Ads
related to: convergence training by vector solutionslearningpool.com has been visited by 10K+ users in the past month
Search results
Results From The WOW.Com Content Network
A comparison of the convergence of gradient descent with optimal step size (in green) and conjugate vector (in red) for minimizing a quadratic function associated with a given linear system. Conjugate gradient, assuming exact arithmetic, converges in at most n steps, where n is the size of the matrix of the system (here n = 2).
In the case of gradient descent, that would be when the vector of independent variable adjustments is proportional to the gradient vector of partial derivatives. The gradient descent can take many iterations to compute a local minimum with a required accuracy, if the curvature in different directions is very different for the given function.
This is equivalent to performing gradient descent in the feature space. It’s known that if the weight vector is initialized close to zero, least-squares gradient descent converges to the minimum-norm solution, i.e., the final weight vector has the minimum Euclidean norm of all the interpolating solutions.
Very rapid convergence is guaranteed and no more than a few iterations are needed in practice to obtain a reasonable approximation. The Rayleigh quotient iteration algorithm converges cubically for Hermitian or symmetric matrices, given an initial vector that is sufficiently close to an eigenvector of the matrix that is being analyzed.
Sequential minimal optimization (SMO) is an algorithm for solving the quadratic programming (QP) problem that arises during the training of support-vector machines (SVM). It was invented by John Platt in 1998 at Microsoft Research. [1] SMO is widely used for training support vector machines and is implemented by the popular LIBSVM tool.
Perceptron convergence theorem — Given a dataset , such that (,) ‖ ‖ =, and it is linearly separable by some unit vector , with margin : := (,) () Then the perceptron 0-1 learning algorithm converges after making at most ( R / γ ) 2 {\textstyle (R/\gamma )^{2}} mistakes, for any learning rate, and any method of sampling from the dataset.
If an equation can be put into the form f(x) = x, and a solution x is an attractive fixed point of the function f, then one may begin with a point x 1 in the basin of attraction of x, and let x n+1 = f(x n) for n ≥ 1, and the sequence {x n} n ≥ 1 will converge to the solution x.
Convergence of the sequence of solutions (aka, stability analysis, converging) in which all particles have converged to a point in the search-space, which may or may not be the optimum, Convergence to a local optimum where all personal bests p or, alternatively, the swarm's best known position g , approaches a local optimum of the problem ...