A DCA-Like Algorithm and its Accelerated Version with Application in Data Visualization
This work addresses convergence speed issues in optimization algorithms for researchers and practitioners in data visualization, but it is incremental as it builds on existing DCA methods.
The authors tackled the problem of slow convergence in the Difference of Convex functions Algorithm (DCA) by proposing two variants, DCA-Like and Accelerated DCA-Like, which improve convergence speed through iterative decomposition and Nesterov's acceleration, as demonstrated in numerical experiments on benchmark datasets for t-SNE visualization.
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.