To avoid the hard task concerning the choice of a suitable grouping function for any given image, we propose to use a combination of several of them. We study different ways of choosing the weights for this combination.Jurio, Aranzazu
Suppose x,y\in dom f and f(y)\leq f(x), z is convex combination of x,y,which indicates z=\theta x+(1-\theta) y let \alpha = f(x),A_\alpha =\{u|f(u)\leq f(x)=\alpha \},显然x\in A_\alpha,y\in A_\alpha,我们要证明f(z)\leq f(x)=\alpha,对于\forall \theta\...
can be extended to convex combination of more than two points if f is convex: f(θ1x1+...+θkxk)≤θ1f(x1)+...+θkf(xk) The inequality can be extended to infinite sums: f(∫Sp(x)xdx)≤∫Sf(x)p(x)dx Provided the integral exists. If x is a random variable such that x...
conic (nonnegative) combination of x1x1 and x2x2: any point of the form x=θ1x1+θ2x2x=θ1x1+θ2x2 with θ1≥0,θ2≥0θ1≥0,θ2≥0 convex cone: set that contains all conic combinations of points in the set hyperplane and half-sapces hyperplane: set of the form {x|aTx=b}(...
Integrally convex functions constitute a fundamental function class in discrete convex analysis, including M-convex functions, L-convex functions, and many
convex function in the sense of Jensen convex hull convex linear combination convex linear hull convex polygon convex polyhedron convex polytope convex programming convex sequence convex set convex span Convexity and Concavity convexo-concave conveyance ...
Th. Linear combination of two convex functions考虑两个凸函数的加和,有: 若ff 为α1α1-strongly convex,gg 为α2α2-strongly convex,则 f+gf+g 为(α1+α2)(α1+α2)-strongly convex 若ff 为β1β1-smooth,gg 为β2β2-smooth,则 f+gf+g 为(β1+β2)(β1+β2)-smooth 考虑凸函数...
Conic Combination Polyhedral Set Extreme point of a convex set Direction Convex & Concave Function Jensen's Inequality Differentiable Convex Function Sufficient & Necessary Conditions for Global Optima Quasiconvex & Quasiconcave functions Differentiable Quasiconvex Function Strictly Quasiconvex Function Strongly...
Convex Combination Kernel FunctionOwing 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 ...
If are functions and if are positive functionals providing the unit equality (4) then (5) Respecting the requirement of unit equality in (4), the sum could be called the functional convex combination. In the case n = 1, the functional L = L1 must be unital by the unit equality in...