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  • Expediting Precomputation for Reduced Deformable Simulation
    precomputation namely modal matrix construction cubature training and training dataset generation and accelerate each of them Even with complex deformable models our method has achieved orders of magnitude speedups over the traditional precomputation steps while retaining comparable runtime simulation quality downloads Paper Paper low resolution Video 145MB Youtube bibtex citation article Yang 2015 fastprecomp title Expediting Precomputation for Reduced Deformable Simulation author Yang Yin and Li Dingzeyu and Xu Weiwei

    Original URL path: http://www.cs.columbia.edu/cg/fastprecomp/ (2016-02-17)
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  • Legolization: Optimizing LEGO Designs
    1 an ordering in the strength so that we know which structure is more stable and 2 a threshold for stability so that we know which one is stable enough In addition our stability analysis tells us the weak portion of the sculpture Building atop our stability analysis we present a layout refinement algorithm that iteratively improves the structure around the weak portion allowing for automatic generation of a LEGO brick layout from a given 3D model accounting for color information required workload in terms of the number of bricks and physical stability We demonstrate the success of our method with real LEGO sculptures built up from a wide variety of 3D models and compare against previous methods Keywords LEGO stability aware design fabrication Acknowledgements We thank anonymous reviewers for encouragements and thoughtful suggestions We thank Christopher Batty Gabriel Cirio Anne Fleming and Eitan Grinspun for helping to prepare the final version of this paper We thank Intel for donating computing hardware Figures 2 a to d are courtesy of Robin Sather Brickville DesignWorks LEGO Certified Professional Builder Figure 2 e is courtesy of the LEGO club of The University of Tokyo We thank the providers of the free 3D

    Original URL path: http://www.cs.columbia.edu/~yonghao/siga15/abstsiga15.html (2016-02-17)
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  • Nested Cages
    that coarser layers strictly encage finer layers nesting one another Existing techniques such as surface mesh decimation voxelization or contouring distance level sets do not provide sufficient control over the quality of the output surfaces while maintaining strict nesting We propose a solution that enables use of application specific decimation and quality metrics The method constructs each next coarsest level of the hierarchy using a sequence of decimation flow and contact aware optimization steps From coarse to fine each layer then fully encages the next while retaining a snug fit The method is applicable to a wide variety of shapes of complex geometry and topology We demonstrate the effectiveness of our nested cages not only for multigrid solvers but also for conservative collision detection domain discretization for elastic simulation and cage based geometric modeling Downloads Paper Paper low res TWIG Poster Supplemental Data Code Presentation Video BibTeX article Sacht 2015 NC author Leonardo Sacht and Etienne Vouga and Alec Jacobson title Nested Cages journal ACM Transactions on Graphics TOG volume 34 number 6 year 2015 Acknowledgements We thank Derek Bradley Keenan Crane Eitan Grinspun and Daniele Panozzo for illuminating discussions Eric Price for brainstorming the NP completeness proof Henrique Maia

    Original URL path: http://www.cs.columbia.edu/cg/nested-cages/ (2016-02-17)
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  • Columbia Vision + Graphics Center
    Columbia University School of Engineering and Applied Science Computer Science Department

    Original URL path: http://www.cs.columbia.edu/cvgc/cvgchead.html (2016-02-17)
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  • Columbia Vision + Graphics Center
    Research People Events Courses Sponsors Contact Research Labs Computer Graphics UI Graphics High Level Vision Machine Learning Physics of Vision Robotics Visual Appearance

    Original URL path: http://www.cs.columbia.edu/cvgc/cvgcside.html (2016-02-17)
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  • Peter N. Belhumeur
