A simultaneous sparse approximation problem requests a good approximation of several input signals at once using different linear combinations of the same elementary signals. At the same time, the problem balances the error in approximation against the total number of elementary signals that participate. These elementary signals typically model coherent structures in the input signals, and they...

In general, approximating classes of functions deened over high-dimensional input spaces by linear combinations of a xed set of basis functions or \features" is known to be hard. Typically, the worst-case error of the best basis set decays only as fast as ? n ?1=d , where n is the number of basis functions and d is the input dimension. However , there are many examples of high-dimensional patte...

Much recent attention, both experimental and theoretical, has been focussed on classii-cation algorithms which produce voted combinations of classiiers. Recent theoretical work has shown that the impressive generalization performance of algorithms like AdaBoost can be attributed to the classiier having large margins on the training data. We present abstract algorithms for nding linear and conve...

Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of non-zero elements of the factors is assumed fixed and known. The formulation counts sparse PCA with multiple factors, subspace clustering and low-rank sparse bilinear regression as potential applications. We compute slow rates and an upper bound on the statistical dime...

A fundamental problem in geometry processing is that of expressing a point inside a convex polyhedron as a combination of the vertices of the polyhedron. Instances of this problem arise often in mesh parameterization and 3D deformation. A related problem is to express a vector lying in a convex cone as a non-negative combination of edge rays of this cone. This problem also arises in many applic...

In this paper we find a characterization type result for (η1,η2)-convex functions. The Fejér integral inequality related to (η1,η2)-convex functions is obtained as a generalization of Fejér inequality related to the preinvex and η-convex functions. Also some Fejér trapezoid and midpoint type inequalities are given in the case that the absolute value of the derivative of considered function is (...

The fundamental challenge of the millimeter-wave (mmWave) frequency band is sensitivity radio channel to blockages, which gives rise unstable connectivity and impacts reliability a system. To this end, multi-point promising approach for ensuring desired rate requirements. A robust beamformer design proposed improve communication by exploiting spatial macro-diversity pessimistic estimate rates o...

The concepts of $L$-convex systems and Scott-hull spaces are proposed on frame-valued setting. Also, we establish the categorical isomorphism between  $L$-convex systems and Scott-hull spaces. Moreover, it is proved that the category of $L$-convex structures is  bireflective in the category of $L$-convex systems. Furthermore, the quotient systems of $L$-convex systems are studied.

we first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a banach space and next show that if the banach space is having the opial condition, then the fixed points set of such a mapping with the convex range is nonempty. in particular, we establish that if the banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...