Above are papers related to the following paper: [Paper_ID] Paper #708945. 	[Title] Massive Data Discrimination via Linear Support Vector Machines [Abstract] A linear support vector machine formulation is used to generate a fast, finitely-terminating linear-programming algorithm for discriminating between two massive sets in n-dimensional space, where the number of points can be orders of magnitude larger than n. The algorithm creates a succession of sufficiently small linear programs that separate chunks of the data at a time. The key idea is that a small number of support vectors, corresponding to linear programming constraints with positive dual variables, are carried over between the successive small linear programs, each of which containing a chunk of the data. We prove that this procedure is monotonic and terminates in a finite number of steps at an exact solution that leads to a globally optimal separating plane for the entire dataset. Numerical results on fully dense publicly available datasets, numbering 20,000 to 1 million points in 32-dimensional space, confirm the theoretical results and demonstrate the ability to handle very large problems. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #15076. 	[Title] Support Vector Machines: Training and Applications [Abstract] The Support Vector Machine (SVM) is a new and very promising classification technique developed by Vapnik and his group at AT&T Bell Laboratories [3, 6, 8, 24]. This new learning algorithm can be seen as an alternative training technique for Polynomial, Radial Basis Function and Multi-Layer Perceptron classifiers. The main idea behind the technique is to separate the classes with a surface that maximizes the margin between them. An interesting property of this approach is that it is an approximate implementation of the Structural Risk Minimization (SRM) induction principle [23]. The derivation of Support Vector Machines, its relationship with SRM, and its geometrical insight, are discussed in this paper. Since Structural Risk Minimization is an inductive principle that aims at minimizing a bound on the generalization error of a model, rather than minimizing the Mean Square Error over the data set (as Empirical Risk Minimization methods do), training a SVM to obtain the maximum margin classifier requires a different objective function. This objective function is then optimized by solving a large-scale quadratic programming problem with linear and box constraints. The problem is considered challenging, because the quadratic form is completely dense, so the memory needed to store the problem grows with the square of the number of data points. Therefore, training problems arising in some real applications with large data sets are impossible to load into memory, and cannot be solved using standard non-linear constrained optimization algorithms. We present a decomposition algorithm that can be used to train SVM's over large data sets. The main idea behind the decomposition is the iterative solution of sub-problems and the evaluation of, and also establish the stopping criteria for the algorithm. We present previous approaches, as well as results and important details of our implementation of the algorithm using a second-order variant of the Reduced Gradient Method as the solver of the sub-problems. As an application of SVM's, we present preliminary results in Frontal Human Face Detection in images. This application opens many interesting questions and future research opportunities, both in the context of faster and better optimization algorithms, and in the use of SVM's in other pattern classification, recognition, and detection applications. This report describes research done within the Center for Biological and Computational Learning in the Department of Brain and Cognitive Sciences and the Artificial Intelligence Laboratory at the Massachusetts Institute of Technology. This research is sponsored by MURI grant N00014-95-1-0600; by a grant from ONR/ARPA under contract N00014-92-J-1879 and by the National Science Foundation under contract ASC-9217041 (this award includes funds from ARPA provided under the HPCC program). Edgar Osuna was supported by Fundacion Gran Mariscal de Ayacucho and Daimler Benz. Additional support is provided by Daimler-Benz, Eastman Kodak Company, Siemens Corporate Research, Inc. and AT&T. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #25702. 	[Title] Nonlinear Prediction of Chaotic Time Series Using Support Vector Machines [Abstract] A novel method for regression has been recently proposed by V. Vapnik et al. [8, 9]. The technique, called Support Vector Machine (SVM), is very well founded from the mathematical point of view and seems to provide a new insight in function approximation. We implemented the SVM and tested it on the same data base of chaotic time series that was used in [1] to compare the performances of different approximation techniques, including polynomial and rational approximation, local polynomial techniques, Radial Basis Functions, and Neural Networks. The SVM performs better than the approaches presented in [1]. We also study, for a particular time series, the variability in performance with respect to the few free parameters of SVM. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #307336. 	[Title] A Support Vector Machine Approach to Decision Trees [Abstract] Key ideas from statistical learning theory and support vector machines are generalized to decision trees. A support vector machine is used for each decision in the tree. The "optimal" decision tree is characterized, and both a primal and dual space formulation for constructing the tree are proposed. The result is a method for generating logically simple decision trees with multivariate linear or nonlinear decisions. The preliminary results indicate that the method produces simple trees that generalize well with respect to other decision tree algorithms and single support vector machines. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3243. 	[Title] A System for Induction of Oblique Decision Trees [Abstract] This article describes a new system for induction of oblique decision trees. This system, OC1, combines deterministic hill-climbing with two forms of randomization to find a good oblique split (in the form of a hyperplane) at each node of a decision tree. Oblique decision tree methods are tuned especially for domains in which the attributes are numeric, although they can be adapted to symbolic or mixed symbolic/numeric attributes. We present extensive empirical studies, using both real and artificial data, that analyze OC1's ability to construct oblique trees that are smaller and more accurate than their axis-parallel counterparts. We also examine the benefits of randomization for the construction of oblique decision trees. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #285675. 	[Title] Parsimonious Least Norm Approximation [Abstract] A theoretically justifiable fast finite successive linear approximation algorithm is proposed for obtaining a parsimonious solution to a corrupted linear system Ax = b + p, where the corruption p is due to noise or error in measurement. The proposed linear-programming-based algorithm finds a solution x by parametrically minimizing the number of nonzero elements in x and the error k Ax b p k 1 . Numerical tests on a signal-processing-based example indicate that the proposed method is comparable to a method that parametrically minimizes the 1-norm of the solution x and the error k Ax b p k 1 , and that both methods are superior, by orders of magnitude, to solutions obtained by least squares as well by combinatorially choosing an optimal solution with a specific number of nonzero elements. