#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

#主要內容

##Markov Blanket（Markov毯）

$F$ — 所有特徵的集合 $C$ — 類別

一個特徵$F_i$的Markov毯 定義如下：

定義（Markov毯） $M$ — 一個特徵子集（不包含$F_i$） 即，$M \in F$且$F_i \notin M$。 $M$為$F_i$的一個Markov毯，若 給定$M$，$F_i$是對於 $\left( F \cup C \right) - M - \left\{ F_i \right\}$條件獨立的， 即，$P \left( F - M - \left\{ F_i \right\}, C | F_i, M \right) = P \left( F - M - \left\{ F_i \right\}, C | M \right)$

給定X，兩個屬性A與B是條件獨立的，若$P \left( A | X, B \right) = P \left( A | X \right) $，也就是說，B並不能在X之外提供關於A的資訊。若一個特徵$F_i$在當前選擇的特徵子集中有一個Markov毯$M$，那麼$F_i$在$M$之外關於$C$不能提供其他選擇的特徵的資訊，因此，$F_i$能夠安全移除。然而，決定特徵的條件獨立的計算複雜度通常非常高，因此，只使用一個特徵來估計$F_i$的Markov毯。

定義（近似Markov毯） 對於兩個特徵$F_i$與$F_j$ $i\neq j$，$F_j$可看作為$F_i$的近似Markov毯，若$SU_{j,C} \geq SU_{i,C}$ 且 $SU_{i,j} \geq SU_{i,C}$，其中， 對稱不確定性（symmetrical uncertainty，SU）度量特徵（包括類，$C$）間的相關性，定義為：

$IG \left( F_i | F_j \right)$ — 特徵$F_i$與$F_j$間的資訊增益 $H \left( F_i \right)$與$H \left( F_j \right)$ — 特徵$F_i$與$F_j$的熵 $SU_{i,C}$ — 特徵$F_i$與類$C$間的相關性，稱為C-correlation 一個特徵被認為是相關的若其C-correlation高於使用者給定的閾值$\gamma$，即，$S_{i,C} > \gamma$ 沒有任何近似Markov毯的特徵為predominant feature主導特徵

##馬爾可夫毯式嵌入式遺傳演算法

若適應值差異小於$\varepsilon$，則特徵數較少的個體較好

Lamarckian learning： 通過將區域性改進的個體放回種群競爭繁殖的機會，來迫使基因型反映改進的效果

$X$ — 選擇的特徵子集 $Y$ — 排除的特徵子集

C-correlation 只計算一次

搜尋範圍$L$ — 定義了$Add$與$Del$操作的最大數目 — $L^2$個操作組合 隨機順序 — 直到得到改進提升效果

Lamarckian learning process

之後是 usual evolutionary operations：

1. linear ranking selection
2. uniform crossover
3. mutation operators with elitism

##試驗

MBEGA method

考慮了：

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 $\gamma$
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 僅當 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

1. ranking the genes according to some measure of interest
2. 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

$BIRS_F$ or $BIRS_W$ — 基於 — C-correlation (i.e., symmetrical uncertainty between feature $F_i$ and the class $C$) or individual predictive power

$BIRS_F$ 耗時更少

###synthetic data 合成數據

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 微陣列資料

The .632+ bootstrap

K次重取樣

the support vector machine (SVM) — microarray classification problems

one-versus-rest strategy — multi-class datasets

the linear kernel SVM