Nuffield Foundation.
2 Electropalatography (EPG) A plastic pseudopalate fitted to a person s mouth detects the presence or absence of contact between the tongue and the palate in 6 different locations during an utterance (sampled at Hz). Result: sequence of 6dimensional binary EPG frames. Data reduction necessary, traditionally via fixed linear indices. ACCORII database: synchronised data (EPG, acoustic, etc.) for different utterances and speakers. The mapping phonemetoepg is not onetoone, e.g. / or /. Miguel Á. CarreiraPerpiñán and Steve Renals Experimental Evaluation of Latent Variable Models for Dimensionality Reduction
3 Electropalatography (cont.) wires to PC lips palate teeth teeth wires to PC teeth teeth lips velum palate electrodes velum electrodes Pseudopalate and representative EPGs for the typical stable phase of different phonemes. Miguel Á. CarreiraPerpiñán and Steve Renals Experimental Evaluation of Latent Variable Models for Dimensionality Reduction
4 NNSP8, AUG. SEP., 8, CARIDGE, UK  The Reading pseudopalate. Sfrag replacements EXPERIMENTAL EVALUATION OF LATENT VARIABLE MODELS FOR DIMENSIONALITY REDUCTION
5 Latent variable models Prior p(x) Induced p(t Θ) t x x f f(x; Θ) t Manifold M t t x Latent space of dimension L = Data space of dimension D = Marginalisation in latent space: p(t) = p(t x)p(x) dx. Maximum likelihood parameter estimation: l(θ) = N n= log p(t n Θ). Inverse mapping given by informative point (mean, mode) of posterior: p(x t) = p(t x)p(x) p(t). Miguel Á. CarreiraPerpiñán and Steve Renals Experimental Evaluation of Latent Variable Models for Dimensionality Reduction
6 Examples of latent variable models Factor analysis: prior is normal N (, I), mapping is linear, noise model is normal with diagonal covariance matrix. : like but noise model has isotropic covariance. : prior is uniform over discrete latent grid, mapping is a generalised linear model, noise model is normal with isotropic covariance matrix. Mixtures of factor analysers (one mean parameter and one factor per analyser, noise model covariance matrix common to all analysers). We also tried mixtures of multivariate Bernoulli distributions (not really a latent variable model). All these models can be trained via an EM algorithm. Miguel Á. CarreiraPerpiñán and Steve Renals Experimental Evaluation of Latent Variable Models for Dimensionality Reduction
7 Factors / prototypes (speaker RK) λ λ λ λ λ 5 λ 6 λ 7 λ 8 λ λ λ λ λ λ 5 λ 6 λ 7 λ 8 λ λ λ λ λ λ 5 λ 6 λ 7 λ 8 λ λ λ λ λ 5 λ 6 λ 7 λ 8 λ M Λ µ π =. Λ µ π =. Λ µ π =. Λ µ π =.7 p π =.5 p π =. p π =.7 p π =. p 5 π 5 =.5 p 6 π 6 =. p 7 π 7 =. p 8 π 8 =.5 p π =. Miguel Á. CarreiraPerpiñán and Steve Renals Experimental Evaluation of Latent Variable Models for Dimensionality Reduction 5
8 and reconstruction error (speaker RK) Training set Test set x 5 5 x M M Squared reconstruction error M M Miguel Á. CarreiraPerpiñán and Steve Renals Experimental Evaluation of Latent Variable Models for Dimensionality Reduction 6
9 ! " #,. # ) *,+  %, Twodimensional representation (speaker RK) Factor analysis frag replacements Factor Factor Factor Factor Trajectory in latent space of the highlighted utterance fragment I prefer Kant to Hobbes for a good bedtime book ( #(! " $&% /. ). Miguel Á. CarreiraPerpiñán and Steve Renals Experimental Evaluation of Latent Variable Models for Dimensionality Reduction 7
10 Conclusions Adaptive methods outperform fixed data reduction indices. and performed similarly in terms of likelihood. Mixtures of factor analysers and multivariate Bernoulli distributions did not perform well. Twodimensional outperformed all other methods in terms of likelihood and error reconstruction and reveals nonlinear structure in the data. This suggests a low intrinsic dimensionality for the EPG data. Additional results available via the web at miguel/research/epg.html Miguel Á. CarreiraPerpiñán and Steve Renals Experimental Evaluation of Latent Variable Models for Dimensionality Reduction 8
11 Factors / prototypes (speaker HD) λ λ λ λ λ 5 λ 6 λ 7 λ 8 λ λ λ λ λ λ 5 λ 6 λ 7 λ 8 λ λ λ λ λ λ 5 λ 6 λ 7 λ 8 λ λ λ λ λ 5 λ 6 λ 7 λ 8 λ M Λ µ π =. Λ µ π =.6 Λ µ π =. Λ µ π =.6 p π =. p π =. p π =. p π =. p 5 π 5 =. p 6 π 6 =.7 p 7 π 7 =. p 8 π 8 =.7 p π =. Miguel Á. CarreiraPerpiñán and Steve Renals Experimental Evaluation of Latent Variable Models for Dimensionality Reduction
