simple_similarity {CFF}

Finding Neighbor Users And Their Similarity Values

Description

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.

Usage

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

Arguments

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 (1\le ac \le length of users).

Details

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 ith column user and u_a is an active user.

r_{(u_a, j)} is the rating of active user in the jth row and r_{(u_i, j)} is the rating of the ith user in the jth row.

dif_{(u_i, j)} is the difference of the rating for the ith user with the active user in the jth row.

sim_{dif_{(u_i, j)}} is the similarity of the ith user with the active user in the jth 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.

Value

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.

Author(s)

Farimah Houshmand Nanehkaran

Maintainer: Farimah Houshmand Nanehkaran <[e-mail]>

References

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.

Examples

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)