Machine Learning. Classification, Discriminative learning. Marc Toussaint University of Stuttgart Summer 2014
|
|
- Hannah Newton
- 5 years ago
- Views:
Transcription
1 Machine Learning Classification, Discriminative learning Structured output, structured input, discriminative function, joint input-output features, Likelihood Maximization, Logistic regression, binary & multi-class case, conditional random fields Marc Toussaint University of Stuttgart Summer 24
2 Structured Output & Structured Input regression: R n R structured output: R n binary class label {, } R n integer class label {, 2,.., M} R n sequence labelling y :T R n image labelling y :W,:H R n graph labelling y :N structured input: relational database R labelled graph/sequence R 2/3
3 Examples for Structured Output Text tagging X = sentence Y = tagging of each word Image segmentation X = image Y = labelling of each pixel Depth estimation X = single image Y = depth map 3/3
4 CRFs in image processing 4/3
5 CRFs in image processing Google conditional random field image Multiscale Conditional Random Fields for Image Labeling (CVPR 24) Scale-Invariant Contour Completion Using Conditional Random Fields (ICCV 25) Conditional Random Fields for Object Recognition (NIPS 24) Image Modeling using Tree Structured Conditional Random Fields (IJCAI 27) A Conditional Random Field Model for Video Super-resolution (ICPR 26) 5/3
6 From Regression to Structured Output Our first step in regression was to define f : R n R as we defined a loss function derived optimal parameters β f(x) = φ(x) β How could we represent a discrete-valued function F : R n Y? 6/3
7 From Regression to Structured Output Our first step in regression was to define f : R n R as we defined a loss function derived optimal parameters β f(x) = φ(x) β How could we represent a discrete-valued function F : R n Y? Discriminative Function 6/3
8 Discriminative Function Represent a discrete-valued function F : R n Y via a discriminative function f : R n Y R such that F : x argmax y f(x, y) A discriminative function f(x, y) maps an input x to an output ŷ(x) = argmax f(x, y) y A discriminative function f(x, y) has high value if y is a correct answer to x; and low value if y is a false answer In that way a discriminative function e.g. discriminates correct sequence/image/graph-labelling from wrong ones 7/3
9 Example Discriminative Function Input: x R 2 ; output y {, 2, 3} displayed are p(y = x), p(y =2 x), p(y =3 x) (here already scaled to the interval [,]... explained later) 8/3
10 How could we parameterize a discriminative function? Well, linear in features! f(x, y) = k j= φ j(x, y)β j = φ(x, y) β Example: Let x R and y {, 2, 3}. Typical features might be φ(x, y) = [y = ] x [y = 2] x [y = 3] x [y = ] x 2 [y = 2] x 2 [y = 3] x 2 Example: Let x, y {, } be both discrete. Features might be φ(x, y) = [x = ][y = ] [x = ][y = ] [x = ][y = ] [x = ][y = ] 9/3
11 more intuition... Features connect input and output. Each φ j (x, y) allows f to capture a certain dependence between x and y If both x and y are discrete, a feature φ j (x, y) is typically a joint indicator function (logical function), indicating a certain event Each weight β j mirrors how important/frequent/infrequent a certain dependence described by φ j (x, y) is f(x) is also called energy, and the following methods are also called energy-based modelling, esp. in neural modelling /3
12 In the remainder: Logistic regression: binary case Multi-class case Preliminary comments on the general structured output case (Conditional Random Fields) /3
13 Logistic regression: Binary case 2/3
14 Binary classification example (MT/plot.h -> gnuplot pipe) 3 train decision boundary Input x R 2 Output y {, } Example shows RBF Ridge Logistic Regression 3/3
15 A loss function for classification Data D = {(x i, y i )} n i= with x i R d and y i {, } Bad idea: Squared error regression (See also Hastie 4.2) 4/3
16 A loss function for classification Data D = {(x i, y i )} n i= with x i R d and y i {, } Bad idea: Squared error regression (See also Hastie 4.2) Maximum likelihood: We interpret the discriminative function f(x, y) as defining class probabilities p(y x) = ef(x,y) y ef(x,y ) p(y x) should be high for the correct class, and low otherwise 4/3
17 A loss function for classification Data D = {(x i, y i )} n i= with x i R d and y i {, } Bad idea: Squared error regression (See also Hastie 4.2) Maximum likelihood: We interpret the discriminative function f(x, y) as defining class probabilities p(y x) = ef(x,y) y ef(x,y ) p(y x) should be high for the correct class, and low otherwise For each (x i, y i ) we want to maximize the likelihood p(y i x i ): L neg-log-likelihood (β) = n i= log p(y i x i ) 4/3
18 Logistic regression In the binary case, we have two functions f(x, ) and f(x, ). W.l.o.g. we may fix f(x, ) = to zero. Therefore we choose features φ(x, y) = [y = ] φ(x) with arbitrary input features φ(x) R k We have and conditional class probabilities else ŷ = argmax f(x, y) = y if φ(x) β > p( x) = with the logistic sigmoid function σ(z) = e f(x,) = σ(f(x, )) e f(x,) + ef(x,) ez =. +e z e z + exp(x)/(+exp(x)) Given data D = {(x i, y i)} n i=, we minimize L logistic (β) = n i= log p(yi xi) + λ β 2 = [ ] n i= y i log p( x i ) + ( y i ) log[ p( x i )] + λ β 2 5/3