12 and reconstruction error (speaker HD) Training set Test set Squared reconstruction error x M M 6 6 x M M Miguel Á. CarreiraPerpiñán and Steve Renals Experimental Evaluation of Latent Variable Models for Dimensionality Reduction
13 ! " #,. # ) *,+  %, Twodimensional representation (speaker HD) Factor analysis 7 frag replacements Factor Factor Factor Factor Trajectory in latent space of the highlighted utterance fragment I prefer Kant to Hobbes for a good bedtime book ( #(! " $&% /. ). Miguel Á. CarreiraPerpiñán and Steve Renals Experimental Evaluation of Latent Variable Models for Dimensionality Reduction
14 !!! # ) *,+  %,!! " #,. Discontinuities in latent space (speaker RK) Factor analysis.5.8 Factor Frame 5 Frame Factor Frame 7 Selected subsequence of the utterance fragment I prefer Kant to Hobbes for a good bedtime book ( #! " $ % /. ). The abrupt transition from to (frames 5 6) produces a discontinuity in latent space. Miguel Á. CarreiraPerpiñán and Steve Renals Experimental Evaluation of Latent Variable Models for Dimensionality Reduction
15 factors before and after varimax rotation (speaker HD) BEFORE λ λ λ λ λ 5 λ 6 λ 7 λ 8 λ AFTER λ λ λ λ λ 5 λ 6 λ 7 λ 8 λ Both sets of components span the same linear subspace, but the varimaxrotated one is more easily interpretable. Miguel Á. CarreiraPerpiñán and Steve Renals Experimental Evaluation of Latent Variable Models for Dimensionality Reduction
Experimental Evaluation of Latent Variable Models for Dimensionality Reduction
In: Proc. of the 18 IEEE Signal Processing Society Workshop on Neural Networks for Signal Processing (NNSP8), pp.517, Cambridge, UK. URL: http://www.dcs.shef.ac.uk/ miguel/papers/nnsp8.html Experimental
More informationExperimental Evaluation of Latent Variable Models for Dimensionality Reduction
Experimental Evaluation of Latent Variable Models for Dimensionality Reduction Miguel A. CarreiraPerpiiian Steve Renals Dept. of Computer Science, University of Sheffield, Sheffield S1 4DP, UK {M.Carreira,S.Renals}@dcs.shef.ac.uk
More informationSpeech Recognition Lecture 8: Acoustic Models. Eugene Weinstein Google, NYU Courant Institute Slide Credit: Mehryar Mohri
Speech Recognition Lecture 8: Acoustic Models. Eugene Weinstein Google, NYU Courant Institute eugenew@cs.nyu.edu Slide Credit: Mehryar Mohri Speech Recognition Components Acoustic and pronunciation model:
More informationThe Laplacian Eigenmaps Latent Variable Model
The Laplacian Eigenmaps Latent Variable Model with applications to articulated pose tracking Miguel Á. CarreiraPerpiñán EECS, UC Merced http://faculty.ucmerced.edu/mcarreiraperpinan Articulated pose
More informationClustering Lecture 5: Mixture Model
Clustering Lecture 5: Mixture Model Jing Gao SUNY Buffalo 1 Outline Basics Motivation, definition, evaluation Methods Partitional Hierarchical Densitybased Mixture model Spectral methods Advanced topics
More informationMonocular Human Motion Capture with a Mixture of Regressors. Ankur Agarwal and Bill Triggs GRAVIRINRIACNRS, Grenoble, France
Monocular Human Motion Capture with a Mixture of Regressors Ankur Agarwal and Bill Triggs GRAVIRINRIACNRS, Grenoble, France IEEE Workshop on Vision for HumanComputer Interaction, 21 June 2005 Visual
More informationTrajectory Inverse Kinematics By Conditional Density Models
Trajectory Inverse Kinematics By Conditional Density Models Chao Qin and Miguel Á. CarreiraPerpiñán EECS, School of Engineering, UC Merced ICRA 08, Pasadena 1 Introduction Robot arm inverse kinematics
More informationNote Set 4: Finite Mixture Models and the EM Algorithm
Note Set 4: Finite Mixture Models and the EM Algorithm Padhraic Smyth, Department of Computer Science University of California, Irvine Finite Mixture Models A finite mixture model with K components, for
More informationClustering Kmeans. Machine Learning CSEP546 Carlos Guestrin University of Washington February 18, Carlos Guestrin
Clustering Kmeans Machine Learning CSEP546 Carlos Guestrin University of Washington February 18, 2014 Carlos Guestrin 20052014 1 Clustering images Set of Images [Goldberger et al.] Carlos Guestrin 20052014
More informationProblem 1 (20 pt) Answer the following questions, and provide an explanation for each question.
