thesis kanade

MathSciNet Ph.D. Harvard University 2012 Dissertation: Computational Questions in Evolution Mathematics Subject Classification: 68—Computer science Advisor 1: Leslie Gabriel ValiantNo students known. If you have additional information or corrections regarding this mathematician, please use the update form. To submit students of this mathematician, please use the new data form, noting this mathematician's MGP ID of 181187 for the advisor ID.
Research: Research Interests - Vertex operator algebras, affine Lie algebras, partition identities Publications/Pre-prints - IdentityFinder and some new identities of Rogers-Ramanujan type [abstract]  [1411.5346] [maple code] S. Kanade, M. C. Russell Accepted for publication in Experimental Mathematics The Rogers-Ramanujan identities and various analogous identities (Gordon, Andrews-Bressoud, Capparelli, etc.) form a family of very deep identities concerned with integer partitions. These identities (written in generating function form) are typically of the form product side equals sum side, with the product side enumerating partitions obeying certain congruence conditions and the sum side obeying certain initial conditions and difference conditions (along with possibly other restrictions). We use symbolic computation to generate various such sum sides and then use Euler's algorithm to see which of them actually do produce elegant conjectured product sides. We not only rediscover many of the known identities but also discover some apparently new ones, as conjectures supported by strong mathematical evidence. Ghost series and a motivated proof of the Andrews-Bressoud Identities [abstract]  [1411.2048] S. Kanade, J. Lepowsky, M. C. Russell, A. V. Sills We present what we call a ``motivated proof'' of the Andrews-Bressoud partition identities for even moduli. A ``motivated proof'' of the Rogers-Ramanujan identities was given by G. E. Andrews and R. J. Baxter, and this proof was generalized to the odd-moduli case of Gordon's identities by J. Lepowsky and M. Zhu. Recently, a ``motivated proof'' of the somewhat analogous G\ ollnitz-Gordon-Andrews identities has been found. In the present work, we introduce ``shelves'' of formal series incorporating what we call ``ghost series,'' which allow us to pass from one shelf to the next via natural recursions, leading to our.
My research interests are in the areas of computer vision, visual and multi-media technology, and robotics. Common themes that my students and I emphasize in performing research are the formulation of sound theories which use the physical, geometrical, and semantic properties involved in perceptual and control processes in order to create intelligent machines, and the demonstration of the working systems based on these theories. My current projects include basic research and system development in computer vision (motion, stereo and object recognition), recognition of facial expressions, virtual(ized) reality, content-based video and image retrieval, VLSI-based computational sensors, medical robotics, and an autonomous helicopter. Computer vision Within the Image Understanding (IU) project, my students and I are conducting basic research in interpretation and sensing for computer vision. My major thrust is the science of computer vision. Traditionally, many computer vision algorithms were derived heuristically either by introspection or biological analogy. In contrast, my approach to vision is to transform the physical, geometrical, optical and statistical processes, which underlie vision, into mathematical and computational models. This approach results in algorithms that are far more powerful and revealing than traditional ad hoc methods based solely on heuristic knowledge. With this approach we have developed a new class of algorithms for color, stereo, motion, and texture. The two most successful examples of this approach are the factorization method and the multi-baseline stereo method. The factorization method is for the robust recovering of shape and motion from an image sequence. Based on this theory we have been developing a system for modeling by video taping ; a user takes a video tape of a scene or an object by either moving a camera or moving the object.
Online Learning in Markov Decision Processes with Adversarially Chosen Transition Probability Distributions [pdf] (arxiv version in preparation) Yasin Abbasi-Yadkori, Peter Bartlett, Varun Kanade, Yevgeny Seldin, and Csaba Szepsvári In the 26th Advances in Neural Informatin Processing Systems, NIPS 2013.
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Scholar Commons > Graduate School > Theses and Dissertations > 1104 Graduate Theses and Dissertations Title Fuzzy ants as a clustering concept Author Parag M. Kanade, University of South Florida Graduation Year 2004 Document Type Thesis Degree M.S.C.S. Degree Granting Department Computer Science Major Professor Hall, Lawrence O. Keywords Hard C Means Algorithm, Fuzzy C Means Algorithm, Ant Colony Optimization, swarm intelligence, cluster analysis Abstract We present two Swarm Intelligence based approaches for data clustering. The first algorithm, Fuzzy Ants, presented in this thesis clusters data without the initial knowledge of the number of clusters. It is a two stage algorithm. In the first stage the ants cluster data to initially create raw clusters which are refined using the Fuzzy C Means algorithm. Initially, the ants move the individual objects to form heaps. The centroids of these heaps are redefined by the Fuzzy C Means algorithm. In the second stage the objects obtained from the Fuzzy C Means algorithm are hardened according to the maximum membership criteria to form new heaps. These new heaps are then moved by the ants. The final clusters formed are refined by using the Fuzzy C Means algorithm. Results from experiments with 13 datasets show that the partitions produced are competitive with those from FCM. The second algorithm, Fuzzy ant clustering with centroids, is also a two stage algorithm, it requires an initial knowledge of the number of clusters in the data. In the first stage of the algorithm ants move the cluster centers in feature space. The cluster centers found by the ants are evaluated using a reformulated Fuzzy C Means criterion. In the second stage the best cluster centers found are used as the initial cluster centers for the Fuzzy C Means algorithm. Results on 18 datasets show that the partitions found by FCM using the ant initialization.