Hence•Machinelearning(Clustering,Kerneloptimization,Featureselection,…)•Engineering(Qualitycontrol,...)•…2.1DCFunctions•Definition2.1.LetCbeaconvexsubsetofRn.Areal-valuedfunctionf:C RiscalledDConC,ifthereexisttwoconvexfunctionsg,h:C Rsuchthatfcanbeexpressedintheformf(x)=g(x)-h(x)(1)h...
The DC programming and its DC algorithm (DCA) address the problem of minimizing a function f = g h (with g , h being lower semicontinuous proper convex functions on R n ) on the whole space. Based on local optimality conditions and DC duality, DCA was suc...
今天介绍的这种算法,Difference of Convex Algorithm,也就是DCA,以便咱们解决非凸优化问题。 但这种问题仅仅针对某些特定情况。 首先,咱们对这串英文进行解读,Difference理解为差,convex是凸,即凸函数,algorithm嘛,你们自己查词典,哈哈哈。所以呢,DCA就是两个凸函数的差的算法。 你们肯定懵逼了,啥凸函数的差?Emmm, ...
The DC programming and its DC algorithm (DCA) address the problem of minimizing a function f = g h (with g , h being lower semicontinuous proper convex functions on R n ) on the whole space. Based on local optimality conditions and DC duality, DCA was successfully applied to a lot of...
We introduce a new class of parameter estimation methods for log-linear models. Our approach relies on the fact that minimizing a rational function of mixtures of exponentials is equivalent to minimizing a difference of convex functions. This allows us to construct convex aux...
Block Clustering Based on DC Programming and Algorithms 2787 For a convex function θ , the subdifferential of θ at x0 ∈ dom θ := {x ∈ IR p : θ (x0 ) < +∞}, denoted by ?θ (x0 ), is de?ned by ?θ (x0 ) := {y ∈ IR p : θ (x ) ≥θ (x0 ) + x ?
Robust Kernel-Based Fuzzy Clustering Using Difference of Convex Functions A nonconvex optimization approach is presented for the robust kernel-based clustering algorithms represented by the radial basis function and the Euler kernel function. The presented approach can handle local optimum problem caused ...
Due to the use of the ramp loss function, the corresponding objective function is nonconvex, making it more challenging. To overcome this limitation, we formulate our distance metric learning problem as an instance of difference of convex functions (DC) programming. This allows us to design a ...
Due to the use of the ramp loss function, the corresponding objective function is nonconvex, making it more challenging. To overcome this limitation, we formulate our distance metric learning problem as an instance of difference of convex functions (DC) programming. This allows us to design a ...
On the Subdifferentiability of Convex Functions Each lower semi-continuous proper convex function f on a Banach space E defines a certain multivalued mapping of from E to E * called the subdifferential of f. It is shown here that the mappings arising this way are precisely the ones wh... ...