simple_similarity {CFF} | R Documentation |

Steps of calculating the similarity of one user to an active user :

1- Calculating the difference between the desired user ratings with the active user in common items.

2- Calculating the similarity value for each common item.

3- Calculating the mean value of similarities.

```
simple_similarity(ratings, max_score=5, min_score=1, ac)
```

`ratings` |
A rating matrix whose rows are items and columns are users. |

`max_score` |
The maximum range of ratings. |

`min_score` |
The minimum range of ratings. |

`ac` |
The id of an active user as an integer ( |

The similarity of the active user with other users is obtained by the following formulas :

`dif_{(u_i, j)}=|r_{(u_a, j)}-r_{(u_i, j)}|`

`sim_{dif_{(u_i, j)}}=\frac{-dif_{(u_i, j)}}{max_score-min_score}+1`

`sim_{(u_a, u_j)}=\frac{\sum_{j=1}^{N_j}sim_{(dif_{(u_i,j)})}}{N_j}`

j is the row number for the items and i is the column number for the users in the ratings matrix.

`u_i`

is a i*th* column user and `u_a`

is an active user.

`r_{(u_a, j)}`

is the rating of active user in the j*th* row and `r_{(u_i, j)}`

is the rating of the i*th* user in the j*th* row.

`dif_{(u_i, j)}`

is the difference of the rating for the i*th* user with the active user in the j*th* row.

`sim_{dif_{(u_i, j)}}`

is the similarity of the i*th* user with the active user in the j*th* row.

`sim_{(u_a, u_i)}`

is the similarity of the user i, with the active user.

`N_j`

is the number of common items.

For example, suppose active user ratings are: {2, nan, 3, nan, 5} and one user ratings are: {3, 4, nan, nan, 1} then for ratings between 1 and 5:

dif={1, nan, nan, nan, 4} and

sim(dif)={`\frac{-1}{5-1}+1`

, nan, nan, nan, `\frac{-4}{5-1}+1`

}={0.75, nan, nan, nan, 0}

and mean of sim(dif) is sim=0.375.

An object of class `"simple_similarity"`

, a list with components:

`call` |
The call used. |

`sim_x` |
Neighboring user similarity values in descending order. |

`sim_index` |
Number of columns for neighboring users in descending order of similarity. |

Farimah Houshmand Nanehkaran

Maintainer: Farimah Houshmand Nanehkaran <hoshmandcomputer@gmail.com>

Mongia, A., & Majumdar, A. (2019). *Matrix completion on multiple graphs: Application in collaborative filtering*. Signal Processing, vol. 165, pp. 144-148.

Hong, B., & Yu, M. (2019). *A collaborative filtering algorithm based on correlation coefficient*. Neural Computing and Applications, vol. 31, no. 12, pp. 8317-8326.

```
ratings <- matrix(c( 2, 5, NaN, NaN, NaN, 4,
NaN, NaN, NaN, 1, NaN, 5,
NaN, 4, 5, NaN, 4, NaN,
4, NaN, NaN, 5, NaN, NaN,
5, NaN, 2, NaN, NaN, NaN,
NaN, 1, NaN, 4, 2, NaN),nrow=6,byrow=TRUE)#items*users
sim <- simple_similarity(ratings, max_score=5, min_score=1, ac=1)
```

[Package *CFF* version 1.0 Index]