Large scale nonsmooth convex optimization is a common problem for a range of computational areas including machine learning and computer vision. Problems in these areas contain special domain structures and characteristics. Special treatment of such problem domains, exploiting their structures, can significantly improve the computational burden. We present a weighted Mirror Descent method to so...

Gaussian graphical models are useful to analyze and visualize conditional dependence relationships between interacting units. Motivated from network analysis under di erent experimental conditions, such as gene networks for disparate cancer subtypes, we model structural changes over multiple networks with possible heterogeneities. In particular, we estimate multiple precision matrices describin...

In this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. In particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. Then we study fuzzy...

In this paper, we propose a new method for fuzzy numbers. In this method, we assume that Ai= (ai1, ai2, ai3, ai4) is to be a fuzzy number. So, the convex combination of ai1 and ai2 and also the convex combination of ai3 and ai4 are obtained separately. Then, Mic and Mis that are to be the convex combinations and the standard deviation respectively we acquire them from these components. Finally,...

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...

in this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.

knowing the fact that the main weakness of the most standard methods including k-means and hierarchical data clustering is their sensitivity to initialization and trapping to local minima, this paper proposes a modification of convex data clustering  in which there is no need to  be peculiar about how to select initial values. due to properly converting the task of optimization to an equivalent...

‎In this paper‎, ‎we study the convex combinations of harmonic mappings obtained by shearing a class of slit conformal mappings‎. ‎Sufficient conditions for the convex combinations of harmonic mappings of this family to be univalent and convex in the horizontal direction are derived‎. ‎Several examples of univalent harmonic mappings constructed by using these methods are presented to illustrate...