Problem 1 Answer the following questions, and provide an explanation for each question. (5 pt) Can linear regression work when all X values are the same? When all Y values are the same? (5 pt) Can linear
More informationThe Kmodes and Laplacian Kmodes algorithms for clustering
The Kmodes and Laplacian Kmodes algorithms for clustering Miguel Á. CarreiraPerpiñán Electrical Engineering and Computer Science University of California, Merced http://faculty.ucmerced.edu/mcarreiraperpinan
More informationPattern Recognition. Kjell Elenius. Speech, Music and Hearing KTH. March 29, 2007 Speech recognition
Pattern Recognition Kjell Elenius Speech, Music and Hearing KTH March 29, 2007 Speech recognition 2007 1 Ch 4. Pattern Recognition 1(3) Bayes Decision Theory MinimumErrorRate Decision Rules Discriminant
More informationTime Series Analysis by State Space Methods
Time Series Analysis by State Space Methods Second Edition J. Durbin London School of Economics and Political Science and University College London S. J. Koopman Vrije Universiteit Amsterdam OXFORD UNIVERSITY
More informationMachine Learning. B. Unsupervised Learning B.1 Cluster Analysis. Lars SchmidtThieme, Nicolas Schilling
Machine Learning B. Unsupervised Learning B.1 Cluster Analysis Lars SchmidtThieme, Nicolas Schilling Information Systems and Machine Learning Lab (ISMLL) Institute for Computer Science University of Hildesheim,
More information22 October, 2012 MVA ENS Cachan. Lecture 5: Introduction to generative models Iasonas Kokkinos
Machine Learning for Computer Vision 1 22 October, 2012 MVA ENS Cachan Lecture 5: Introduction to generative models Iasonas Kokkinos Iasonas.kokkinos@ecp.fr Center for Visual Computing Ecole Centrale Paris
More informationLocally Linear Landmarks for largescale manifold learning
Locally Linear Landmarks for largescale manifold learning Max Vladymyrov and Miguel Á. CarreiraPerpiñán Electrical Engineering and Computer Science University of California, Merced http://eecs.ucmerced.edu
More informationMachine Learning A W 1sst KU. b) [1 P] Give an example for a probability distributions P (A, B, C) that disproves
Machine Learning A 708.064 11W 1sst KU Exercises Problems marked with * are optional. 1 Conditional Independence I [2 P] a) [1 P] Give an example for a probability distribution P (A, B, C) that disproves
More informationSemiSupervised Construction of General Visualization Hierarchies
SemiSupervised Construction of General Visualization Hierarchies Peter Tiňo Yi Sun Ian Nabney Aston University, Aston Triangle, Birmingham, B4 7ET United Kingdom Abstract We have recently developed a
More informationSelforganizing mixture models
Selforganizing mixture models Jakob Verbeek, Nikos Vlassis, Ben Krose To cite this version: Jakob Verbeek, Nikos Vlassis, Ben Krose. Selforganizing mixture models. Neurocomputing / EEG Neurocomputing,
More informationGenerative and discriminative classification techniques
Generative and discriminative classification techniques Machine Learning and Category Representation 20142015 Jakob Verbeek, November 28, 2014 Course website: http://lear.inrialpes.fr/~verbeek/mlcr.14.15
More informationCSC 411: Lecture 14: Principal Components Analysis & Autoencoders
CSC 411: Lecture 14: Principal Components Analysis & Autoencoders Raquel Urtasun & Rich Zemel University of Toronto Nov 4, 2015 Urtasun & Zemel (UofT) CSC 411: 14PCA & Autoencoders Nov 4, 2015 1 / 18
More informationLearning a Manifold as an Atlas Supplementary Material
Learning a Manifold as an Atlas Supplementary Material Nikolaos Pitelis Chris Russell School of EECS, Queen Mary, University of London [nikolaos.pitelis,chrisr,lourdes]@eecs.qmul.ac.uk Lourdes Agapito
More informationConstrained Hidden Markov Models
Constrained Hidden Markov Models Sam Roweis roweis@gatsby.ucl.ac.uk Gatsby Unit, University College London Abstract By thinking of each state in a hidden Markov model as corresponding to some spatial region
More informationClustering algorithms
Clustering algorithms Machine Learning Hamid Beigy Sharif University of Technology Fall 1393 Hamid Beigy (Sharif University of Technology) Clustering algorithms Fall 1393 1 / 22 Table of contents 1 Supervised
More informationCSC 411: Lecture 14: Principal Components Analysis & Autoencoders
