引用
LaTex
@article{ZHU20073236,
title = “Markov blanket-embedded genetic algorithm for gene selection”,
journal = “Pattern Recognition”,
volume = “40”,
number = “11”,
pages = “3236 - 3248”,
year = “2007”,
issn = “0031-3203”,
doi = “https://doi.org/10.1016/j.patcog.2007.02.007“,
url = “http://www.sciencedirect.com/science/article/pii/S0031320307000945“,
author = “Zexuan Zhu and Yew-Soon Ong and Manoranjan Dash”,
keywords = “Microarray, Feature selection, Markov blanket, Genetic algorithm (GA), Memetic algorithm (MA)”
}
Normal
Zexuan Zhu, Yew-Soon Ong, Manoranjan Dash,
Markov blanket-embedded genetic algorithm for gene selection,
Pattern Recognition,
Volume 40, Issue 11,
2007,
Pages 3236-3248,
ISSN 0031-3203,
https://doi.org/10.1016/j.patcog.2007.02.007.
(http://www.sciencedirect.com/science/article/pii/S0031320307000945)
Keywords: Microarray; Feature selection; Markov blanket; Genetic algorithm (GA); Memetic algorithm (MA)
摘要
Microarray technologies
the smallest possible set of genes
Markov blanket-embedded genetic algorithm (MBEGA) for gene selection problem
Markov blanket and predictive power in classifier model
filter, wrapper, and standard GA
evaluation criteria:
classification accuracy, number of selected genes, computational cost, and robustness
主要内容
Markov Blanket(Markov毯)
— 所有特征的集合
— 类别
一个特征 的Markov毯 定义如下:
定义(Markov毯)
— 一个特征子集(不包含
)
即,
且
。
为
的一个Markov毯,若
给定
,
是对于
条件独立的,
即,
给定X,两个属性A与B是条件独立的,若 ,也就是说,B并不能在X之外提供关于A的信息。若一个特征 在当前选择的特征子集中有一个Markov毯 ,那么 在 之外关于 不能提供其他选择的特征的信息,因此, 能够安全移除。然而,决定特征的条件独立的计算复杂度通常非常高,因此,只使用一个特征来估计 的Markov毯。
定义(近似Markov毯)
对于两个特征
与
,
可看作为
的近似Markov毯,若
且
,其中,
对称不确定性(symmetrical uncertainty,SU)度量特征(包括类,
)间的相关性,定义为:
— 特征
与
间的信息增益
与
— 特征
与
的熵
— 特征
与类
间的相关性,称为C-correlation
一个特征被认为是相关的若其C-correlation高于用户给定的阈值
,即,
没有任何近似Markov毯的特征为predominant feature主导特征
马尔可夫毯式嵌入式遗传算法
若适应值差异小于 ,则特征数较少的个体较好
Lamarckian learning:
通过将局部改进的个体放回种群竞争繁殖的机会,来迫使基因型反映改进的效果
— 选择的特征子集
— 排除的特征子集
C-correlation 只计算一次
搜索范围
— 定义了
与
操作的最大数目 —
个操作组合
随机顺序 — 直到得到改进提升效果
Lamarckian learning process
之后是
usual evolutionary operations:
1. linear ranking selection
2. uniform crossover
3. mutation operators with elitism
试验
MBEGA method
考虑了:
1. the FCBF (fast correlation-based filter)
2. BIRS (best incremental ranked subset)
3. standard GA feature selection algorithms
FCBF —
a fast correlation based filter method
1. selecting a subset of relevant features whose C-correlation are larger than a given threshold
2. sorts the relevant features in descending order in terms of C-correlation
3. redundant features are eliminated one-by-one in a descending order
A feature is redundant 仅当 it has an approximate Markov blanket
predominant features with zero redundant features in terms of C-correlation
BIRS — a similar scheme as the FCBF
evaluates the goodness of features using a classifier
- ranking the genes according to some measure of interest
- sequentially selects the ranked features one-by-one based on their incremental usefulness
calls to the classifier as many times as the number of features
or — 基于 — C-correlation (i.e., symmetrical uncertainty between feature and the class ) or individual predictive power
耗时更少
synthetic data 合成数据
ten 10-fold crossvalidations
with C4.5 classifier
10 independent runs
The maximum number of selected features in each chromosome, m, is set to 50.
microarray data 微阵列数据
The .632+ bootstrap
K次重采样
the support vector machine (SVM) — microarray classification problems
one-versus-rest strategy — multi-class datasets
the linear kernel SVM