### Program Information

Name: Filter Feature Selection (FS) algorithm
Domain: Machine learning
Functionality: Playing a critical role in many data-intensive areas.
Input:
T:The training samples(Type: Set),which contains a list of feature and a set of class label as follows: $F=<F_{1},F_{2},\cdots,F_n>$:A list of feature(Type: List) $L=\{L_{1},L_{2}\cdots,L_k\}$:A set of class label(Type: List) Each sample $s_i$ consists of an n dimension vector$<f^i_{1}, f^i_{2},\cdots,f^i_n>$ and a class label $C_i$, where $f^i_j$ is the value of feature $F_j$ in sample $s_i$, and $C_i \in L$ is the class of $s_i$.
Output:
O: The output feature subset.

#### Reference

Bottom-up Integration Testing with the Technique of Metamorphic Testing http://dx.doi.org/10.1109/QSIC.2014.29 Testing Approach for Dynamic Web Applications Based on Automated Test Strategies http://dx.doi.org/10.1007/978-3-319-03095-1_43

### MR Information

#### MR1

Source input: $F_s,L_s$ ; Source output: $O_s$
Follow-up input: $F_f,L_f$ ; Follow-up output: $O_f$
Input relation: $F_f$ = Applying the same arbitrary affine transformation $f(x)=kx+b, (k \ne 0)$ to the values of all continuous features of $F_s$. $L_f=L_s$
Output relation: $O_f=O_s$

#### MR2

Source input: $F_s,L_s$ ; Source output: $O_s$
Follow-up input: $F_f,L_f$ ; Follow-up output: $O_f$
Input relation: $F_f=F_s$ $L_f$ = Applying the same arbitrary affine transformation $f(x)=kx+b, (k \ne 0)$ to the values of all continuous class label of $L_s$.
Output relation: $O_f=O_s$

#### MR3

Source input: $T_s$ ; Source output: $O_s$
Follow-up input: $T_f$ ; Follow-up output: $O_f$
Input relation: $T_f$ = Permuting some of the samples in $T_s$
Output relation: $O_f=O_s$

#### MR4

Source input: $T_s$ ; Source output: $O_s$
Follow-up input: $T_f$ ; Follow-up output: $O_f$
Input relation: $T_f$ = Adding an uninformative sample into $T_s$
Output relation: $O_f=O_s$

#### MR5

Source input: $T_s$ ; Source output: $O_s$
Follow-up input: $T_f$ ; Follow-up output: $O_f$
Input relation: $T_f$ = Duplicating the all training samples in $T_s$ for k times, with keeping their original class labels unchanged.
Output relation: $O_f=O_s$

#### MR6

Source input: $T_s$ ; Source output: $O_s$
Follow-up input: $T_f$ ; Follow-up output: $O_f$
Input relation: $T_f$ = Duplicating any sample in the $T_s$ and assign a new class label that does not belong to L.
Output relation: $O_f=O_s$

#### MR7

Source input: $F_s,L_s$ ; Source output: $O_s$
Follow-up input: $F_f,L_f$ ; Follow-up output: $O_f$
Input relation: $F_f$=Adding an uninformative feature $F_{new}$ at the end of $F_s$ $L_f$ = $L_s$.
Output relation: $O_f=O_s$

#### MR8

Source input: $F_s,L_s$ ; Source output: $O_s$
Follow-up input: $F_f,L_f$ ; Follow-up output: $O_f$
Input relation: $F_f$=Duplicating the whole column of the unselected feature $F^s_i$ in $F_s$. $L_f$ = $L_s$.
Output relation: $O_f=O_s$

#### MR9

Source input: $F_s,L_s$ ; Source output: $O_s$
Follow-up input: $F_f,L_f$ ; Follow-up output: $O_f$
Input relation: $F_f$=Duplicating the whole column of the selected feature $F^s_i$ in $F_s$. $L_f$ = $L_s$.
Output relation: $O_f=O_s$

#### MR10

Source input: $F_s,L_s$ ; Source output: $O_s$
Follow-up input: $F_f,L_f$ ; Follow-up output: $O_f$
Input relation: $F_f$=Deleting the whole column of the unselected feature $F^s_i$ in $F_s$. $L_f$ = $L_s$.
Output relation: $O_f=O_s$

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