    approach is useful for imaging dim objects as well as objects having a specular reflection component We give the optimal scheme by which lighting should be multiplexed to obtain the highest quality output for signal independent noise The scheme is based on Hadamard codes The consequences of imperfections such as stray light saturation and noisy illumination sources are then studied In addition the paper analyzes the implications of shot noise which is signal dependent to Hadamard multiplexing The approach facilitates practical lighting setups having high directional resolution This is shown by a setup we devise which is flexible scalable and programmable We used it to demonstrate the benefit of multiplexing in experiments 2006 Time Varying Surface Appearance We have captured the first time varying surface appearance database with 26 samples which includes a variety of natural processes burning drying decay and corrosion We have developed a novel Space Time Appearance Factorization STAF model which factors space and time varying appearance effects The STAF model includes an overall temporal appearance variation characteristic function two spatially varying textures corresponding to the initial and final frames and two spatially varying textures corresponding to the rates and offsets at each point on the material that determine the evolution of the appearance over time Helmholtz Stereopsis Image based object reconstruction is the process of estimating the shape and surface reflectance properties on an object from its images Applications include graphics accurate rendering for virtual and augmented reality and shape measurement reverse engineering visual inspection digital object archival Graphical Properties of Easily Localizable Sensor The sensor network localization problem is one of determining the Euclidean positions of all sensors in a network given knowledge of the Euclidean positions of some and knowledge of a number of inter sensor distances This paper identifies graphical properties which can ensure unique localizability and further sets of properties which can ensure not only unique localizability but also provide guarantees on the associated computational complexity which can even be linear in the number of sensors on occasions Sensor networks with minimal connectedness properties in which sensor transmit powers can be increased to increase the sensing radius lend themselves to the acquiring of the needed graphical properties Results are presented for networks in both two and three dimensions Specularity Removal in Images and Videos We present a unifed framework for separating specular and diffuse reflection components in images and videos of textured scenes This can be used for specularity removal and for independently processing filtering and recombining the two components Beginning with a partial separation provided by an illumination dependent color space the challenge is to complete the separation using spatio temporal information This is accomplished by evolving a partial differential equation PDE that iteratively erodes the specular component at each pixel A family of PDEs appropriate for differing image sources still images vs videos differing prior information e g highly vs lightly textured scenes or differing prior computations e g optical ow is introduced In contrast to many other methods explicit segmentation and or manual intervention are not required We present results on high quality images and video acquired in the laboratory in addition to images taken from the Internet Results on the latter demonstrate robustness to low dynamic range JPEG artifacts and lack of knowledge of illuminant color Empirical comparison to physical removal of specularities using polarization is provided Finally an application termed dichromatic editing is presented in which the diffuse and the specular components are processed independently to produce a variety of visual effects NAE Lecture Ongoing Challenges in Face Recognition It has been observed that the variations between the images of the same face due to lighting and pose are almost always larger than image variations due to change in facial identity The same person with the same facial expression can appear strikingly different when light source direction and viewpoint vary These variations are made even greater by additional factors such as facial expression perspiration hair styles cosmetics and even changes due to aging 2005 Reflectance Sharing By framing the problem as scattered data interpolation in a mixed spatial and angular domain reflectance information is shared across the surface exploiting the high spatial resolution that images provide to fill the holes between sparsely observed view and lighting directions Since the BRDF typically varies slowly from point to point over much of an object s surface this method enables image based rendering from a sparse set of images without assuming a parametric reflectance model In fact the method can even be applied in the limiting case of a single input image SUV Color Space We present a photometric stereo method for non diffuse materials that does not require an explicit reflectance model or reference object By computing a data dependent rotation of RGB color space we show that the specular reflection effects can be separated from the much simpler diffuse approximately Lambertian reflection effects for surfaces that can be modeled with dichromatic reflectance Images in this transformed color space are used to obtain photometric reconstructions that are independent of the specular reflectance In contrast to other methods for highlight removal based on dichromatic color separation e g color histogram analysis and or polarization we do not explicitly recover the