Genetic algorithms and particle swarm optimization for exploratory projection pursuit

Abstract

Exploratory Projection Pursuit (EPP) methods have been developed thirty years ago in the context of exploratory analysis of large data sets. These methods consist in looking for low-dimensional projections that reveal some interesting structure existing in the data set but not visible in high dimension. Each projection is associated with a real valued index which optima correspond to valuable projections. Several EPP indices have been proposed in the statistics literature but the main problem lies in their optimization. In the present paper, we propose to apply Genetic Algorithms (GA) and recent Particle Swarm Optimization (PSO) algorithm to the optimization of several projection pursuit indices. We explain how the EPP methods can be implemented in order to become an efficient and powerful tool for the statistician. We illustrate our proposal on several simulated and real data sets.

A survey of Particle Swarm Optimization techniques for solving university Examination Timetabling Problem

“…PSO can rapidly achieve fit particles (not constantly the best fit), but who are commonly good enough to be considered as solutions to problems. PSO generally performed well in a large number of hard combinatorial optimization problems, especially in continuous optimization (Sandeep Rana et al 2011;Berro et al 2010). In these recent years, PSO has confirmed more encouraging results in undertaking discrete optimization problems (Jordehi and Jasni 2015).…”

“…For more details about the parameters setting, the reader can refer to Berro et al (2010). Equation 2 calculates the new position of a particle i according to the current position X i j and the current velocity V i j .…”

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

“…Early approaches in this respect were based on the gradient techniques [30,29] and Newton-Raphson [31,37,14,13], where the projections are performed in at most three dimensions for visual exploratory tasks, the so-called exploratory projection pursuit (EPP). 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.…”

“…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.…”

Detection and visualization of non-linear structures in large datasets using Exploratory Projection Pursuit Laboratory (EPP-Lab) software

“…Among the different bio-inspired algorithms, Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and a hybrid Particle Swarm Optimization method called Tribes are employed. The performance of these selected methods combined with PP has been validated in Berro et al (2010) and Mari-Sainte et al (2010).…”