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Berkeley COMPSCI 294 - Segmentation and Kernels Lecture

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CS294‐43: Multiple Kernel and Segmentation methodsSegmentation methodsProf. Trevor DarrellSpring 2009Spring 2009April 7th, 2009Last Lecture – Category Discovery• R. Fergus, L. Fei-Fei, P. Perona, and A. Zisserman, "Learning object categories from google's image search," ICCV vol. 2, 2005LJLiGW dLFiF i "O ti l t ti li i t ll ti i•L.-J. Li, G. Wang, and L. Fei-Fei, "Optimol: automatic online picture collection via incremental model learning," in Computer Vision and Pattern Recognition, 2007. CVPR '07• F. Schroff, A. Criminisi, and A. Zisserman, "Harvesting image databases from the web," in Computer Vision, 2007. ICCV 2007•T Berg and D Forsyth"Animals on the Web"In Proceedings of the 2006 IEEET. Berg and D. Forsyth, Animals on the Web. In Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR). • K. Saenko and T. Darrell, "Unsupervised Learning of Visual Sense Models for Polysemous Words"Proc NIPS December 2008Polysemous Words. Proc. NIPS, December 2008Today – Kernel Combination, Segmentation, and Structured Output p• M. Varma and D. Ray, "Learning the discriminative power-invariance trade-off," in Computer Vision 2007 ICCV 2007 IEEE 11th International Conference on 2007Computer Vision, 2007. ICCV 2007. IEEE 11th International Conference on, 2007, • Q. Yuan, A. Thangali, V. Ablavsky, and S. Sclaroff, "Multiplicative kernels: Object detection, segmentation and pose estimation," in Computer Vision and Pattern Recognition 2008 CVPR 2008Recognition, 2008. CVPR 2008• M. B. Blaschko and C. H. Lampert, "Learning to localize objects with structured output regression," in ECCV 2008. • C. Pantofaru, C. Schmid, and M. Hebert, "Object recognition by integrating multiple image segmentations," CVPR 2008, • Chunhui Gu, Joseph J. Lim, Pablo Arbelaez, Jitendra Malik, Recognition using Regions, CVPR 2009, to appearMultiple Kernel LearningMultiple Kernel LearningMultiple Kernel LearningMultiple Kernel LearningManik VarmaManik VarmaMicrosoft Research IndiaAlex Berg, Anna Bosch, Varun Gulshan, Jitendra Malik & Andrew ZissermanShanmugananthan Raman & Lihi Zelnik-ManorRakesh Babu & C. V. JawaharDebajyoti RaySVMs and MKL• SVMs are basic tools in machine learning that can be used for classification regressionetccan be used for classification, regression, etc.• MKL can be utilized whenever a single kernel iliblSVM is applicable.•SVMs/MKL find applications inSVMs/MKL find applications in• Video, audio and speech processing.• NLP, information retrieval and search.•Software engineering.So w e e g ee g.• We focus on examples from vision in this talk.Object CategorizationChairSchooner=?KetchNovel image to be classifiedTajjPandaLabelled images comprise training dataOutline of the Talk• Introduction to SVMs and kernel learning.• Our Multiple Kernel Learning (MKL) formulation.• Application to object recognition.• Extending our MKL formulation.•Applications to feature selection and predictingApplications to feature selection and predicting facial attractiveness.Introduction to SVMsIntroduction to SVMsIntroduction to SVMs Introduction to SVMs and Kernel Learningand Kernel Learningand Kernel Learningand Kernel LearningBinary Classification With SVMsMargin = 2 / wtw > 1K(xi,xj) = t(xi)(xj)Misclassified point  < 1bSupport VectorSupport Vectorpp = 0wt(x)+b=0wt(x) + b = -1ww(x) b 0wt(x) + b = +1The C-SVM Primal Formulation• Minimisew,b,½wtw + C iibj•Subject to•yi[wt(xi) + b] ≥ 1 –iyi[(i)] ≥i•i≥ 0•where•(xiyi)istheithtraining point(xi, yi) is the itraining point.• C is the misclassification penalty.The C-SVM Dual Formulation• Maximise1t –½tYKYSbj•Subject to• 1tY = 0• 0 C•where•where•  are the Lagrange multipliers di h ffcorresponding to the support vector coeffs• Y is a diagonal matrix such that Yii= yiiii• K is the kernel matrix with Kij= t(xi)(xj)Some Popular Kernels• Linear: K(xi,xj) = xit-1xj• Polynomial: K(xi,xj) = (xit-1xj + c)d• RBF: K(xi,xj) = exp(–kk(xik– xjk)2)(i,j)p(kk(ikjk))ChiSK()(2())•Chi-Square: K(xi,xj) = exp(–2(xi,xj))Advantages of Learning the Kernel• Learn the kernel parameters• Improve accuracy and generalisationAdvantages of Learning the Kernel• Learn the kernel parameters• Improve accuracy and generalisation•Perform feature component selection•Perform feature component selectionLearn K(xi,xj) = exp(– kk(xik– xjk)2)Advantages of Learning the Kernel• Learn the kernel parameters• Improve accuracy and generalisation•Perform feature component selection•Perform feature component selection• Perform dimensionality reductionLearn K(Pxi, Pxj) where P is a low dimensional projection matrix parameteriseddimensional projection matrix parameterised by .Advantages of Learning the Kernel• Learn the kernel parameters• Improve accuracy and generalisation•Perform feature component selection•Perform feature component selection• Perform dimensionality reduction• Learn a linear combination of base kernels• K(xi,xj) = kdkKk(xi,xj)•Combine heterogeneous sources of data•Combine heterogeneous sources of data• Perform feature selectionAdvantages of Learning the Kernel• Learn the kernel parameters• Improve accuracy and generalisation•Perform feature component selection•Perform feature component selection• Perform dimensionality reduction• Learn a linear combination of base kernels• Learn a product of base kernels•K(xx)=K(xx)•K(xi,xj) = kKk(xi,xj)Advantages of Learning the Kernel• Learn the kernel parameters• Improve accuracy and generalisation•Perform feature component selection•Perform feature component selection• Perform dimensionality reduction• Learn a linear combination of base kernels• Learn a product of base kernels•Combine some of the above•Combine some of the aboveLinear Combinations of Base Kernels• Learn a linear combination of base kernels• K(xi,xj) = kdkKk(xi,xj)d11d22=dd33Linear Combinations of Base KernelsSchoonerKetchSimplistic 1D colour featureSimplistic 1D colour featurec• Linear colour kernel : Kc(ci,cj) = t(ci)(ci) = cicjcijiiij• Classification accuracy = 50%Linear Combinations of Base KernelsSchoonerKetchSimplistic 1D shape featureSimplistic 1D shape features• Linear shape kernel : Ks(si,sj) =


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Berkeley COMPSCI 294 - Segmentation and Kernels Lecture

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