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #24043. 	[Title] Human Face Detection in Visual Scenes [Abstract] We present a neural network-based face detection system. A retinally connected neural network examines small windows of an image, and decides whether each window contains a face. The system arbitrates between multiple networks to improve performance over a single network. We use a bootstrap algorithm for training, which adds false detections into the training set as training progresses. This eliminates the difficult task of manually selecting non-face training examples, which must be chosen to span the entire space of non-face images. Comparisons with another state-of-the-art face detection system are presented; our system has better performance in terms of detection and false-positive rates. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #191216. 	[Title] Ridge Regression Learning Algorithm in Dual Variables [Abstract] In this paper we study a dual version of the Ridge Regression procedure. It allows us to perform non-linear regression by constructing a linear regression function in a high dimensional feature space. The feature space representation can result in a large increase in the number of parameters used by the algorithm. In order to combat this "curse of dimensionality", the algorithm allows the use of kernel functions, as used in Support Vector methods. We also discuss a powerful family of kernel functions which is constructed using the ANOVA decomposition method from the kernel corresponding to splines with an infinite number of nodes. This paper introduces a regression estimation algorithm which is a combination of these two elements: the dual version of Ridge Regression is applied to the ANOVA enhancement of the infinite-node splines. Experimental results are then presented (based on the Boston Housing data set) which indicate the performance of this algorithm relative to other algorithms. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #174418. 	[Title] Improving the Accuracy and Speed of Support Vector Machines [Abstract] Support Vector Learning Machines (SVM) are finding application in pattern recognition, regression estimation, and operator inversion for ill-posed problems. Against this very general backdrop, any methods for improving the generalization performance, or for improving the speed in test phase, of SVMs are of increasing interest. In this paper we combine two such techniques on a pattern recognition problem. The method for improving generalization performance (the "virtual support vector" method) does so by incorporating known invariances of the problem. This method achieves a drop in the error rate on 10,000 NIST test digit images of 1.4% to 1.0%. The method for improving the speed (the "reduced set" method) does so by approximating the support vector decision surface. We apply this method to achieve a factor of fifty speedup in test phase over the virtual support vector machine. The combined approach yields a machine which is both 22 times faster than the original machine, and which has better generalization performance, achieving 1.1% error. The virtual support vector method is applicable to any SVM problem with known invariances. The reduced set method is applicable to any support vector machine. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #32276. 	[Title] Extracting Support Data for a Given Task [Abstract] We report a novel possibility for extracting a small subset of a data base which contains all the information necessary to solve a given classification task: using the Support Vector Algorithm to train three different types of handwritten digit classifiers, we observed that these types of classifiers construct their decision surface from strongly overlapping small ( 4%) subsets of the data base. This finding opens up the possibility of compressing data bases significantly by disposing of the data which is not important for the solution of a given task. In addition, we show that the theory allows us to predict the classifier that will have the best generalization ability, based solely on performance on the training set and characteristics of the learning machines. This finding is important for cases where the amount of available data is limited. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #191222. 	[Title] Support Vector Machines, Reproducing Kernel Hilbert Spaces and the Randomized GACV 1 [Abstract] 1 Prepared for the NIPS 97 Workshop on Support Vector Machines. Research sponsored in part by NSF under Grant DMS-9704758 and in part by NEI under Grant R01 EY09946. This is a second revised and corrected version of a report of the same number and title dated November 29, 1997 Please summarise all the given information.

Paper #708945 has the title `Massive Data Discrimination via Linear Support Vector Machines  
` and the abstract `A linear support vector machine formulation is used to generate a fast, finitely-terminating linear-programming algorithm for discriminating between two massive sets in n-dimensional space, where the number of points can be orders of magnitude larger than n. The algorithm creates a succession of sufficiently small linear programs that separate chunks of the data at a time. The key idea is that a small number of support vectors, corresponding to linear programming constraints with positive dual variables, are carried over between the successive small linear programs, each of which containing a chunk of the data. We prove that this procedure is monotonic and terminates in a finite number of steps at an exact solution that leads to a globally optimal separating plane for the entire dataset. Numerical results on fully dense publicly available datasets, numbering 20,000 to 1 million points in 32-dimensional space, confirm the theoretical results and demonstrate the ability to handle very large problems.
`.
Question: Which category should Paper #708945 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #708945 has the title `Massive Data Discrimination via Linear Support Vector Machines  
` and the abstract `A linear support vector machine formulation is used to generate a fast, finitely-terminating linear-programming algorithm for discriminating between two massive sets in n-dimensional space, where the number of points can be orders of magnitude larger than n. The algorithm creates a succession of sufficiently small linear programs that separate chunks of the data at a time. The key idea is that a small number of support vectors, corresponding to linear programming constraints with positive dual variables, are carried over between the successive small linear programs, each of which containing a chunk of the data. We prove that this procedure is monotonic and terminates in a finite number of steps at an exact solution that leads to a globally optimal separating plane for the entire dataset. Numerical results on fully dense publicly available datasets, numbering 20,000 to 1 million points in 32-dimensional space, confirm the theoretical results and demonstrate the ability to handle very large problems.
`.
Question: Which category should Paper #708945 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Neural_Networks