Instance selection by genetic-based biological algorithm

Abstract

Instance selection is an important research problem of data pre-processing in the data mining field. The aim of instance selection is to reduce the data size by filtering out noisy data, which may degrade the mining performance, from a given dataset. Genetic algorithms have presented an effective instance selection approach to improve the performance of data mining algorithms. However, current approaches only pursue the simplest evolutionary process based on the most reasonable and simplest rules. In this paper, we introduce a novel instance selection algorithm, namely a genetic-based biological algorithm (GBA). GBA fits a “biological evolution” into the evolutionary process, where the most streamlined process also complies with the reasonable rules. In other words, after long-term evolution, organisms find the most efficient way to allocate resources and evolve. Consequently, we can closely simulate the natural evolution of an algorithm, such that the algorithm will be both efficient and effective. Our experiments are based on comparing GBA with five state-of-the-art algorithms over 50 different domain datasets from the UCI Machine Learning Repository. The experimental results demonstrate that GBA outperforms these baselines, providing the lowest classification error rate and the least storage requirement. Moreover, GBA is very computational efficient, which only requires slightly larger computational cost than GA.

Appendix: The schema theorems corresponding to GA and GBA

The original model of GA is

$$\begin{aligned} m( {H,t+1})&= m( {H,t})\times \frac{f( H)}{\overline{f} }\nonumber \\&\times \left[ {1-r_c \frac{\delta ( H)}{l-1}-o( H)r_m } \right] , \end{aligned}$$

where $H$ represents the schema, $t$ is the generation, $m(H,t)$ is the number of strings belonging to schema $H$ at generation $t$, $f(H)$ is the observed fitness, $r_{c }$ is the crossover rate, $\delta (H$) is the defining length, $l$ is the length of the code, $r_{m }$ is the mutation rate, and $o(H)$ is the order of a schema.

The modified model of GBA is

$$\begin{aligned}&m( {H,t+1})=m( {H,t})\times \frac{Nf( H)}{\overline{Nf} }\\&\quad \times \left[ {1\!-\!r_c \frac{\delta ( H)}{l\!-\!1}\!-\!o( H)r_m \!-\!o(H)r_{mg} \!\times \! MGT(m( {H,t}),t)} \right] \nonumber \\&\quad +\,GK(H), \end{aligned}$$

where $H$ represents the schema, $t$ is the generation, $m(H,t)$ is the number of strings belonging to schema $H$ at generation $t$, $Nf(H)$ is the nonlinear fitness functions, $r_{c }$ is the crossover rate, $\delta (H)$ is the defining length, $l$ is the length of the code, $r_{m}$ is the mutation rate, $o(H)$ is the order of a schema, $r_{mg}$ is the great migration rate, $MGT(m(H,t),t)$ is the trigger of the Great Migration, and $GK(K)$ is the genetic king protection mechanisms, which can retain the good schema $H$.

The definition of nonlinear fitness functions Nf($H)$ is

$$\begin{aligned} { Nf}=\frac{{ Hyperbolic} { tangent} \left( \frac{f(H)-0.5}{\sigma ^2}\right) +1}{2} \end{aligned}$$

It will increase/reduce the fitness strength depends on the threshold.

In addition, the GK($H)$ represents the Genetic King Protection Mechanisms, and the definition of GK is

If $Nf(H)\ge Threshold$ then $GK(H)=1$ else $GK(H)=0$.

If the schema $H$ is good enough, it will be retained by genetic king protection mechanisms.

The definition of great migration $MGT(m(H,t),t)$ is

If the best fitness value is stable then $MGT(m(H,t),t)=1$, else $MGT(m(H,t),t)=0$.

If the best fitness value is stable, then apply the great migration (A strong mutation) (c.f. Fig. 6 for the pseudo code of GBA).