Predicts user u's rating of item i. For two items j and i let
S_{j,i}(chi) be the set of users who rated both. The average
deviation of item i with respect to item j is
dev_{j,i} = sum_{u in S_{j,i}} (u_j - u_i) / card(S_{j,i}).
Since dev_{j,i} + u_i is itself a prediction of u_j, the
SLOPE ONE prediction averages them,
P(u)_j = sum_{i in R_j} (dev_{j,i} + u_i) / card(R_j) with
R_j the items the user rated other than j that have at least one
co-rating user, and the WEIGHTED SLOPE ONE prediction weights each term
by how many users support it,
P_wS1(u)_j = sum (dev_{j,i} + u_i) c_{j,i} / sum c_{j,i} over the
items the user rated other than j, where c_{j,i} is
card(S_{j,i}(chi)).
Value
List with estimate (weighted prediction),
weighted_slope_one, slope_one, user_mean,
n_pairs, support, fallback, observed,
error, n_users, n_items, user, item,
method.
Details
Both are returned; estimate is the weighted form, the scheme
Lemire & Maclachlan recommend. When no co-rated pair supports the target
item the prediction falls back to the user's own mean and
fallback is set to 1.
References
Lemire, D. & Maclachlan, A. (2005). Slope one predictors for online rating-based collaborative filtering. Proceedings of the 2005 SIAM International Conference on Data Mining, 471-475. doi:10.1137/1.9781611972757.43
Examples
R <- matrix(c(5, 3, NA, 4, NA, 2, NA, 5, 3), 3, 3, byrow = TRUE)
Slope1(R, u = 0, i = 2)
#> $estimate
#> [1] 2
#>
#> $weighted_slope_one
#> [1] 2
#>
#> $slope_one
#> [1] 2
#>
#> $user_mean
#> [1] 4
#>
#> $n_pairs
#> [1] 2
#>
#> $support
#> [1] 2
#>
#> $fallback
#> [1] 0
#>
#> $observed
#> [1] NA
#>
#> $error
#> [1] NA
#>
#> $n_users
#> [1] 3
#>
#> $n_items
#> [1] 3
#>
#> $user
#> [1] 0
#>
#> $item
#> [1] 2
#>
#> $method
#> [1] "Weighted Slope One predictor (Lemire & Maclachlan 2005)"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"