CSC 411: Lecture 14: Principal Components Analysis & Autoencoders Richard Zemel, Raquel Urtasun and Sanja Fidler University of Toronto Zemel, Urtasun, Fidler (UofT) CSC 411: 14PCA & Autoencoders 1 / 18
More informationGaussian Process Latent Variable Models for Visualisation of High Dimensional Data
Gaussian Process Latent Variable Models for Visualisation of High Dimensional Data Neil D. Lawrence Department of Computer Science University of Sheffield Regent Court, 211 Portobello Street, Sheffield,
More informationRobust cartogram visualization of outliers in manifold learning
Robust cartogram visualization of outliers in manifold learning Alessandra Tosi 1 and Alfredo Vellido 1 1 Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Edifici Omega, Campus
More information10701/15781, Fall 2006, Final
7/78, Fall 6, Final Dec, :pm8:pm There are 9 questions in this exam ( pages including this cover sheet). If you need more room to work out your answer to a question, use the back of the page and clearly
More informationVariational Autoencoders. Sargur N. Srihari
Variational Autoencoders Sargur N. srihari@cedar.buffalo.edu Topics 1. Generative Model 2. Standard Autoencoder 3. Variational autoencoders (VAE) 2 Generative Model A variational autoencoder (VAE) is a
More informationDeep Generative Models Variational Autoencoders
Deep Generative Models Variational Autoencoders Sudeshna Sarkar 5 April 2017 Generative Nets Generative models that represent probability distributions over multiple variables in some way. Directed Generative
More informationMixture Models and the EM Algorithm
Mixture Models and the EM Algorithm Padhraic Smyth, Department of Computer Science University of California, Irvine c 2017 1 Finite Mixture Models Say we have a data set D = {x 1,..., x N } where x i is
More informationHierarchical Gaussian Process Latent Variable Models
Neil D. Lawrence neill@cs.man.ac.uk School of Computer Science, University of Manchester, Kilburn Building, Oxford Road, Manchester, M13 9PL, U.K. Andrew J. Moore A.Moore@dcs.shef.ac.uk Dept of Computer
More informationAudioVisual Speech Activity Detection
Institut für Technische Informatik und Kommunikationsnetze Semester Thesis at the Department of Information Technology and Electrical Engineering AudioVisual Speech Activity Detection Salome Mannale Advisors:
More information( ) =cov X Y = W PRINCIPAL COMPONENT ANALYSIS. Eigenvectors of the covariance matrix are the principal components
Review Lecture 14 ! PRINCIPAL COMPONENT ANALYSIS Eigenvectors of the covariance matrix are the principal components 1. =cov X Top K principal components are the eigenvectors with K largest eigenvalues
More informationDiscriminative training and Feature combination
Discriminative training and Feature combination Steve Renals Automatic Speech Recognition ASR Lecture 13 16 March 2009 Steve Renals Discriminative training and Feature combination 1 Overview Hot topics
More informationSpatial Outlier Detection
Spatial Outlier Detection ChangTien Lu Department of Computer Science Northern Virginia Center Virginia Tech Joint work with Dechang Chen, Yufeng Kou, Jiang Zhao 1 Spatial Outlier A spatial data point
More informationA New Manifold Representation for Visual Speech Recognition
A New Manifold Representation for Visual Speech Recognition Dahai Yu, Ovidiu Ghita, Alistair Sutherland, Paul F. Whelan School of Computing & Electronic Engineering, Vision Systems Group Dublin City University,
More informationSegmentation: Clustering, Graph Cut and EM
Segmentation: Clustering, Graph Cut and EM Ying Wu Electrical Engineering and Computer Science Northwestern University, Evanston, IL 60208 yingwu@northwestern.edu http://www.eecs.northwestern.edu/~yingwu
More informationAn Efficient Model Selection for Gaussian Mixture Model in a Bayesian Framework
IEEE SIGNAL PROCESSING LETTERS, VOL. XX, NO. XX, XXX 23 An Efficient Model Selection for Gaussian Mixture Model in a Bayesian Framework Ji Won Yoon arxiv:37.99v [cs.lg] 3 Jul 23 Abstract In order to cluster
More informationHybrid QuasiMonte Carlo Method for the Simulation of State Space Models
The Tenth International Symposium on Operations Research and Its Applications (ISORA 211) Dunhuang, China, August 28 31, 211 Copyright 211 ORSC & APORC, pp. 83 88 Hybrid QuasiMonte Carlo Method for the
More informationBo#leneck Features from SNR Adap9ve Denoising Deep Classifier for Speaker Iden9fica9on
