Improved Feature-Selection Method Considering the Imbalance Problem in Text Categorization

Table 2

The improved formula of nine feature-selection algorithms listed in Section 2.

	Local feature selection	Global feature selection
IG	IGX𝑡𝑘,𝑐𝑖=1𝑝(𝑐𝑖)𝑐𝑐∑∈𝑖,𝑐𝑖∑𝑡𝑡∈𝑘,𝑡𝑘𝑃(𝑡,𝑐)log𝑃(𝑡,𝑐)𝑃(𝑡)𝑃(𝑐)	IGX𝑡𝑘=∑^|𝐶|𝑖=1∑𝑐𝑐∈𝑖,𝑐𝑖∑𝑡𝑡∈𝑘,𝑡𝑘𝑃(𝑡,𝑐)log𝑃(𝑡,𝑐)𝑃(𝑡)𝑃(𝑐)
CHI	CHIX𝑡𝑘,𝑐𝑖=𝑁(𝑎𝑘𝑖𝑑𝑘𝑖−𝑏𝑘𝑖𝑐𝑘𝑖)^2(𝑎𝑘𝑖+𝑏𝑘𝑖)(𝑎𝑘𝑖+𝑐𝑘𝑖)(𝑏𝑘𝑖+𝑑𝑘𝑖)(𝑐𝑘𝑖+𝑑𝑘𝑖)𝑃(𝑐𝑖)	CHIX𝑡𝑘=∑^|𝐶|𝑖=1𝑁(𝑎𝑘𝑖𝑑𝑘𝑖−𝑏𝑘𝑖𝑐𝑘𝑖)^2(𝑎𝑘𝑖+𝑏𝑘𝑖)(𝑎𝑘𝑖+𝑐𝑘𝑖)(𝑏𝑘𝑖+𝑑𝑘𝑖)(𝑐𝑘𝑖+𝑑𝑘𝑖)
MI	MIX𝑡𝑘,𝑐𝑖=1𝑃(𝑐𝑖)log𝑃(𝑡𝑘,𝑐𝑖)𝑃(𝑡𝑘)𝑃(𝑐𝑖)	MIX𝑡𝑘=∑^|𝐶|𝑖=1log𝑃(𝑡𝑘,𝑐𝑖)𝑃(𝑡𝑘)𝑃(𝑐𝑖)
DF	DFX𝑡𝑘,𝑐𝑖=𝑃(𝑡𝑘∣𝑐𝑖)𝑃(𝑐𝑖)	DFX𝑡𝑘=∑^|𝐶|𝑖=1𝑃(𝑡𝑘∣𝑐𝑖)
GINI	—	GINIX𝑡𝑘=∑^|𝐶|𝑖=1𝑃(𝑡𝑘∣𝑐𝑖)^2𝑃(𝑐𝑖∣𝑡𝑘)^2𝑃(𝑐𝑖)
DIA	DIAX𝑡𝑘,𝑐𝑖=𝑃(𝑐𝑖∣𝑡𝑘)𝑃(𝑐𝑖)	DIAX𝑡𝑘=∑^|𝐶|𝑖=1𝑃(𝑐𝑖∣𝑡𝑘)
CMFS	CMFSX𝑡𝑘,𝑐𝑖=𝑃(𝑡𝑘∣𝑐𝑖)𝑃(𝑐𝑖∣𝑡𝑘)𝑃(𝑐𝑖)	CMFSX𝑡𝑘=∑^|𝐶|𝑖=1𝑃(𝑡𝑘∣𝑐𝑖)𝑃(𝑐𝑖∣𝑡𝑘)
OCFS	OCFSX𝑡𝑘,𝑐𝑖=(𝑚^𝑘𝑖−𝑚^𝑘)^2𝑃(𝑐𝑖)	OCFSX𝑡𝑘=∑^|𝐶|𝑖=1(𝑚^𝑘𝑖−𝑚^𝑘)^2
DFPFS	DFPFSX𝑡𝑖,𝐶𝑗; =1𝑃(𝑐𝑗)𝑎𝑖𝑗−𝑎𝑖𝑗^2𝑎𝑖𝑗+𝑏𝑖𝑗−𝑏̂𝑖𝑗^2𝑏̂𝑖𝑗+𝑐𝑖𝑗−𝑐̂𝑖𝑗^2𝑐̂𝑖𝑗+𝑑𝑖𝑗−𝑑𝑖𝑗^2𝑑𝑖𝑗	DFPFSX𝑡𝑖; =∑^|𝐶|𝑖=1𝑎𝑖𝑗−𝑎𝑖𝑗^2𝑎𝑖𝑗+𝑏𝑖𝑗−𝑏̂𝑖𝑗^2𝑏̂𝑖𝑗+𝑐𝑖𝑗−𝑐̂𝑖𝑗^2𝑐̂𝑖𝑗+𝑑𝑖𝑗−𝑑𝑖𝑗^2𝑑𝑖𝑗