19 Optimal parameters β Gradient (see exercises): n = i= (p i y i )φ(x i ) + 2λIβ = X (p y) + 2λIβ, L logistic (β) β p i := p(y = x i ), X = L logistic (β) β φ(x ). φ(x n ) R n k is non-linear in β (it enters also the calculation of p i ) does not have analytic solution 6/3
20 Optimal parameters β Gradient (see exercises): n = i= (p i y i )φ(x i ) + 2λIβ = X (p y) + 2λIβ, L logistic (β) β p i := p(y = x i ), X = L logistic (β) β φ(x ). φ(x n ) R n k is non-linear in β (it enters also the calculation of p i ) does not have analytic solution Newton algorithm: iterate β β H - L logistic (β) β with Hessian H = 2 L logistic (β) β = X W X + 2λI 2 W diagonal with W ii = p i ( p i ) 6/3
21 RBF ridge logistic regression: 3 (MT/plot.h -> gnuplot pipe) train decision boundary /x.exe -mode 2 -modelfeaturetype 4 -lambda e+ -rbfbias -rbfwidth.2 7/3
22 polynomial (cubic) logistic regression: 3 (MT/plot.h -> gnuplot pipe) train decision boundary /x.exe -mode 2 -modelfeaturetype 3 -lambda e+ 8/3
23 Recap: Classification Regression parameters β predictive function f(x) = φ(x) β least squares loss L ls (β) = n i= (yi f(xi))2 parameters β discriminative function f(x, y) = φ(x, y) β class probabilities p(y x) e f(x,y) neg-log-likelihood L neg-log-likelihood (β) = n i= log p(yi xi) 9/3
24 Logistic regression: Multi-class case 2/3
25 Logistic regression: Multi-class case Data D = {(x i, y i )} n i= with x i R d and y i {,.., M} We choose f(x, y) = φ(x, y) β with φ(x, y) = [y = ] φ(x) [y = 2] φ(x). [y = M] φ(x) where φ(x) are arbitrary features. We have M (or M-) parameters β Conditional class probabilties p(y x) = ef(x,y) y ef(x,y ) (optionally we may set f(x, M) = and drop the last entry) f(x, y) = log p(y x) p(y =M x) (the discriminative functions model log-ratios ) Given data D = {(x i, y i )} n i=, we minimize L logistic (β) = n i= log p(y =y i x i ) + λ β 2 2/3
26 Optimal parameters β Gradient: L logistic (β) β c = n i= (p ic y ic )φ(x i ) + 2λIβ c = X (p c y c ) + 2λIβ c, p ic = p(y =c x i ) Hessian: H = 2 L logistic (β) β c β d = X W cd X + 2[c = d] λi W cd diagonal with W cd,ii = p ic ([c = d] p id ) 22/3
27 polynomial (quadratic) ridge 3-class logistic regression: 3 2 (MT/plot.h -> gnuplot pipe) train p= /x.exe -mode 3 -modelfeaturetype 3 -lambda e+ 23/3
28 Conditional Random Fields 24/3
29 Conditional Random Fields (CRFs) CRFs are a generalization of logistic binary and multi-class classification The output y may be an arbitrary (usually discrete) thing (e.g., sequence/image/graph-labelling) Hopefully we can minimize efficiently argmax f(x, y) y over the output! f(x, y) should be structured in y so this optimization is efficient. The name CRF describes that p(y x) e f(x,y) defines a probability distribution (a.k.a. random field) over the output y conditional to the input x. The word field usually means that this distribution is structured (a graphical model; see later part of lecture). 25/3
30 CRFs: Core equations f(x, y) = φ(x, y) β p(y x) = ef(x,y) y ef(x,y ) = ef(x,y) Z(x,β) Z(x, β) = log y e f(x,y ) (log partition function) L(β) = i log p(y i x i ) = i [φ(x, y) β Z(x i, β)] β Z(x, β) = y 2 β 2 Z(x, β) = y p(y x) φ(x, y) [ ][ ] p(y x) φ(x, y) φ(x, y) β Z β Z This gives the neg-log-likelihood L(β), its gradient and Hessian 26/3
31 Training CRFs Maximize conditional likelihood But Hessian is typically too large (Images: pixels, 5 features) If f(x, y) has a chain structure over y, the Hessian is usually banded computation time linear in chain length Alternative: Efficient gradient method, e.g.: Vishwanathan et al.: Accelerated Training of Conditional Random Fields with Stochastic Gradient Methods Other loss variants, e.g., hinge loss as with Support Vector Machines ( Structured output SVMs ) Perceptron algorithm: Minimizes hinge loss using a gradient method 27/3
32 CRFs: the structure is in the features Assume y = (y,.., y l ) is a tuple of individual (local) discrete labels We can assume that f(x, y) is linear in features f(x, y) = k φ j (x, y j )β j = φ(x, y) β j= where each feature φ j (x, y j ) depends only on a subset y j of labels. φ j (x, y j ) effectively couples the labels y j. Then e f(x,y) is a factor graph. 28/3
33 CRFs: examples structures Assume y = (y,.., y l ) is a tuple of individual (local) discrete labels We can assume that f(x, y) is linear in features f(x, y) = k φ j (x, y j )β j = φ(x, y) β j= where each feature φ j (x, y j ) depends only on a subset y j of labels. φ j (x, y j ) effectively couples the labels y j. Then e f(x,y) is a factor graph. 29/3
34 Example: pair-wise coupled pixel labels x y y 2 y 3 y 4 y W y 2 y 3 y H Each black box corresponds to features φ j (y j ) which couple neighboring pixel labels y j Each gray box corresponds to features φ j (x j, y j ) which couple a local pixel observation x j with a pixel label y j 3/3