Bo#leneck Features from SNR Adap9ve Denoising Deep Classifier for Speaker Iden9fica9on TAN Zhili & MAK ManWai APSIPA 2015 Department of Electronic and Informa2on Engineering The Hong Kong Polytechnic
More informationStatistical Techniques in Robotics (16831, F12) Lecture#05 (Wednesday, September 12) Mapping
Statistical Techniques in Robotics (16831, F12) Lecture#05 (Wednesday, September 12) Mapping Lecturer: Alex Styler (in for Drew Bagnell) Scribe: Victor Hwang 1 1 Occupancy Mapping When solving the localization
More informationSMEM Algorithm for Mixture Models
LETTER Communicated by Christopher Bishop SMEM Algorithm for Mixture Models Naonori Ueda Ryohei Nakano NTT Communication Science Laboratories, Hikaridai, Seikacho, Sorakugun, Kyoto 6190237 Japan Zoubin
More informationMachine Learning. B. Unsupervised Learning B.1 Cluster Analysis. Lars SchmidtThieme
Machine Learning B. Unsupervised Learning B.1 Cluster Analysis Lars SchmidtThieme Information Systems and Machine Learning Lab (ISMLL) Institute for Computer Science University of Hildesheim, Germany
More informationCIS 520, Machine Learning, Fall 2015: Assignment 7 Due: Mon, Nov 16, :59pm, PDF to Canvas [100 points]
CIS 520, Machine Learning, Fall 2015: Assignment 7 Due: Mon, Nov 16, 2015. 11:59pm, PDF to Canvas [100 points] Instructions. Please write up your responses to the following problems clearly and concisely.
More informationTight Clusters and Smooth Manifolds with the Harmonic Topographic Map.
Proceedings of the th WSEAS Int. Conf. on SIMULATION, MODELING AND OPTIMIZATION, Corfu, Greece, August 9, (pp8) Tight Clusters and Smooth Manifolds with the Harmonic Topographic Map. MARIAN PEÑA AND
More informationECE521: Week 11, Lecture March 2017: HMM learning/inference. With thanks to Russ Salakhutdinov
ECE521: Week 11, Lecture 20 27 March 2017: HMM learning/inference With thanks to Russ Salakhutdinov Examples of other perspectives Murphy 17.4 End of Russell & Norvig 15.2 (Artificial Intelligence: A Modern
More informationGrundlagen der Künstlichen Intelligenz
Grundlagen der Künstlichen Intelligenz Unsupervised learning Daniel Hennes 29.01.2018 (WS 2017/18) University Stuttgart  IPVS  Machine Learning & Robotics 1 Today Supervised learning Regression (linear
More informationPictorial Structures for Object Recognition
Pictorial Structures for Object Recognition Felzenszwalb and Huttenlocher Presented by Stephen Krotosky Pictorial Structures Introduced by Fischler and Elschlager in 1973 Objects are modeled by a collection
More informationMETRIC PLANE RECTIFICATION USING SYMMETRIC VANISHING POINTS
METRIC PLANE RECTIFICATION USING SYMMETRIC VANISHING POINTS M. Lefler, H. HelOr Dept. of CS, University of Haifa, Israel Y. HelOr School of CS, IDC, Herzliya, Israel ABSTRACT Video analysis often requires
More informationSplit Merge Incremental LEarning (SMILE) of Mixture Models
Split Merge Incremental LEarning (SMILE of Mixture Models Konstantinos Blekas and Isaac E. Lagaris Department of Computer Science, University of Ioannina, 45 Ioannina, Greece {kblekas,lagaris}@cs.uoi.gr
More informationRandom projection for nongaussian mixture models
Random projection for nongaussian mixture models Győző Gidófalvi Department of Computer Science and Engineering University of California, San Diego La Jolla, CA 92037 gyozo@cs.ucsd.edu Abstract Recently,
More informationClustering Kmeans. Machine Learning CSEP546 Carlos Guestrin University of Washington February 18, Carlos Guestrin
Clustering Kmeans Machine Learning CSEP546 Carlos Guestrin University of Washington February 18, 2014 Carlos Guestrin 20052014 1 Clustering images Set of Images [Goldberger et al.] Carlos Guestrin 20052014
More informationNonlinear Image Interpolation using Manifold Learning
Nonlinear Image Interpolation using Manifold Learning Christoph Bregler Computer Science Division University of California Berkeley, CA 94720 bregler@cs.berkeley.edu Stephen M. Omohundro'" Int. Computer
More informationAssignment 2. Unsupervised & Probabilistic Learning. Maneesh Sahani Due: Monday Nov 5, 2018
Assignment 2 Unsupervised & Probabilistic Learning Maneesh Sahani Due: Monday Nov 5, 2018 Note: Assignments are due at 11:00 AM (the start of lecture) on the date above. he usual College late assignments
