Multiple kernel learning for feature selection (MKLFS) utilizes kernels to explore complex properties of features and performs better in embedded methods. However, the kernels in MKL-FS are generally limited to be positive definite. In fact, indefinite kernels often emerge in actual applications and can achieve better empirical performance. But due to the non-convexity of indefinite kernels, ex...

An important theorem of Banaszczyk (Random Structures & Algorithms ‘98) states that for any sequence of vectors of `2 norm at most 1/5 and any convex body K of Gaussian measure 1/2 in R, there exists a signed combination of these vectors which lands inside K. A major open problem is to devise a constructive version of Banaszczyk’s vector balancing theorem, i.e. to find an efficient algorithm wh...

It is an open question whether a non-trivial convex combination of triangular norms (resp. conorms) can be a triangular norm (resp. conorm). We investigate the analogous question for S-implications and R-implications.

The rational cubic function with three parameters has been extended to rational bi-cubic function to visualize the shape of regular convex surface data. The rational bi-cubic function involves six parameters in each rectangular patch. Data dependent constraints are derived on four of these parameters to visualize the shape of convex surface data while other two are free to refine the shape of s...

We consider the second variation for the volume of convex bodies associated with the Lp Minkowski-Firey combination and obtain a Poincaré-type inequality on the Euclidean unit sphere Sn−1 . Mathematics subject classification (2010): 52A20.

We show that every upper semicontinuous and equi-affine invariant valuation on the space of d-dimensional convex bodies is a linear combination of affine surface area, volume and the Euler characteristic. 1991 AMS subject classification: Primary 52A20; Secondary 53A15.

A semiparametric estimate of a density may be formed via the convex combination of a parametric and a nonparametric density estimate. It is shown that the some trimming is often necessary to obtain an appropriate proportion of

It is well-known that model combination can improve prediction performance of regression model. We investigate the model combination of Support Vector Regression (SVR) with regularization path in this paper. We first define Lε-risk of SVR, and prove that SVR regularization path leads to at least one Lε-risk consistent fitted model. Then we establish the Lε-risk consistency for convex combinatio...

The notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $CAT(0)$ space, where the curvature is bounded from above by zero. In fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. In this paper, w...

In this paper, the shape influence of piezoelectric beams including triangle, trapezoid, rectangle, inverted trapezoid, convex parabola, concave parabola, and comb-shaped (a combination of two triangular beams with a connector of 4 mm length) are addressed and analyzed by FEM. The analysis is performed for a bimorph piezoelectric beam. The analyzed parameters include the beam length, thickness ...