CRF and Structured Perceptron
CRF and Structured Perceptron CS 585, Fall 2015 -- Oct. 6 Introduction to Natural Language Processing http://people.cs.umass.edu/~brenocon/inlp2015/ Brendan O Connor Viterbi exercise solution CRF & Structured
More informationMachine Learning for Language Technology
Machine Learning for Language Technology Generative and Discriminative Models Joakim Nivre Uppsala University Department of Linguistics and Philology joakim.nivre@lingfil.uu.se Machine Learning for Language
More informationKernels and Support Vector Machines
Kernels and Support Vector Machines Machine Learning CSE446 Sham Kakade University of Washington November 1, 2016 2016 Sham Kakade 1 Announcements: Project Milestones coming up HW2 You ve implemented GD,
More informationLesson 08. Convolutional Neural Network. Ing. Marek Hrúz, Ph.D. Katedra Kybernetiky Fakulta aplikovaných věd Západočeská univerzita v Plzni.
Lesson 08 Convolutional Neural Network Ing. Marek Hrúz, Ph.D. Katedra Kybernetiky Fakulta aplikovaných věd Západočeská univerzita v Plzni Lesson 08 Convolution we will consider 2D convolution the result
More informationLearning Structured Predictors
Learning Structured Predictors Xavier Carreras Xerox Research Centre Europe Supervised (Structured) Prediction Learning to predict: given training data { (x (1), y (1) ), (x (2), y (2) ),..., (x (m), y
More informationANSWER KEY. (a) For each of the following partials derivatives, use the contour plot to decide whether they are positive, negative, or zero.
Math 2130-101 Test #2 for Section 101 October 14 th, 2009 ANSWE KEY 1. (10 points) Compute the curvature of r(t) = (t + 2, 3t + 4, 5t + 6). r (t) = (1, 3, 5) r (t) = 1 2 + 3 2 + 5 2 = 35 T(t) = 1 r (t)
More informationLecture 3 - Regression
Lecture 3 - Regression Instructor: Prof Ganesh Ramakrishnan July 25, 2016 1 / 30 The Simplest ML Problem: Least Square Regression Curve Fitting: Motivation Error measurement Minimizing Error Method of
More informationAdvanced Techniques for Mobile Robotics Location-Based Activity Recognition
Advanced Techniques for Mobile Robotics Location-Based Activity Recognition Wolfram Burgard, Cyrill Stachniss, Kai Arras, Maren Bennewitz Activity Recognition Based on L. Liao, D. J. Patterson, D. Fox,
More informationIBM SPSS Neural Networks
IBM Software IBM SPSS Neural Networks 20 IBM SPSS Neural Networks New tools for building predictive models Highlights Explore subtle or hidden patterns in your data. Build better-performing models No programming
More informationContents. List of Figures List of Tables. Structure of the Book How to Use this Book Online Resources Acknowledgements
Contents List of Figures List of Tables Preface Notation Structure of the Book How to Use this Book Online Resources Acknowledgements Notational Conventions Notational Conventions for Probabilities xiii
More informationStatistical Tests: More Complicated Discriminants
03/07/07 PHY310: Statistical Data Analysis 1 PHY310: Lecture 14 Statistical Tests: More Complicated Discriminants Road Map When the likelihood discriminant will fail The Multi Layer Perceptron discriminant
More informationAn Efficient Color Image Segmentation using Edge Detection and Thresholding Methods
19 An Efficient Color Image Segmentation using Edge Detection and Thresholding Methods T.Arunachalam* Post Graduate Student, P.G. Dept. of Computer Science, Govt Arts College, Melur - 625 106 Email-Arunac682@gmail.com
More informationSSB Debate: Model-based Inference vs. Machine Learning
SSB Debate: Model-based nference vs. Machine Learning June 3, 2018 SSB 2018 June 3, 2018 1 / 20 Machine learning in the biological sciences SSB 2018 June 3, 2018 2 / 20 Machine learning in the biological
More informationThe Automatic Classification Problem. Perceptrons, SVMs, and Friends: Some Discriminative Models for Classification
Perceptrons, SVMs, and Friends: Some Discriminative Models for Classification Parallel to AIMA 8., 8., 8.6.3, 8.9 The Automatic Classification Problem Assign object/event or sequence of objects/events
More informationIntroduction to Machine Learning
Introduction to Machine Learning Deep Learning Barnabás Póczos Credits Many of the pictures, results, and other materials are taken from: Ruslan Salakhutdinov Joshua Bengio Geoffrey Hinton Yann LeCun 2
More informationMath 148 Exam III Practice Problems
Math 48 Exam III Practice Problems This review should not be used as your sole source for preparation for the exam. You should also re-work all examples given in lecture, all homework problems, all lab
More informationElevation Matrices of Surfaces
Elevation Matrices of Surfaces Frank Uhlig, Mesgana Hawando Department of Mathematics, Auburn University Auburn, AL 36849 5310, USA uhligfd@auburn.edu www.auburn.edu/ uhligfd hawanmt@auburn.edu [coimbraelmatr04.tex]
More informationWe like to depict a vector field by drawing the outputs as vectors with their tails at the input (see below).