More informationAutomatic Singular Spectrum Analysis for TimeSeries Decomposition
Automatic Singular Spectrum Analysis for TimeSeries Decomposition A.M. ÁlvarezMeza and C.D. AcostaMedina and G. CastellanosDomínguez Universidad Nacional de Colombia, Signal Processing and Recognition
More informationLec 08 Feature Aggregation II: Fisher Vector, Super Vector and AKULA
Image Analysis & Retrieval CS/EE 5590 Special Topics (Class Ids: 44873, 44874) Fall 2016, M/W 45:15pm@Bloch 0012 Lec 08 Feature Aggregation II: Fisher Vector, Super Vector and AKULA Zhu Li Dept of CSEE,
More informationProbabilistic Facial Feature Extraction Using Joint Distribution of Location and Texture Information
Probabilistic Facial Feature Extraction Using Joint Distribution of Location and Texture Information Mustafa Berkay Yilmaz, Hakan Erdogan, Mustafa Unel Sabanci University, Faculty of Engineering and Natural
More informationWarped Mixture Models
Warped Mixture Models Tomoharu Iwata, David Duvenaud, Zoubin Ghahramani Cambridge University Computational and Biological Learning Lab March 11, 2013 OUTLINE Motivation Gaussian Process Latent Variable
More informationExperimental Analysis of GTM
Experimental Analysis of GTM Elias Pampalk In the past years many different data mining techniques have been developed. The goal of the seminar KosiceVienna is to compare some of them to determine which
More informationLast week. MultiFrame Structure from Motion: MultiView Stereo. Unknown camera viewpoints
Last week MultiFrame Structure from Motion: MultiView Stereo Unknown camera viewpoints Last week PCA Today Recognition Today Recognition Recognition problems What is it? Object detection Who is it? Recognizing
More informationPart I. Hierarchical clustering. Hierarchical Clustering. Hierarchical clustering. Produces a set of nested clusters organized as a
Week 9 Based in part on slides from textbook, slides of Susan Holmes Part I December 2, 2012 Hierarchical Clustering 1 / 1 Produces a set of nested clusters organized as a Hierarchical hierarchical clustering
More informationDeep Mixtures of Factor Analysers
Yichuan Tang tang@cs.toronto.edu Ruslan Salakhutdinov rsalakhu@cs.toronto.edu Geoffrey Hinton hinton@cs.toronto.edu Department of Computer Science, University of Toronto, Toronto, Ontario, CANADA Abstract
More informationESTIMATING HEAD POSE WITH AN RGBD SENSOR: A COMPARISON OF APPEARANCEBASED AND POSEBASED LOCAL SUBSPACE METHODS
ESTIMATING HEAD POSE WITH AN RGBD SENSOR: A COMPARISON OF APPEARANCEBASED AND POSEBASED LOCAL SUBSPACE METHODS Donghun Kim, Johnny Park, and Avinash C. Kak Robot Vision Lab, School of Electrical and
More informationCS839: Probabilistic Graphical Models. Lecture 10: Learning with Partially Observed Data. Theo Rekatsinas
CS839: Probabilistic Graphical Models Lecture 10: Learning with Partially Observed Data Theo Rekatsinas 1 Partially Observed GMs Speech recognition 2 Partially Observed GMs Evolution 3 Partially Observed
More informationUnsupervised Learning
Unsupervised Learning Learning without Class Labels (or correct outputs) Density Estimation Learn P(X) given training data for X Clustering Partition data into clusters Dimensionality Reduction Discover
More informationFACE RECOGNITION USING INDEPENDENT COMPONENT
Chapter 5 FACE RECOGNITION USING INDEPENDENT COMPONENT ANALYSIS OF GABORJET (GABORJETICA) 5.1 INTRODUCTION PCA is probably the most widely used subspace projection technique for face recognition. A major
More information08 An Introduction to Dense Continuous Robotic Mapping
NAVARCH/EECS 568, ROB 530  Winter 2018 08 An Introduction to Dense Continuous Robotic Mapping Maani Ghaffari March 14, 2018 Previously: Occupancy Grid Maps Pose SLAM graph and its associated dense occupancy
More informationMultipose lipreading and audiovisual speech recognition
RESEARCH Open Access Multipose lipreading and audiovisual speech recognition Virginia Estellers * and JeanPhilippe Thiran Abstract In this article, we study the adaptation of visual and audiovisual
More informationarxiv: v1 [condmat.disnn] 30 Dec 2018
A General Deep Learning Framework for Structure and Dynamics Reconstruction from Time Series Data arxiv:1812.11482v1 [condmat.disnn] 30 Dec 2018 Zhang Zhang, Jing Liu, Shuo Wang, Ruyue Xin, Jiang Zhang
