The negative gradient direction of the current position is adopted for optimization in the gradient descent method. The method is the earliest and simplest and one of the most commonly used methods. Chaudhury et al. [50] used a gradient descent algorithm to optimize the dexterous workspace of a...
6) gradient descent algorithm 梯度下降法 1. Comparison between GA and gradient descent algorithm in parameter optimization of UPFC fuzzy damping controller; 基于遗传算法的UPFC模糊阻尼控制器参数优化及与梯度下降法的比较 2. A few or all of the parameters of the controller are adjusted by using ...
Then a negative gradient descent strategy based on negative gradient descent is introduced to improve the learning rate, which not only enhances initial global search ability, but also avoids premature convergence. Noteworthily, the convergence of the algorithm is analyzed for single-peak and multi-...
More recently other algorithms have been developed. Some approaches are based on alternating non-negative least squares: in each step of such an algorithm, first H is fixed and W found by a non-negative least squares solver, then W is fixed and H is found analogously. The procedures used t...
The monotonic convergence of both algorithms can be proven using an auxiliary function analogous to that used for proving convergence of the ExpectationMaximization algorithm. The algorithms can also be interpreted as diagonally rescaled gradient descent, where the rescaling factor is optimally chosen to ...
Proposition 9: The objective function for the perturbed KL-NMF problem (1) is non-increasing under the updates of Algorithm 2.ProofWe note that if g(x) is a self-concordant function with constant \(\mathbf{c}\) then \(\mathbf{c}^2\, g(x)\) is a standard self-concordant function....
Maximization algorithm.The algorithms can also be interpreted as diag- onally rescaled gradient descent,where the rescaling factor is optimally chosen to ensure convergence.1Introduction Unsupervised learning algorithms such as principal components analysis and vector quan-tization can be understood as ...
Gradient descent methods have better behavior, but only apply to smooth losses such as the least-squares loss. In this article, we propose a first-order primal-dual algorithm for non-negative decomposition problems (where one factor is fixed) with the KL divergence, based on the Chambolle-Pock...
In [7] the authors showed that the minimization of the upper bound indeed reduces the cost function but does not guarantee the convergence of the algorithm to the stationary point of the original optimization problem. In [8] the authors proposed two projected gradient-based methods for NMF that...
The underlying idea of variational inference is to pick a family of distributions q(β,γ)∈Q, with free variational parameter θ, and then use the gradient descent algorithm on θ to minimise the Kullback–Leibler (KL) divergence between the variational approximation q and the posterior ...