specular and diffuse components of an image Instead we simply find a transformation of color space that yields more direct access to shape information The method is purely local and is able to handle surfaces with arbitrary texture Rigid Formations with Leader Follower Architecture This paper is concerned with information structures used in rigid formations of autonomous agents that have leader follower architecture The focus of this paper is on sensor network topologies to secure control of rigidity We extend our previous approach for formations with symmetric neighbor relations to include formations with leader follower architecture Necessary and sufficient conditions for stably rigid directed formations are given including both cyclic and acyclic directed formations Some useful steps for creating topologies of directed rigid formations are developed An algorithm to determine the directions of links to create stably rigid directed formations from rigid undirected formations is presented It is shown that k cycles k 3 do not cause inconsistencies when measurements are noisy while 2 cycles do Simulation results are presented for i a rigid acyclic formation i a flexible formation and iii a rigid formation with cycles 2004 Lighting Sensitive Display Although display devices have been used for decades they have functioned without taking into account the illumination of their environment In this project an initial step has been taken towards addressing this limitation We are exploring the concept of a lighting sensitive display LSD a display that measures the surrounding illumination and modifies its content accordingly Making One Object Look Like Another We present a method for controlling the appearance of an arbitrary 3D object using a projector and a camera Our goal is to make one object look like another by projecting a carefully determined compensation image onto the object The determination of the appropriate compensation image requires accounting for spatial variation in the object s reflectance the effects of environmental lighting and the spectral responses spatially varying fall offs and non linear responses in the projector camera system Addressing each of these effects we present a compensation method which calls for the estimation of only a small number of parameters as part of a novel off line radiometric calibration This calibration is accomplished by projecting and acquiring a minimal set of 6 images irrespective of the object Results of the calibration are then used on line to compensate each input image prior to projection Several experimental results are shown that demonstrate the ability of this method to control the appearance of everyday objects Our method has direct applications in several areas including smart environments product design and presentation adaptive camouflages interactive education and entertainment Coordinated Motion and Rigid Formation Here we work out the mathematical details and assorted applications for coordinated motion using rigid formations This work appears in a number of different publications Operations on Rigid Formations of Autonomous Agents Rigidity Computation and Randomization in Network Localization Information Structures to Secure Control of Globally Rigid Formations Information Structures to Control Formation Splitting and Merging Merging Globally Rigid Formations 2003 Volumetric Surface Texture Database Natural materials often exhibit complex reflectance and intricate geometry posing a real challenge in surface modeling We investigate this problem in our volumetric surface reconstruction and modeling project In the process we have compiled a database of several complex volumetric surface textures We have decided to make this valuable resource available to other researchers interested in the topic A Projection System with Radiometric Compensation for Screen Imperfections A major limitation of existing projection display systems is that they rely on a high quality screen for projecting images We believe that relaxing this restriction will make projectors more useful and widely applicable The fundamental problem with using an arbitrary surface for a screen is that the surface is bound to have its own colors and textures bricks of a wall painting on a wall tiles of a ceiling grain of a wooden door etc or surface markings paint imperfections scratches nails etc As a result when an image is projected onto the surface the appearance of the image is modulated by the spatially varying reflectance properties of the surface Humans are very sensitive to such modulations In this paper we present a method that enables a projector to display images onto an arbitrary surface such that the quality of the images is preserved and the effects of the surface imperfections are minimized Our method is based on an efficient off line radiometric calibration that uses a camera to obtain measurements from the surface corresponding to a set of projected images The calibration results are then used on line to compensate each display image