Math 55 - Vector Calculus II Notes 4. Vector Fields A function F is a vector field on a subset S of R n if F is a function from S to R n. particular, this means that F(x, x,..., x n ) = f (x, x,..., x
More informationVoice Activity Detection
Voice Activity Detection Speech Processing Tom Bäckström Aalto University October 2015 Introduction Voice activity detection (VAD) (or speech activity detection, or speech detection) refers to a class
More informationMidterm for Name: Good luck! Midterm page 1 of 9
Midterm for 6.864 Name: 40 30 30 30 Good luck! 6.864 Midterm page 1 of 9 Part #1 10% We define a PCFG where the non-terminals are {S, NP, V P, V t, NN, P P, IN}, the terminal symbols are {Mary,ran,home,with,John},
More informationDiscriminative Training for Automatic Speech Recognition
Discriminative Training for Automatic Speech Recognition 22 nd April 2013 Advanced Signal Processing Seminar Article Heigold, G.; Ney, H.; Schluter, R.; Wiesler, S. Signal Processing Magazine, IEEE, vol.29,
More informationarxiv: v1 [cs.ni] 23 Jan 2019
Machine Learning for Wireless Communications in the Internet of Things: A Comprehensive Survey Jithin Jagannath, Nicholas Polosky, Anu Jagannath, Francesco Restuccia, and Tommaso Melodia ANDRO Advanced
More informationFunctions of several variables
Chapter 6 Functions of several variables 6.1 Limits and continuity Definition 6.1 (Euclidean distance). Given two points P (x 1, y 1 ) and Q(x, y ) on the plane, we define their distance by the formula
More informationLog-linear models (part 1I)
Log-linear models (part 1I) Lecture, Feb 2 CS 690N, Spring 2017 Advanced Natural Language Processing http://people.cs.umass.edu/~brenocon/anlp2017/ Brendan O Connor College of Information and Computer
More informationFeature Selection for Activity Recognition in Multi-Robot Domains
Feature Selection for Activity Recognition in Multi-Robot Domains Douglas L. Vail and Manuela M. Veloso Computer Science Department Carnegie Mellon University Pittsburgh, PA USA {dvail2,mmv}@cs.cmu.edu
More informationDeep Neural Networks (2) Tanh & ReLU layers; Generalisation and Regularisation
Deep Neural Networks (2) Tanh & ReLU layers; Generalisation and Regularisation Steve Renals Machine Learning Practical MLP Lecture 4 9 October 2018 MLP Lecture 4 / 9 October 2018 Deep Neural Networks (2)
More informationAutomatic Speech Recognition (CS753)
Automatic Speech Recognition (CS753) Lecture 9: Brief Introduction to Neural Networks Instructor: Preethi Jyothi Feb 2, 2017 Final Project Landscape Tabla bol transcription Music Genre Classification Audio
More informationReview Sheet for Math 230, Midterm exam 2. Fall 2006
Review Sheet for Math 230, Midterm exam 2. Fall 2006 October 31, 2006 The second midterm exam will take place: Monday, November 13, from 8:15 to 9:30 pm. It will cover chapter 15 and sections 16.1 16.4,
More informationClassification of Road Images for Lane Detection
Classification of Road Images for Lane Detection Mingyu Kim minkyu89@stanford.edu Insun Jang insunj@stanford.edu Eunmo Yang eyang89@stanford.edu 1. Introduction In the research on autonomous car, it is
More informationExam 1 Study Guide. Math 223 Section 12 Fall Student s Name
Exam 1 Study Guide Math 223 Section 12 Fall 2015 Dr. Gilbert Student s Name The following problems are designed to help you study for the first in-class exam. Problems may or may not be an accurate indicator
More informationProject. B) Building the PWM Read the instructions of HO_14. 1) Determine all the 9-mers and list them here:
Project Please choose ONE project among the given five projects. The last three projects are programming projects. hoose any programming language you want. Note that you can also write programs for the
More information(i) Understanding the basic concepts of signal modeling, correlation, maximum likelihood estimation, least squares and iterative numerical methods
Tools and Applications Chapter Intended Learning Outcomes: (i) Understanding the basic concepts of signal modeling, correlation, maximum likelihood estimation, least squares and iterative numerical methods
More informationEmpirical Assessment of Classification Accuracy of Local SVM
Empirical Assessment of Classification Accuracy of Local SVM Nicola Segata Enrico Blanzieri Department of Engineering and Computer Science (DISI) University of Trento, Italy. segata@disi.unitn.it 18th
More informationLearning Structured Predictors
Learning Structured Predictors Xavier Carreras 1/70 Supervised (Structured) Prediction Learning to predict: given training data { (x (1), y (1) ), (x (2), y (2) ),..., (x (m), y (m) ) } learn a predictor
More informationAn Enhanced Fast Multi-Radio Rendezvous Algorithm in Heterogeneous Cognitive Radio Networks
1 An Enhanced Fast Multi-Radio Rendezvous Algorithm in Heterogeneous Cognitive Radio Networks Yeh-Cheng Chang, Cheng-Shang Chang and Jang-Ping Sheu Department of Computer Science and Institute of Communications
More informationA comparative study of different feature sets for recognition of handwritten Arabic numerals using a Multi Layer Perceptron
Proc. National Conference on Recent Trends in Intelligent Computing (2006) 86-92 A comparative study of different feature sets for recognition of handwritten Arabic numerals using a Multi Layer Perceptron
