一种类似DCA的算法及其加速版本在数据可视化中的应用
A DCA-Like Algorithm and its Accelerated Version with Application in Data Visualization
AI总结：
本文提出两种DCA变体，旨在加速约束下可微函数和复合函数的最小化问题。通过引入新的分解技术改进DCA，进而结合Nesterov加速技术得到加速DCA。算法在Kurdyka-Lojasiewicz假设下的收敛性被严格研究，并应用于t-分布随机邻居嵌入。
摘要：
本文提出两种DCA变体，旨在加速约束下可微函数和复合函数的最小化问题。在第一种变体DCA-Like中，我们引入了一种新的技术来迭代修改目标函数的分解。这种连续分解可以导致更好的主导性，从而比基本DCA有更快的收敛速度。然后，我们将Nesterov的加速技术纳入DCA-Like中，得到第二种变体，称为加速DCA-Like。两种变体的收敛性质和在Kurdyka-Lojasiewicz假设下的收敛率被严格研究。作为应用，我们研究了我们的算法用于t-分布随机邻居嵌入。在几个基准数据集上的数值实验展示了我们算法的有效性。
英文摘要：
In this paper, we present two variants of DCA (Different of Convex functions Algorithm) to solve the constrained sum of differentiable function and composite functions minimization problem, with the aim of increasing the convergence speed of DCA. In the first variant, DCA-Like, we introduce a new technique to iteratively modify the decomposition of the objective function. This successive decomposition could lead to a better majorization and consequently a better convergence speed than the basic DCA. We then incorporate the Nesterov's acceleration technique into DCA-Like to give rise to the second variant, named Accelerated DCA-Like. The convergence properties and the convergence rate under Kudyka-Lojasiewicz assumption of both variants are rigorously studied. As an application, we investigate our algorithms for the t-distributed stochastic neighbor embedding. Numerical experiments on several benchmark datasets illustrate the efficiency of our algorithms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