prior to projection Several experimental results are shown that demonstrate the advantages of using our compensation method Binocular Helmholtz Stereopsis Helmholtz stereopsis has been introduced recently as a surface reconstruction technique that does not assume a model of surface reflectance In the reported formulation correspondence was established using a rank constraint necessitating at least three viewpoints and three pairs of images Here it is revealed that the fundamental Helmholtz stereopsis constraint defines a nonlinear partial differential equation which can be solved using only two images It is shown that unlike conventional stereo binocular Helmholtz stereopsis is able to establish correspondence and thereby recover surface depth for objects having an arbitrary and unknown BRDF and in textureless regions i e regions of constant or slowly varying BRDF An implementation and experimental results validate the method for specular surfaces with and without texture 2001 Image based Rendering and Reconstruction of Surfaces with Arbitrary BRDFs Surface properties of many real life objects often cannot be effectively captured by any existing lighting models such as Phong Not only can the reflectance properties be arbitrary but they can also vary over the entire surface This project deals with this problem specifically how to reconstruct the surface of an object with arbitrary and spatially varying BRDF and how to render synthetic images of that object under novel illumination The Bas Relief Ambiguity When an unknown object with Lambertian ressectance is viewed orthographically there is an implicit ambiguity in determining its 3 d structure we show that the visible surface of an object is indistinguishable from a three parameter family of Generalized Bas Relief transformations on the shape of the object For each image of the object illuminated by an arbitrary number of distant light sources there exists an identical image of the transformed object illuminated by similarly transformed light sources This result holds both for the illuminated regions of the object as well as those in cast and attached shadows Furthermore neither small motion of the object nor of the viewer will resolve the ambiguity in determining the ssattening or scaling of the objectOs surface Implications of this ambiguity on structure recovery and shape representation are discussed 2000 In Search of Illumination Invariants We consider the problem of determining functions of an image of an object that are insensitive to illumination changes We first show that for an object with Lambertian reflectance there are no discriminative functions that are invariant to illumination This result leads us to adopt a probabilistic approach in which we analytically determine a probability distribution for the image gradient as a function of the surface s geometry and reflectance Our distribution reveals that the direction of the image gradient is insensitive to changes in illumination direction We verify this empirically by constructing a distribution for the image gradient from more than 20 million samples of gradients in a database of 1 280 images of 20 inanimate objects taken under varying lighting condition Using this distribution we develop an illumination insensitive measure of image comparison and test it on the problem of face recognition 1998 Illumination Cones The appearance of an object depends on both the viewpoint from which it is observed and the light sources by which it is illuminated If the appearance of two objects is never identical for any pose or lighting conditions then in theory the objects can always be distinguished or recognized The question arises What is the set of images of an object under all lighting conditions and pose In this paper we consider only the set of images of an object under variable illumination including multiple extended light sources and shadows We prove that the set of n pixel images of a convex object with a Lambertian reflectance function illuminated by an arbitrary number of point light sources at infinity forms a convex polyhedral cone in IRn and that the dimension of this illumination cone equals the number of distinct surface normals Furthermore the illumination cone can be constructed from as few as three images In addition the set of n pixel images of an object of any shape and with a more general reflectance function seen under all possible illumination conditions still forms a convex cone in IRn Extensions of these results to color images are presented These results immediately suggest certain approaches to object recognition Throughout we present results demonstrating the illumination cone representation 1997 Eigenfaces vs Fisherfaces Recognition Using Class Specific Linear Projection We develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression Taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space We take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3D linear subspace of the high dimensional image space if the face is a