This document describes an approach to building a package recommendation engine for R packages. It uses a modified k-nearest neighbors algorithm that incorporates package relationships, user and package averages, and user-maintainer affinity. It then uses matrix factorization to model residuals from the initial model. The final model achieves a public AUC of 0.984914 and final AUC of 0.979565, demonstrating an effective approach for recommending related R packages.

1. An Approach to R Package
Recommendation Engine
Alex Lin
alin@intelligentmining.com
Twitter: @alinatwork

2. Initial Thoughts
 The data set expected to have very strong
package-package relationships (dependencies and
related package functionalities).
 The data set (training + test) is not sparse.
 Most of matrix factorization (MF) techniques in
the recommender field optimize square errors on
the predicted user ratings not directly optimize
for AUC.

3. Steps
1. Modified k-Nearest Neighbor algorithm.
2. User average & package average as prior bias.
3. User-specific package Maintainer Affinity.
4. Matrix factorization (MF) to post-process the
residuals.
5. Other rules.

4. Modified k-Nearest Neighbor algorithm
 Calculate cosine similarity for each pkg-pkg pair.
 Scale the cosine similarity with “square user
support” ie. cosine * (support / ttl_user_cnt)**2
 Unlike the regular kNN that is only additive, we use
the same kNN rules to penalize the package if other
related package was not installed.
 For unknown records, we choose to take ZAN
approach. We treat the unknown entries as negative.
 k=all

5. User average and Package average as
prior bias
 User average =
user installed pkg count / user observation count
 Package average =
pkg installed by users count / pkg observation count
 Add them into the kNN result score.

6. User-specific Package Maintainer
Affinity
 This metric measured as the installed package
percent of a given maintainer for an user.
 We use the percentage to predict how likely the
user will install the other package from the same
maintainer. Combine with kNN result score with
weight of 0.25.

7. So Far – baseline model
 Very heuristic
 Public AUC = 0.976x

8. Matrix Factorization
 Analyze the residuals only. The goal is to find out
structural errors in our baseline prediction.
 prediction := baseline_output + residual
 residual := pkg_bias + user_bias + pkgFactors . userFactors
 residuals is related to Wilcoxon-Mann-Whitney (WMW)
statistics
P −1 N −1
∑ ∑i= 0 j= 0
I(mi ,n j )
m ∈ PostiveClass
AUC = n ∈ NegativeClass
MN
1 if (mi < n j )
€
I(mi ,n j ) €
 0 otherwise
€
€

9. Matrix Factorization – cont.
 Minimizes truncated square error with batch gradient
descent (BGD)
x ui = sui + bi + bu + qT pu
i
1 2 2
min
q*. p*
∑ 2 (Lrank (x ui )) 2 + λ( qi + pu + bi2 + bu )
2
(u,i)∈K
Pairwise comparison
€ U −1 I −1
Lrank = ∑ ∑ I(x ui , x vj )(x vj − x ui )
v= 0 j= 0
 1 if (x ui < x vj )
€  x ui ∈ P x vj ∈ N 
 0 otherwise
€ I(x ui , x vj )
x ∈ N 1 if (x ui > x vj )
x vj ∈ P 
 ui
 0 otherwise
€

10. Other Rules
 For those duplicate records found exist in both testing
and training set, copy answers from training set.
 Assume when a user install a package P, the user also
installs the packages that P depends on.

11. Final Result
 Public AUC = 0.984914
 Final AUC = 0.979565