More informationResearch Seminar. Stefano CARRINO fr.ch
Research Seminar Stefano CARRINO stefano.carrino@hefr.ch http://aramis.project.eia- fr.ch 26.03.2010 - based interaction Characterization Recognition Typical approach Design challenges, advantages, drawbacks
More informationVEHICLE LICENSE PLATE DETECTION ALGORITHM BASED ON STATISTICAL CHARACTERISTICS IN HSI COLOR MODEL
VEHICLE LICENSE PLATE DETECTION ALGORITHM BASED ON STATISTICAL CHARACTERISTICS IN HSI COLOR MODEL Instructor : Dr. K. R. Rao Presented by: Prasanna Venkatesh Palani (1000660520) prasannaven.palani@mavs.uta.edu
More informationA Primer on Image Segmentation. Jonas Actor
A Primer on Image Segmentation It s all PDE s anyways Jonas Actor Rice University 21 February 2018 Jonas Actor Segmentation 21 February 2018 1 Table of Contents 1 Motivation 2 Simple Methods 3 Edge Methods
More informationAutomatic Detection Of Optic Disc From Retinal Images. S.Sherly Renat et al.,
International Journal of Technology and Engineering System (IJTES) Vol 7. No.3 2015 Pp. 203-207 gopalax Journals, Singapore available at : www.ijcns.com ISSN: 0976-1345 AUTOMATIC DETECTION OF OPTIC DISC
More informationECC419 IMAGE PROCESSING
ECC419 IMAGE PROCESSING INTRODUCTION Image Processing Image processing is a subclass of signal processing concerned specifically with pictures. Digital Image Processing, process digital images by means
More informationDemosaicing Algorithm for Color Filter Arrays Based on SVMs
www.ijcsi.org 212 Demosaicing Algorithm for Color Filter Arrays Based on SVMs Xiao-fen JIA, Bai-ting Zhao School of Electrical and Information Engineering, Anhui University of Science & Technology Huainan
More informationStudent: Nizar Cherkaoui. Advisor: Dr. Chia-Ling Tsai (Computer Science Dept.) Advisor: Dr. Eric Muller (Biology Dept.)
Student: Nizar Cherkaoui Advisor: Dr. Chia-Ling Tsai (Computer Science Dept.) Advisor: Dr. Eric Muller (Biology Dept.) Outline Introduction Foreground Extraction Blob Segmentation and Labeling Classification
More informationSIGNAL PROCESSING OF POWER QUALITY DISTURBANCES
SIGNAL PROCESSING OF POWER QUALITY DISTURBANCES MATH H. J. BOLLEN IRENE YU-HUA GU IEEE PRESS SERIES I 0N POWER ENGINEERING IEEE PRESS SERIES ON POWER ENGINEERING MOHAMED E. EL-HAWARY, SERIES EDITOR IEEE
More informationDecoding of Ternary Error Correcting Output Codes
Decoding of Ternary Error Correcting Output Codes Sergio Escalera 1,OriolPujol 2,andPetiaRadeva 1 1 Computer Vision Center, Dept. Computer Science, UAB, 08193 Bellaterra, Spain 2 Dept. Matemàtica Aplicada
More informationExtraction and Recognition of Text From Digital English Comic Image Using Median Filter
Extraction and Recognition of Text From Digital English Comic Image Using Median Filter S.Ranjini 1 Research Scholar,Department of Information technology Bharathiar University Coimbatore,India ranjinisengottaiyan@gmail.com
More informationCS231A Final Project: Who Drew It? Style Analysis on DeviantART
CS231A Final Project: Who Drew It? Style Analysis on DeviantART Mindy Huang (mindyh) Ben-han Sung (bsung93) Abstract Our project studied popular portrait artists on Deviant Art and attempted to identify
More informationEvaluation of Image Segmentation Based on Histograms
Evaluation of Image Segmentation Based on Histograms Andrej FOGELTON Slovak University of Technology in Bratislava Faculty of Informatics and Information Technologies Ilkovičova 3, 842 16 Bratislava, Slovakia
More informationDIGITAL IMAGE PROCESSING (COM-3371) Week 2 - January 14, 2002
DIGITAL IMAGE PROCESSING (COM-3371) Week 2 - January 14, 22 Topics: Human eye Visual phenomena Simple image model Image enhancement Point processes Histogram Lookup tables Contrast compression and stretching
More information6. FUNDAMENTALS OF CHANNEL CODER
82 6. FUNDAMENTALS OF CHANNEL CODER 6.1 INTRODUCTION The digital information can be transmitted over the channel using different signaling schemes. The type of the signal scheme chosen mainly depends on
More informationCompound Object Detection Using Region Co-occurrence Statistics
Compound Object Detection Using Region Co-occurrence Statistics Selim Aksoy 1 Krzysztof Koperski 2 Carsten Tusk 2 Giovanni Marchisio 2 1 Department of Computer Engineering, Bilkent University, Ankara,
More informationStudy Impact of Architectural Style and Partial View on Landmark Recognition
Study Impact of Architectural Style and Partial View on Landmark Recognition Ying Chen smileyc@stanford.edu 1. Introduction Landmark recognition in image processing is one of the important object recognition
More informationTable of contents. Vision industrielle 2002/2003. Local and semi-local smoothing. Linear noise filtering: example. Convolution: introduction
Table of contents Vision industrielle 2002/2003 Session - Image Processing Département Génie Productique INSA de Lyon Christian Wolf wolf@rfv.insa-lyon.fr Introduction Motivation, human vision, history,
More informationCarnegie Mellon University, University of Pittsburgh
Carnegie Mellon University, University of Pittsburgh Carnegie Mellon University, University of Pittsburgh Artificial Intelligence (AI) and Deep Learning (DL) Overview Paola Buitrago Leader AI and BD Pittsburgh
More informationSYLLABUS CHAPTER - 2 : INTENSITY TRANSFORMATIONS. Some Basic Intensity Transformation Functions, Histogram Processing.