Lambertian surface without shadowing However since faces are not truly Lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace Rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation Our projection method is based on Fisher s Linear Discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions The Eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements Yet extensive experimental results demonstrate that the proposed Fisherface method has error rates that are lower than those of the Eigenface technique for tests on the Harvard and Yale Face Databases Publications 2009 Attribute and Simile Classifiesrs for Face Verification International Conference on Computer Vision 2009 N Kumar A Berg P Belhumeur S K Nayar PDF Moving Gradients A Path Based Method for Plausible Image Interpolation ACM Trans on Graphics SIGGRAPH August 2009 D Mahajan F C Huang W Matusik R Ramamoorthi P Belhumeur PDF Removing Image Arifacts Due to Dirty Camera Lenses and Thin Occluders ACM Trans on Graphics SIGGRAPH 2009 J Gu R Ramamoorthi P Belhumeur S K Nayar PDF 2008 Face Swapping Automatically Replacing Faces in Photographs ACM Trans on Graphics SIGGRAPH August 2008 D Bitouk N Kumar P N Belhumeur S K Nayar PDF Rigid Formations with Leader Follower Architecture IEEE Trans on Robotics 2008 T Eren W Whiteley P N Belhumeur PDF Color Subspaces as Photometric Invariants International Journal of Computer Vision 2008 T Zickler S Mallick P N Belhumeur D Kriegman PDF Face Tracer A Search Engine for Large Collections of Images with Faces European Conference on Computer Vision 2008 N Kumar P Belhumeur S K Nayar PDF Compressive Structured Light for Recovering Inhomogeneous Participating Media European Conference on Computer Vision 2008 J Gu S K Nayar E Grinspun P Belhumeur R Ramamoorthi PDF Searching the World s Herbaria A System for the Visual Identification of Plant Species European Conference on Computer Vision 2008 S Shirdhonkar S White S Feiner D Jacobs J Kress P N Belhumeur PDF 2007 Active Refocusing of Images and Video ACM Trans on Graphics SIGGRAPH August 2007 F Moreno Noguer S K Nayar and P N Belhumeur PDF A Theory of Locally Low Dimensional Light Transport ACM Trans on Graphics SIGGRAPH August 2007 D K Mahajan R Ramamoorthi I Kemelmacher P N Belhumeur PDF Photometric Depth Ranging of Non Lambertian Surfaces submitted to International Journal of Computer Vision 2007 S Magda D Kriegman P N Belhumeur Graphical Properties of Easily Localizable Sensor Networks Wireless Networks 2007 B Anderson R Yang D Goldberg A S Morse W Whiteley T Eren P Belhumeur PDF Time Varying BRDFs IEEE Trans on Visualization and Computer Graphics pp 595 609 May June 2007 B Sun K Sunkavalli R Ramamoorthi P N Belhumeur S Nayar PDF A First Order Analysis of Lighting Shading and Shadows to appear in ACM Trans of Graphics 2007 R Ramamoorthi D K Mahajan and P N Belhumeur PDF Dirty Glass Modeling and Rendering Contamination on Transparent Surfaces in the Proc EuroGraphics Symposium on Rendering 2007 J Gu P N Belhumeur R Ramamoorthi and Shree Nayar

    Original URL path: http://www.cs.columbia.edu/~belhumeur/ (2016-02-17)
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  • Research Directions
    The Columbia Machine Learning Laboratory is located at CEPSR 6LE5 It is funded in part by DARPA the Central Intelligence Agency the Office of Naval Research the Department of Homeland

    Original URL path: http://www.cs.columbia.edu/learning/research.html (2016-02-17)
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  • Publications of the Columbia Machine Learning Group
    s method was corrected PDF BIB SLIDES VIDEO B Shaw and T Jebara Structure Preserving Embedding International Conference on Machine Learning ICML June 2009 BEST PAPER AWARD PDF BIB SLIDES VIDEO T Jebara J Wang and S F Chang Graph Construction and b Matching for Semi Supervised Learning International Conference on Machine Learning ICML June 2009 PDF BIB SLIDES VIDEO B Huang and T Jebara Exact Graph Structure Estimation with Degree Priors International Conference on Machine Learning and Applications ICMLA December 2009 PDF BIB P Shivaswamy and T Jebara Structured Prediction with Relative Margin International Conference on Machine Learning and Applications ICMLA December 2009 PDF BIB A Howard and T Jebara Transformation Learning Via Kernel Alignment International Conference on Machine Learning and Applications ICMLA December 2009 PDF BIB A Weller D Ellis and T Jebara Structured Prediction Models for Chord Transcription of Music Audio International Conference on Machine Learning and Applications ICMLA December 2009 PDF BIB D Lazer A Pentland L Adamic S Aral A L Barabasi D Brewer N Christakis N Contractor J Fowler M Gutmann T Jebara G King M Macy D Roy and M Van Alstyne Computational Social Science Science February 6 2009 PDF BIB A Howard and T Jebara Large Margin Transformation Learning To appear in Journal of Machine Learning Research JMLR 2009 Preliminary version awaiting corrections for photoready PDF BIB C Lima U Lall T Jebara and A G Barnston Statistical