This paper presents a new formulation of multi-instance learning as maximum margin problem, which is an extension of the standard C-support vector classification. For linear classification, this extension leads to, instead of a mixed integer quadratic programming, a continuous optimization problem, where the objective function is convex quadratic and the constraints are either linear or bilinea...

In a recent paper by the first author, a simple proof was given of a result by Tutte on the validity of barycentric mappings, recast in terms of the injectivity of piecewise linear mappings over triangulations. In this note, we make a short extension to the proof to deal with arbitrary tilings. We also give a simple counterexample to show that convex combination mappings over tetrahedral meshes...

Owing to the effect of classified models was different in Protein-Protein Interaction (PPI) extraction, which was made by different single kernel functions, and only using single kernel function hardly trained the optimal classified model to extract PPI, this paper presents a strategy to find the optimal kernel function from a kernel function set. The strategy is that in the kernel function set...

In a distributed estimation or tracking system, local estimates are first generated from individual sensors. The state estimates of associated objects are then fused to generate the global estimates. The fusion algorithm has to deal with correlated estimation errors due to common past information or common process noise. Most approaches to estimation fusion use a convex combination of the local...

Several recent publications have proposed methods for mapping images into continuous semantic embedding spaces. In some cases the embedding space is trained jointly with the image transformation. In other cases the semantic embedding space is established by an independent natural language processing task, and then the image transformation into that space is learned in a second stage. Proponents...

When using machine learning techniques for learning a function approximation from given data it can be difficult to select the right modelling technique. Without preliminary knowledge about the function it might be beneficial if the algorithm could learn all models by itself and select the model that suits best to the problem, an approach known as automated model selection. We propose a general...

This paper introduces an estimation scheme aimed at improving the performance of adaptive filters. The basic idea consists of a convex combination of three adaptive filters, all based on the affine projection algorithm with different numbers of normalization hyperplanes. The three filters are adjusted separately and then combined to minimize the MSE and to increase the speed of convergence of t...

Let ugi the unique solutions of an elliptic variational inequality with second member gi (i = 1, 2). We establish necessary and sufficient conditions for the convex combination tug1 + (1 − t)ug2 , to be equal to the unique solution of the same elliptic variational inequality with second member tg1 + (1− t)g2. We also give some examples where this property is valid.

For λ ∈ (0,1) and x,y > 0 we obtain the best possible constants p and r , such that erf(Mp(x,y;λ)) λ erf(x)+(1−λ) erf(y) erf(Mr(x,y;λ)) where erf(x) = 2 √π ∫ x 0 e −tdt and Mp(x,y;λ) = (λxp + (1− λ)yp)1/p(p = 0) , M0(x,y;λ) = xλ y1−λ are error function and weighted power mean, respectively. Furthermore, using these results, we generalized and complement an inequality due to Alzer.

We show that every rigid motion invariant and upper semicontinuous valuation on the space of convex discs is a linear combination of the Euler characteristic, the length, the area, and a suitable curvature integral of the convex disc. 1991 AMS subject classification: 52A10, 53A04