Contents i SYLLABUS UNIT - I CHAPTER - 1 : INTRODUCTION TO DIGITAL IMAGE PROCESSING Introduction, Origins of Digital Image Processing, Applications of Digital Image Processing, Fundamental Steps, Components,
More informationAn Approximation Algorithm for Computing the Mean Square Error Between Two High Range Resolution RADAR Profiles
IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS, VOL., NO., JULY 25 An Approximation Algorithm for Computing the Mean Square Error Between Two High Range Resolution RADAR Profiles John Weatherwax
More informationImage Recognition for PCB Soldering Platform Controlled by Embedded Microchip Based on Hopfield Neural Network
436 JOURNAL OF COMPUTERS, VOL. 5, NO. 9, SEPTEMBER Image Recognition for PCB Soldering Platform Controlled by Embedded Microchip Based on Hopfield Neural Network Chung-Chi Wu Department of Electrical Engineering,
More informationRobust Decentralized Differentially Private Stochastic Gradient Descent
Robust Decentralized Differentially Private Stochastic Gradient Descent István Hegedűs, Árpád Berta, and Márk Jelasity MTA-SZTE Research Group on AI University of Szeged Szeged, Hungary {ihegedus, berta,
More informationHeuristics & Pattern Databases for Search Dan Weld
CSE 473: Artificial Intelligence Autumn 2014 Heuristics & Pattern Databases for Search Dan Weld Logistics PS1 due Monday 10/13 Office hours Jeff today 10:30am CSE 021 Galen today 1-3pm CSE 218 See Website
More informationAN ANALYSIS OF SPEECH RECOGNITION PERFORMANCE BASED UPON NETWORK LAYERS AND TRANSFER FUNCTIONS
AN ANALYSIS OF SPEECH RECOGNITION PERFORMANCE BASED UPON NETWORK LAYERS AND TRANSFER FUNCTIONS Kuldeep Kumar 1, R. K. Aggarwal 1 and Ankita Jain 2 1 Department of Computer Engineering, National Institute
More informationCHAPTER 11 PARTIAL DERIVATIVES
CHAPTER 11 PARTIAL DERIVATIVES 1. FUNCTIONS OF SEVERAL VARIABLES A) Definition: A function of two variables is a rule that assigns to each ordered pair of real numbers (x,y) in a set D a unique real number
More informationMachine Learning for Antenna Array Failure Analysis
Machine Learning for Antenna Array Failure Analysis Lydia de Lange Under Dr DJ Ludick and Dr TL Grobler Dept. Electrical and Electronic Engineering, Stellenbosch University MML 2019 Outline 15/03/2019
More informationStacking Ensemble for auto ml
Stacking Ensemble for auto ml Khai T. Ngo Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Master
More informationName: ID: Section: Math 233 Exam 2. Page 1. This exam has 17 questions:
Page Name: ID: Section: This exam has 7 questions: 5 multiple choice questions worth 5 points each. 2 hand graded questions worth 25 points total. Important: No graphing calculators! Any non scientific
More informationCHAPTER 4 LOCATING THE CENTER OF THE OPTIC DISC AND MACULA
90 CHAPTER 4 LOCATING THE CENTER OF THE OPTIC DISC AND MACULA The objective in this chapter is to locate the centre and boundary of OD and macula in retinal images. In Diabetic Retinopathy, location of
More informationResearch Article n-digit Benford Converges to Benford
International Mathematics and Mathematical Sciences Volume 2015, Article ID 123816, 4 pages http://dx.doi.org/10.1155/2015/123816 Research Article n-digit Benford Converges to Benford Azar Khosravani and
More informationDeep Learning Basics Lecture 9: Recurrent Neural Networks. Princeton University COS 495 Instructor: Yingyu Liang
Deep Learning Basics Lecture 9: Recurrent Neural Networks Princeton University COS 495 Instructor: Yingyu Liang Introduction Recurrent neural networks Dates back to (Rumelhart et al., 1986) A family of
More informationAn Introduction to Machine Learning for Social Scientists
An Introduction to Machine Learning for Social Scientists Tyler Ransom University of Oklahoma, Dept. of Economics November 10, 2017 Outline 1. Intro 2. Examples 3. Conclusion Tyler Ransom (OU Econ) An
More informationImage Denoising using Dark Frames
Image Denoising using Dark Frames Rahul Garg December 18, 2009 1 Introduction In digital images there are multiple sources of noise. Typically, the noise increases on increasing ths ISO but some noise
More informationDeep Learning for Launching and Mitigating Wireless Jamming Attacks
Deep Learning for Launching and Mitigating Wireless Jamming Attacks Tugba Erpek, Yalin E. Sagduyu, and Yi Shi arxiv:1807.02567v2 [cs.ni] 13 Dec 2018 Abstract An adversarial machine learning approach is
More informationLocal Search: Hill Climbing. When A* doesn t work AIMA 4.1. Review: Hill climbing on a surface of states. Review: Local search and optimization
Outline When A* doesn t work AIMA 4.1 Local Search: Hill Climbing Escaping Local Maxima: Simulated Annealing Genetic Algorithms A few slides adapted from CS 471, UBMC and Eric Eaton (in turn, adapted from