Prediction of ENSO from Subsurface Sea Temperature Using a Nonlinear Dimensionality Reduction Journal of Climate Volume 22 Number 17 Pages 4501 4519 September 1 2009 PDF BIB B Huang and T Jebara Approximating the Permanent with Belief Propagation Technical report on the arXiv August 12 2009 PDF BIB B Shaw and T Jebara Dimensionality Reduction Clustering and PlaceRank Applied to Spatiotemporal Flow Data New York Academy of Sciences Machine Learning Symposium November 2009 PDF BIB M Loecher and T Jebara CitySense Multiscale Space Time Clustering of GPS Points and Trajectories Proceedings of the Joint Statistical Meeting JSM August 2009 PDF BIB A Howard Large Margin Transformation Learning PhD Thesis Columbia University 2009 PDF BIB 2008 P Shivaswamy and T Jebara Relative Margin Machines Neural Information Processing Systems 21 NIPS December 2008 PDF BIB B Huang and T Jebara Maximum Likelihood Graph Structure Estimation with Degree Distributions Analyzing Graphs Theory and Applications NIPS Workshop December 2008 PDF BIB B Shaw and T Jebara Visualizing Graphs with Structure Preserving Embedding Analyzing Graphs Theory and Applications NIPS Workshop December 2008 PDF BIB W Jiang S F Chang T Jebara and A C Loui Semantic Concept Classification by Joint Semi Supervised Learning of Feature Subspaces and Support Vector Machiness European Conference on Computer Vision ECCV October 2008 PDF BIB T Jebara Bayesian Out Trees Uncertainty in Artificial Intelligence UAI July 2008 PS PDF BIB T Jebara Out Tree Dependent Nonparametric Bayesian Inference Workshop on Nonparameteric Bayes July 2008 PDF BIB J Wang T Jebara and S F Chang Graph Transduction via Alternating Minimization International Conference on Machine Learning ICML July 2008 PDF BIB T Jebara Learning from Out Tree Dependent Data Snowbird Machine Learning Workshop April 2008 PDF BIB R Kondor Group theoretical methods in machine learning PhD Thesis Columbia University May 2008 PDF BIB 2007 T Jebara Y Song and K Thadani Density Estimation under Independent Similarly Distributed Sampling Assumptions Neural Information Processing Systems NIPS December 2007 PS PDF BIB Addendum A Howard and T Jebara Learning Monotonic Transformations for Classification Neural Information Processing Systems NIPS December 2007 PS PDF BIB S Andrews and T Jebara Graph reconstruction with degree constrained subgraphs Workshop on Statistical Network Models NIPS December 2007 PDF BIB CODE B Shaw and T Jebara Minimum Volume Embedding Artificial Intelligence and Statistics AISTATS March 2007 PDF BIB CODE B Huang and T Jebara Loopy Belief Propagation for Bipartite Maximum Weight b Matching Artificial Intelligence and Statistics AISTATS March 2007 PS PDF BIB CODE P Shivaswamy and T Jebara Ellipsoidal Kernel Machines Artificial Intelligence and Statistics AISTATS March 2007 PS PDF BIB Addendum on computing the kernelized Minimum Volume Ellipsoid PS PDF BIB R Kondor A Howard and T Jebara Multi Object Tracking with Representations of the Symmetric Group Artificial Intelligence and Statistics AISTATS March 2007 PS PDF BIB CODE T Jebara Y Song and K Thadani Spectral Clustering and Embedding with Hidden Markov Models European Conference on Machine Learning ECML September 2007 PDF BIB T Jebara B Shaw and A Howard Optimizing Eigengaps and Spectral Functions using Iterated SDP Learning Workshop 2007 PDF BIB TALK 2006 R Kondor and T Jebara Gaussian and Wishart Hyperkernels In Neural Information Processing Systems NIPS December 2006 PS PDF BIB M Mandel D Ellis and T Jebara An EM Algorithm for Localizing Multiple Sound Sources in Reverberant Environments In Neural Information Processing Systems NIPS December 2006 PDF BIB T Jebara and V Shchogolev B Matching for Spectral Clustering European Conference on Machine Learning ECML September 2006 PDF BIB D Lewis T Jebara and W S Noble Support vector machine learning from heterogeneous data an empirical analysis using protein sequence and structure Bioinformatics 22 22 2753 2760 2006 HTML PS PDF BIB P Shivaswamy and T Jebara Permutation Invariant SVMs International Conference on Machine Learning ICML June 2006 PS PDF BIB D Lewis T Jebara and W Noble Non Stationary Kernel Combination International Conference on Machine Learning ICML June 2006 PDF BIB T Jebara B Shaw and V Shchogolev B Matching for Embedding Snowbird Machine Learning Conference April 2006 PDF BIB D Lewis Combining Kernels for Classification PhD Thesis Columbia University May 2006 PDF BIB 2005 I R Kondor G Csanyi S E Ahnert and T Jebara Multi Facet Learning in Hilbert Spaces Columbia University Computer Science Technical Report CUCS 054 05 2005 PS PDF BIB T Jebara and P Long Tree Dependent Identically Distributed Learning Columbia University Computer Science Technical Report CUCS 050 05 2005 PS PDF BIB A Howard and T Jebara Square Root Propagation Columbia University Computer Science Technical Report CUCS 040 05 2005 PS PDF

    Original URL path: http://www.cs.columbia.edu/learning/papers.html (2016-02-17)
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