Showing papers on "Support vector machine published in 1988"
11 Apr 1988
TL;DR: The QR factor orthogonalizes the data matrix and solves the problem of Cholesky factoring the experimental correlation matrix and its inverse, which means the authors can use generalized Levinson algorithms to derive generalized QR algorithms, which are then used to derived generalized Schur algorithms.
Abstract: The authors pose a sequence of linear prediction problems. By solving this sequence of problems they are able to QR factor all of the data matrices usually associated with correlation, pre-windowed and post-windowed, and covariance methods of linear prediction. Their solutions cover the forward, backward, and forward-backward problems. The QR factor orthogonalizes the data matrix and solves the problem of Cholesky factoring the experimental correlation matrix and its inverse. This means they can use generalized Levinson algorithms to derive generalized QR algorithms, which are then used to derived generalized Schur algorithms. All three algorithms are true lattice algorithms that can be implemented either on a vector machine or on a multiline lattice, and all three algorithms generate generalized reflection coefficients that may be used for filtering or classification. >
1 citations
1 Jan 1988
TL;DR: This paper presents several algorithms for reconstructing 2-D convex sets given support line measurements for which the angles are known precisely but the lateral displacements are noisy and develops a vector decomposition called the Size/Shape/Shift decomposition which helps to provide insight into the detailed geometric relationship between support vectors and 2- D convex objects.
Abstract: In this paper we present several algorithms for reconstructing 2-D convex sets given support line measurements for which the angles are known precisely but the lateral displacements are noisy. We extend the algorithms given in [5] by explicitly incorporating prior information about the shape of the objects to be reconstructed. In particular, the prior shape information is contained in a prior probability on support vectors, where a support vector is a vector formed from the lateral displacements of a particular set of support lines of an object. In order to relate the support vector prior to the expected shape of an object we develop a vector decomposition called the Size/Shape/Shift decomposition which helps to provide insight into the detailed geometric relationship between support vectors and 2-D convex objects. We then use the maximum a posteriori (MAP) criterion to determine the specific form of the support vector estimator. The computations involve a quadratic programming optimization stage, which is used to determine one component of the decomposition, and either a line search or conjugate gradient stage, which is used to determine the remaining components. The performance of the algorithms is demonstrated using simulated support line measurements of an ellipse.