Towards an efficient genetic algorithm optimizer for sequential projection pursuit

A Projection Pursuit framework for supervised dimension reduction of high dimensional small sample datasets

“…Further developments focused on developing more global methods for PP optimization, such as random search [38,39,29], genetic algorithm (GA) [32], random scan sampling algorithm (RSSA) [34], simulated annealing (SA) [21], particle swarm optimization (PSO) [35] and tribes [40]. In a previous work [33] we describe PPGA, a GA optimizer with a specialized crossover operator that often showed to find solutions better than those found by PSO, RSSA, and SA when used inside the SPP framework, reason why it is adopted for the present work.…”

“…In the experiments, the size (w) of the initial population is set as w¼ 3q, formed by 50% of individuals from CPS and 50% created randomly. Projection pursuit genetic algorithm (PPGA): This is the adopted PP optimizer, taken from our previous work [33]. Unlike the original GA optimizer, which uses binary encoding and canonical operators, PPGA uses a real encoding and a specialized crossover operator (called the Inner-outer Hypercone crossover).…”

“…Unlike the original GA optimizer, which uses binary encoding and canonical operators, PPGA uses a real encoding and a specialized crossover operator (called the Inner-outer Hypercone crossover). It was showed that this operator provides a good search capability for PP optimization in high dimensionalities [33]. At each generation, an offspring population is created with crossover.…”

“…Traditional PP optimizers based on the gradients or Newton methods [29][30][31]19] are usually inadequate for such a kind of data due to the vastness of possible projections and, thus, the high susceptibility to find poor local optima [14]. More global PP optimizers were described recently, including genetic algorithms (GA) [32,33], simulating annealing (SA) [21], random scan sampling (RSSA) [34] and particle swarm optimization (PSO) [35]. However, none of these works have been directly applied in dimensionalities as high as those found in microarray data, which shows the difficulty of applying PP in such scenarios.…”

“…For the PP stage, we adopt the Sequential Projection Pursuit (SPP) approach [32] coupled with the GA optimizer (PPGA) we described recently [33], in which a specialized crossover operator showed excelling search capabilities. An experimental study is presented over eight public microarray datasets.…”