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 introduce partial dcpo’s and show their some applications. A partial dcpo is a poset associated with a designated collection of directed subsets. We prove that (i) the dcpo-completion of every partial dcpo exists; (ii) for certain spaces X, the corresponding partial dcpo’s of continuous real valued functions on X are continuous partial dcpos; (iii) if a space X is Hausdorff compact, the latt...

It has been suggested that the \Maximum Realisable Receiver Operating Characteristics" for a combination of classiiers is the convex hull of their individual ROCs Scott et al., 1998]. As expected in at least some cases better ROCs can be produced. We show genetic programming (GP) can automatically produce a combination of classi-ers whose ROC is better than the convex hull of the supplied class...

Genetic programming (GP) can automatically fuse given classifiers of diverse types to produce a combined classifier whose Receiver Operating Characteristics (ROC) are better than [Scott et al.1998b]’s “Maximum Realisable Receiver Operating Characteristics” (MRROC). I.e. better than their convex hull. This is demonstrated on a satellite image processing bench mark using Naive Bayes, Decision Tre...

Genetic programming (GP) can automatically fuse given classifiers to produce a combined classifier whose Receiver Operating Characteristics (ROC) are better than [Scott et al., 1998b]’s “Maximum Realisable Receiver Operating Characteristics” (MRROC). I.e. better than their convex hull. This is demonstrated on artificial, medical and satellite image processing bench marks.

Given a finite set of points P ⊆ R, we would like to find a small subset S ⊆ P such that the convex hull of S approximately contains P . More formally, every point in P is within distance from the convex hull of S. Such a subset S is called an -hull. Computing an -hull is an important problem in computational geometry, machine learning, and approximation algorithms. In many real world applicati...

The anchor words algorithm performs provably efficient topic model inference by finding an approximate convex hull in a high-dimensional word co-occurrence space. However, the existing greedy algorithm often selects poor anchor words, reducing topic quality and interpretability. Rather than finding an approximate convex hull in a high-dimensional space, we propose to find an exact convex hull i...

We study transitivity conditions on the norm of JB∗-triples, C∗-algebras, JBalgebras, and their preduals. We show that, for the predual X of a JBW∗-triple, each one of the following conditions i) and ii) implies that X is a Hilbert space. i) The closed unit ball of X has some extreme point and the norm of X is convex transitive. ii) The set of all extreme points of the closed unit ball of X is ...

If X is a vector space and E is a subset of X, the convex hull of E is defined to be the intersection of all convex sets containing E, and is denoted by co(E). One checks that the convex hull of E is equal to the set of all finite convex combinations of elements of E. If X is a topological vector space, the closed convex hull of E is the intersection of all closed convex sets containing E, and ...