More informationToday. CS 395T Visual Recognition. Course content. Administration. Expectations. Paper reviews
Today CS 395T Visual Recognition Course logistics Overview Volunteers, prep for next week Thursday, January 18 Administration Class: Tues / Thurs 12:30-2 PM Instructor: Kristen Grauman grauman at cs.utexas.edu
More informationKeywords: - Gaussian Mixture model, Maximum likelihood estimator, Multiresolution analysis
Volume 4, Issue 2, February 2014 ISSN: 2277 128X International Journal of Advanced Research in Computer Science and Software Engineering Research Paper Available online at: www.ijarcsse.com Expectation
More informationSegmentation of Fingerprint Images Using Linear Classifier
EURASIP Journal on Applied Signal Processing 24:4, 48 494 c 24 Hindawi Publishing Corporation Segmentation of Fingerprint Images Using Linear Classifier Xinjian Chen Intelligent Bioinformatics Systems
More informationPrinceton ELE 201, Spring 2014 Laboratory No. 2 Shazam
Princeton ELE 201, Spring 2014 Laboratory No. 2 Shazam 1 Background In this lab we will begin to code a Shazam-like program to identify a short clip of music using a database of songs. The basic procedure
More informationDetection of Compound Structures in Very High Spatial Resolution Images
Detection of Compound Structures in Very High Spatial Resolution Images Selim Aksoy Department of Computer Engineering Bilkent University Bilkent, 06800, Ankara, Turkey saksoy@cs.bilkent.edu.tr Joint work
More informationAn Adaptive Intelligence For Heads-Up No-Limit Texas Hold em
An Adaptive Intelligence For Heads-Up No-Limit Texas Hold em Etan Green December 13, 013 Skill in poker requires aptitude at a single task: placing an optimal bet conditional on the game state and the
More informationSYDE 112, LECTURE 34 & 35: Optimization on Restricted Domains and Lagrange Multipliers
SYDE 112, LECTURE 34 & 35: Optimization on Restricted Domains and Lagrange Multipliers 1 Restricted Domains If we are asked to determine the maximal and minimal values of an arbitrary multivariable function
More informationEE 435/535: Error Correcting Codes Project 1, Fall 2009: Extended Hamming Code. 1 Introduction. 2 Extended Hamming Code: Encoding. 1.
EE 435/535: Error Correcting Codes Project 1, Fall 2009: Extended Hamming Code Project #1 is due on Tuesday, October 6, 2009, in class. You may turn the project report in early. Late projects are accepted
More informationMA/CSSE 473 Day 14. Permutations wrap-up. Subset generation. (Horner s method) Permutations wrap up Generating subsets of a set
MA/CSSE 473 Day 14 Permutations wrap-up Subset generation (Horner s method) MA/CSSE 473 Day 14 Student questions Monday will begin with "ask questions about exam material time. Exam details are Day 16
More informationLog-linear models (part III)
Log-linear models (part III) Lecture, Feb 7 CS 690N, Spring 2017 Advanced Natural Language Processing http://people.cs.umass.edu/~brenocon/anlp2017/ Brendan O Connor College of Information and Computer
More informationPrivacy preserving data mining multiplicative perturbation techniques
Privacy preserving data mining multiplicative perturbation techniques Li Xiong CS573 Data Privacy and Anonymity Outline Review and critique of randomization approaches (additive noise) Multiplicative data
More informationGE 113 REMOTE SENSING. Topic 7. Image Enhancement
GE 113 REMOTE SENSING Topic 7. Image Enhancement Lecturer: Engr. Jojene R. Santillan jrsantillan@carsu.edu.ph Division of Geodetic Engineering College of Engineering and Information Technology Caraga State
More informationSegmentation of Fingerprint Images
Segmentation of Fingerprint Images Asker M. Bazen and Sabih H. Gerez University of Twente, Department of Electrical Engineering, Laboratory of Signals and Systems, P.O. box 217-75 AE Enschede - The Netherlands
More informationLecture 5: Pitch and Chord (1) Chord Recognition. Li Su
Lecture 5: Pitch and Chord (1) Chord Recognition Li Su Recap: short-time Fourier transform Given a discrete-time signal x(t) sampled at a rate f s. Let window size N samples, hop size H samples, then the
More informationAn Hybrid MLP-SVM Handwritten Digit Recognizer
An Hybrid MLP-SVM Handwritten Digit Recognizer A. Bellili ½ ¾ M. Gilloux ¾ P. Gallinari ½ ½ LIP6, Université Pierre et Marie Curie ¾ La Poste 4, Place Jussieu 10, rue de l Ile Mabon, BP 86334 75252 Paris
More informationDERIVATION OF TRAPS IN AUDITORY DOMAIN
DERIVATION OF TRAPS IN AUDITORY DOMAIN Petr Motlíček, Doctoral Degree Programme (4) Dept. of Computer Graphics and Multimedia, FIT, BUT E-mail: motlicek@fit.vutbr.cz Supervised by: Dr. Jan Černocký, Prof.