More informationApplication of Principal Components Analysis and Gaussian Mixture Models to Printer Identification
Application of Principal Components Analysis and Gaussian Mixture Models to Printer Identification Gazi. Ali, PeiJu Chiang Aravind K. Mikkilineni, George T. Chiu Edward J. Delp, and Jan P. Allebach School
More informationEnergy Based Models, Restricted Boltzmann Machines and Deep Networks. Jesse Eickholt
Energy Based Models, Restricted Boltzmann Machines and Deep Networks Jesse Eickholt ???? Who s heard of Energy Based Models (EBMs) Restricted Boltzmann Machines (RBMs) Deep Belief Networks Autoencoders
More informationPassive Differential Matchedfield Depth Estimation of Moving Acoustic Sources
Lincoln Laboratory ASAP2001 Workshop Passive Differential Matchedfield Depth Estimation of Moving Acoustic Sources Shawn Kraut and Jeffrey Krolik Duke University Department of Electrical and Computer
More informationThe Multi Stage Gibbs Sampling: Data Augmentation Dutch Example
The Multi Stage Gibbs Sampling: Data Augmentation Dutch Example Rebecca C. Steorts Bayesian Methods and Modern Statistics: STA 360/601 Module 8 1 Example: Data augmentation / Auxiliary variables A commonlyused
More informationDeveloping a Data Driven System for Computational Neuroscience
Developing a Data Driven System for Computational Neuroscience Ross Snider and Yongming Zhu Montana State University, Bozeman MT 59717, USA Abstract. A data driven system implies the need to integrate
More informationOverview of machine learning
Overview of machine learning Kevin P. Murphy Last updated November 26, 2007 1 Introduction In this Chapter, we provide a brief overview of the most commonly studied problems and solution methods within
More informationThesis Proposal : Switching Linear Dynamic Systems with Higherorder Temporal Structure. Sang Min Oh
Thesis Proposal : Switching Linear Dynamic Systems with Higherorder Temporal Structure Sang Min Oh sangmin@cc.gatech.edu 28th May 2008 Contents 1 Introduction 1 1.1 Automated Temporal Sequence Analysis.................................
More informationSGN (4 cr) Chapter 11
SGN41006 (4 cr) Chapter 11 Clustering Jussi Tohka & Jari Niemi Department of Signal Processing Tampere University of Technology February 25, 2014 J. Tohka & J. Niemi (TUTSGN) SGN41006 (4 cr) Chapter
More informationStraight Lines and Hough
09/30/11 Straight Lines and Hough Computer Vision CS 143, Brown James Hays Many slides from Derek Hoiem, Lana Lazebnik, Steve Seitz, David Forsyth, David Lowe, FeiFei Li Project 1 A few project highlights
More informationDATA MINING LECTURE 7. Hierarchical Clustering, DBSCAN The EM Algorithm
DATA MINING LECTURE 7 Hierarchical Clustering, DBSCAN The EM Algorithm CLUSTERING What is a Clustering? In general a grouping of objects such that the objects in a group (cluster) are similar (or related)
More informationRecognition: Face Recognition. Linda Shapiro EE/CSE 576
Recognition: Face Recognition Linda Shapiro EE/CSE 576 1 Face recognition: once you ve detected and cropped a face, try to recognize it Detection Recognition Sally 2 Face recognition: overview Typical
More informationData Mining Chapter 3: Visualizing and Exploring Data Fall 2011 Ming Li Department of Computer Science and Technology Nanjing University
Data Mining Chapter 3: Visualizing and Exploring Data Fall 2011 Ming Li Department of Computer Science and Technology Nanjing University Exploratory data analysis tasks Examine the data, in search of structures
More informationStatistical Techniques in Robotics (STR, S15) Lecture#05 (Monday, January 26) Lecturer: Byron Boots
Statistical Techniques in Robotics (STR, S15) Lecture#05 (Monday, January 26) Lecturer: Byron Boots Mapping 1 Occupancy Mapping When solving the localization problem, we had a map of the world and tried
More informationMixture Models and EM
Table of Content Chapter 9 Mixture Models and EM means Clustering Gaussian Mixture Models (GMM) Expectation Maximiation (EM) for Mixture Parameter Estimation Introduction Mixture models allows Complex
More informationMAXIMUM LIKELIHOOD ESTIMATION USING ACCELERATED GENETIC ALGORITHMS
In: Journal of Applied Statistical Science Volume 18, Number 3, pp. 1 7 ISSN: 10675817 c 2011 Nova Science Publishers, Inc. MAXIMUM LIKELIHOOD ESTIMATION USING ACCELERATED GENETIC ALGORITHMS Füsun Akman
