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Bias plus variance decomposition for zeroone loss functions
 In Machine Learning: Proceedings of the Thirteenth International Conference
, 1996
"... We present a biasvariance decomposition of expected misclassi cation rate, the most commonly used loss function in supervised classi cation learning. The biasvariance decomposition for quadratic loss functions is well known and serves as an important tool for analyzing learning algorithms, yet no ..."
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Cited by 212 (5 self)
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We present a biasvariance decomposition of expected misclassi cation rate, the most commonly used loss function in supervised classi cation learning. The biasvariance decomposition for quadratic loss functions is well known and serves as an important tool for analyzing learning algorithms, yet
Decomposition of ObjectOriented Database Schemas
 Annals of Mathematics and Artificial Intelligence
, 2000
"... Based on Flogic, we specify an advanced data model with objectoriented and logicoriented features. For this model we study the decomposition of a class, the counterpart to the wellknown decomposition of a relation scheme under functional dependencies. For this decomposition of a class, the tr ..."
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Cited by 4 (1 self)
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Based on Flogic, we specify an advanced data model with objectoriented and logicoriented features. For this model we study the decomposition of a class, the counterpart to the wellknown decomposition of a relation scheme under functional dependencies. For this decomposition of a class
Descent representations and multivariate statistics
 Trans. Amer. Math. Soc
"... Abstract. Combinatorial identities on Weyl groups of types A and B are derived from special bases of the corresponding coinvariant algebras. Using the GarsiaStanton descent basis of the coinvariant algebra of type A we give a new construction of the Solomon descent representations. An extension of ..."
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Cited by 22 (5 self)
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of the descent basis to type B, using new multivariate statistics on the group, yields a refinement of the descent representations. These constructions are then applied to refine wellknown decomposition rules of the coinvariant algebra and to generalize various identities. 1.
Decomposition of Database Classes under Path Functional Dependencies and Onto Constraints
 In Foundations of Information and Knowledge Systems
, 2000
"... Based on Flogic, we specify an advanced data model with objectoriented and logicoriented features that substantially extend the relational approach. For this model we exhibit and study the counterpart to the wellknown decomposition of a relation scheme according to a nontrivial nonkey functio ..."
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Cited by 17 (2 self)
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Based on Flogic, we specify an advanced data model with objectoriented and logicoriented features that substantially extend the relational approach. For this model we exhibit and study the counterpart to the wellknown decomposition of a relation scheme according to a nontrivial nonkey
Symmetric Venn Diagrams on the Sphere I: Chain Decompositions and Isometry Groups of Order Two
, 2009
"... Let f be an isometry of the sphere which is an involution (that is, f −1 = f). For any n ≥ 1 we prove that there is an ncurve Venn diagram on the sphere whose isometry group is generated by f and which has the property that f(Θ) = Θ, where Θ is a curve of the diagram. One of the constructions uses ..."
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uses a new chain decomposition of the Boolean lattice, a decomposition which is based on the wellknown decomposition of N. G. de Bruijn, C. A. van Ebbenhorst Tengbergen, and D. R. Kruyswijk. 1
factorizations using SMPSs
"... a r t i c l e i n f o ð1Þ and engin r solution c in a direct method that first decomposes A into a simpler form, and then solves the corresponding transformed sys wellknown decomposition for the solution of (1), when the coefficient matrix A is symmetric positive definite (s. the Cholesky factoriza ..."
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a r t i c l e i n f o ð1Þ and engin r solution c in a direct method that first decomposes A into a simpler form, and then solves the corresponding transformed sys wellknown decomposition for the solution of (1), when the coefficient matrix A is symmetric positive definite (s. the Cholesky
Note on the Khaneja Glaser decomposition
, 2004
"... Recently, Vatan and Williams utilize a matrix decomposition of SU(2n) introduced by Khaneja and Glaser to produce CNOTefficient circuits for arbitrary threequbit unitary evolutions. In this note, we place the Khaneja Glaser Decomposition (KGD) in context as a SU(2n) = KAK decomposition by proving ..."
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Cited by 8 (2 self)
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by proving that its Cartan involution is type AIII, given n ≥ 3. The standard type AIII involution produces the CosineSine Decomposition (CSD), a wellknown decomposition in numerical linear algebra which may be computed using mature, stable algorithms. In the course of our proof that the new decomposition
unknown title
"... Abstract—This paper presents a new version of the SVM mixture algorithm initially proposed by Kwok for classification and regression problems. For both cases, a slight modification of the mixture model leads to a standard SVM training problem, to the existence of an exact solution and allows the dir ..."
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the direct use of well known decomposition and working set selection algorithms. Only the regression case is considered in this paper but classification has been addressed in a very similar way. This method has been successfully applied to engine pollutants emission modeling.
An Exact Solution to Support Vector Mixture
"... Abstract—This paper presents a new version of the SVM mixture algorithm initially proposed by Kwok for classification and regression problems. For both cases, a slight modification of the mixture model leads to a standard SVM training problem, to the existence of an exact solution and allows the dir ..."
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the direct use of well known decomposition and working set selection algorithms. Only the regression case is considered in this paper but classification has been addressed in a very similar way. This method has been successfully applied to engine pollutants emission modeling.
Discrete Multiscale Vector Field Decomposition
, 2003
"... While 2D and 3D vector fields are ubiquitous in computational sciences, their use in graphics is often limited to regular grids, where computations are easily handled through finitedifference methods. In this paper, we propose a set of simple and accurate tools for the analysis of 3D discrete vecto ..."
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Cited by 92 (10 self)
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vector fields on arbitrary tetrahedral grids. We introduce a variational, multiscale decomposition of vector fields into three intuitive components: a divergencefree part, a curlfree part, and a harmonic part. We show how our discrete approach matches its wellknown smooth analog, called the Helmotz
Results 11  20
of
1,959