More informationQuestion Score Max Cover Total 149
CS170 Final Examination 16 May 20 NAME (1 pt): TA (1 pt): Name of Neighbor to your left (1 pt): Name of Neighbor to your right (1 pt): This is a closed book, closed calculator, closed computer, closed
More informationFast Blur Removal for Wearable QR Code Scanners (supplemental material)
Fast Blur Removal for Wearable QR Code Scanners (supplemental material) Gábor Sörös, Stephan Semmler, Luc Humair, Otmar Hilliges Department of Computer Science ETH Zurich {gabor.soros otmar.hilliges}@inf.ethz.ch,
More information신경망기반자동번역기술. Konkuk University Computational Intelligence Lab. 김강일
신경망기반자동번역기술 Konkuk University Computational Intelligence Lab. http://ci.konkuk.ac.kr kikim01@kunkuk.ac.kr 김강일 Index Issues in AI and Deep Learning Overview of Machine Translation Advanced Techniques in
More informationHeuristic Search with Pre-Computed Databases
Heuristic Search with Pre-Computed Databases Tsan-sheng Hsu tshsu@iis.sinica.edu.tw http://www.iis.sinica.edu.tw/~tshsu 1 Abstract Use pre-computed partial results to improve the efficiency of heuristic
More informationTHE EXO-200 experiment searches for double beta decay
CS 229 FINAL PROJECT, AUTUMN 2012 1 Classification of Induction Signals for the EXO-200 Double Beta Decay Experiment Jason Chaves, Physics, Stanford University Kevin Shin, Computer Science, Stanford University
More informationAdvances in Computer Vision and Pattern Recognition
Advances in Computer Vision and Pattern Recognition For further volumes: http://www.springer.com/series/4205 Marco Alexander Treiber Optimization for Computer Vision An Introduction to Core Concepts and
More informationCS229: Machine Learning
CS229: Machine Learning Event Identification in Continues Seismic Data Please print out, fill in and include this cover sheet as the first page of your submission. We strongly recommend that you use this
More informationExam 2 Review Sheet. r(t) = x(t), y(t), z(t)
Exam 2 Review Sheet Joseph Breen Particle Motion Recall that a parametric curve given by: r(t) = x(t), y(t), z(t) can be interpreted as the position of a particle. Then the derivative represents the particle
More informationComputational aspects of two-player zero-sum games Course notes for Computational Game Theory Section 3 Fall 2010
Computational aspects of two-player zero-sum games Course notes for Computational Game Theory Section 3 Fall 21 Peter Bro Miltersen November 1, 21 Version 1.3 3 Extensive form games (Game Trees, Kuhn Trees)
More informationAbsolute Value of Linear Functions
Lesson Plan Lecture Version Absolute Value of Linear Functions Objectives: Students will: Discover how absolute value affects linear functions. Prerequisite Knowledge Students are able to: Graph linear
More information[f(t)] 2 + [g(t)] 2 + [h(t)] 2 dt. [f(u)] 2 + [g(u)] 2 + [h(u)] 2 du. The Fundamental Theorem of Calculus implies that s(t) is differentiable and
Midterm 2 review Math 265 Fall 2007 13.3. Arc Length and Curvature. Assume that the curve C is described by the vector-valued function r(r) = f(t), g(t), h(t), and that C is traversed exactly once as t
More informationDIAGNOSIS OF STATOR FAULT IN ASYNCHRONOUS MACHINE USING SOFT COMPUTING METHODS
DIAGNOSIS OF STATOR FAULT IN ASYNCHRONOUS MACHINE USING SOFT COMPUTING METHODS K. Vinoth Kumar 1, S. Suresh Kumar 2, A. Immanuel Selvakumar 1 and Vicky Jose 1 1 Department of EEE, School of Electrical
More information30 Int'l Conf. IP, Comp. Vision, and Pattern Recognition IPCV'15
30 Int'l Conf IP, Comp Vision, and Pattern Recognition IPCV'15 Spectral Collaborative Representation Based Classification by Circulants and its Application to Hand Gesture and Posture Recognition from
More information