More informationNeural Networks for Machine Learning. Lecture 15a From Principal Components Analysis to Autoencoders
Neural Networks for Machine Learning Lecture 15a From Principal Components Analysis to Autoencoders Geoffrey Hinton Nitish Srivastava, Kevin Swersky Tijmen Tieleman Abdelrahman Mohamed Principal Components
More informationLocal Linear Embedding. Katelyn Stringer ASTR 689 December 1, 2015
Local Linear Embedding Katelyn Stringer ASTR 689 December 1, 2015 Idea Behind LLE Good at making nonlinear highdimensional data easier for computers to analyze Example: A highdimensional surface Think
More informationAdaptation of a mixture of multivariate Bernoulli distributions
Adaptation of a mixture of multivariate Bernoulli distributions Content areas: Transfer, Adaptation, Multitask Learning; Sensor Networks Abstract The mixture of multivariate Bernoulli distributions (MMB)
More informationSPARSE COMPONENT ANALYSIS FOR BLIND SOURCE SEPARATION WITH LESS SENSORS THAN SOURCES. Yuanqing Li, Andrzej Cichocki and Shunichi Amari
SPARSE COMPONENT ANALYSIS FOR BLIND SOURCE SEPARATION WITH LESS SENSORS THAN SOURCES Yuanqing Li, Andrzej Cichocki and Shunichi Amari Laboratory for Advanced Brain Signal Processing Laboratory for Mathematical
More informationTreebased Cluster Weighted Modeling: Towards A Massively Parallel Real Time Digital Stradivarius
Treebased Cluster Weighted Modeling: Towards A Massively Parallel Real Time Digital Stradivarius Edward S. Boyden III e@media.mit.edu Physics and Media Group MIT Media Lab 0 Ames St. Cambridge, MA 039
More informationMSA220  Statistical Learning for Big Data
MSA220  Statistical Learning for Big Data Lecture 13 Rebecka Jörnsten Mathematical Sciences University of Gothenburg and Chalmers University of Technology Clustering Explorative analysis  finding groups
More informationFacial Expression Detection Using Implemented (PCA) Algorithm
Facial Expression Detection Using Implemented (PCA) Algorithm Dileep Gautam (M.Tech Cse) Iftm University Moradabad Up India Abstract: Facial expression plays very important role in the communication with
More information3D Human Motion Analysis and Manifolds
D E P A R T M E N T O F C O M P U T E R S C I E N C E U N I V E R S I T Y O F C O P E N H A G E N 3D Human Motion Analysis and Manifolds Kim Steenstrup Pedersen DIKU Image group and EScience center Motivation
More informationData Preprocessing. Javier Béjar. URL  Spring 2018 CS  MAI 1/78 BY: $\
Data Preprocessing Javier Béjar BY: $\ URL  Spring 2018 C CS  MAI 1/78 Introduction Data representation Unstructured datasets: Examples described by a flat set of attributes: attributevalue matrix Structured
More informationRectification and Distortion Correction
Rectification and Distortion Correction Hagen Spies March 12, 2003 Computer Vision Laboratory Department of Electrical Engineering Linköping University, Sweden Contents Distortion Correction Rectification
More informationSTA 4273H: Stascal Machine Learning
STA 4273H: Stascal Machine Learning Russ Salakhutdinov Department of Statistics! rsalakhu@utstat.toronto.edu! h0p://www.cs.toronto.edu/~rsalakhu/ Lecture 3 Parametric Distribu>ons We want model the probability
More informationSingle Particle Reconstruction Techniques
T H E U N I V E R S I T Y of T E X A S S C H O O L O F H E A L T H I N F O R M A T I O N S C I E N C E S A T H O U S T O N Single Particle Reconstruction Techniques For students of HI 6001125 Computational
More informationGuide for inversion of noisy magnetic field using FFT
Guide for inversion of noisy magnetic field using FFT Eitan Levin Alexander Y. Meltzer August 29, 216 In this note, we explain how to use the code packages MagInverter2D and MagInverter1D to invert noisy
More informationThis leads to our algorithm which is outlined in Section III, along with a tabular summary of it's performance on several benchmarks. The last section
An Algorithm for Incremental Construction of Feedforward Networks of Threshold Units with Real Valued Inputs Dhananjay S. Phatak Electrical Engineering Department State University of New York, Binghamton,
More informationt 1 y(x;w) x 2 t 2 t 3 x 1
Neural Computing Research Group Dept of Computer Science & Applied Mathematics Aston University Birmingham B4 7ET United Kingdom Tel: +44 (0)121 333 4631 Fax: +44 (0)121 333 4586 http://www.ncrg.aston.ac.uk/
More information