RecSys Project: Structured SLIM

Intro:

The aim of this project is to learn the weights to assign at each relevant attribute of a given dataset in order to maximize the MAP performance, exploiting SLIM Elasticnet algorithm.

In order to obtain the relative attributes' weight, the algorithm train a model that minimizes the difference between the similarity matrix obtained by a CF method and the ones obtained by a CBF approach. During this process, the only cells that are updated, and from which the algorithm learns, are the ones related to items with common features.

Given a similarity matrix S (random initialized) and a URM matrix, SR = R for each element filtered by the mask. The Learning approach is the classical SGD but is applied only to the relevant items. The error is computed as follow:

and consequently:

Parameters setting:

As we said, in order to create the structure that selects the cells to update, a similarity matrix is computed starting from the ICM. For this reason is also possible to set the parameters that regulate this operation: topK and Shrinkage.

The algorithm takes as input two matrixes: ICM and URM in scipy.sparse.csc_matrix format.

In the fitting phase is possible to set:

top K, shrinkage and a boolean for the normalization used for the structure creation, learning rate λ, l2-norm coefficient β, l1-norm coefficient γ, and epochs number used for the learning process.

Basic usage:

import SLIM_Elastic_Net_Structured

URM_train = sps.load_npz("files/train.npz")
URM_test = sps.load_npz("files/test.npz")
ICM = sps.load_npz("files/icm.npz")

recommender = SLIM_Elastic_Net_Structured(ICM, URM_train)
recommender.fit(k=50, shrink=100, lamb=0.001, beta=0.001, gamma=0.0001, epochs= 50, normalize=True)
evaluation = recommender.evaluateRecommendations(URM_test)

Results comparison:

TheMoviesDataset

ICM: shape = (45433, 49102), sparcity: 0.9996608321471501

	KNN collaborative	KNN content based	SLIM ElasticNet	Structured SLIM
AUC	0.16328739386752908	0.10482457612266392	0.2263805145071017	0.0712925984345927
MRR	0.18905935960684533	0.11191219297558800	0.2645136270923570	0.0714445525835901
NDCG	0.01855725520613782	0.00746201206025480	0.0311315445799227	0.0051277609005780
Map	0.09102503054552336	0.03904454673930252	0.1272435077566548	0.0193769258401597
Precision	0.12380611457273409	0.05838935934579915	0.1696978510621871	0.0329138280140035
Recall	0.00925958646390481	0.00361115681867504	0.0149399014209997	0.0023711798147415

TheMoviesDataset with 10% of features (the most frequent)

ICM: shape = (45433, 4910), sparcity: 0.998379794548074

	KNN collaborative	KNN content based	SLIM ElasticNet	Structured SLIM
AUC	0.16328739386752908	0.08979285527836814	0.2263805145071017	0.07471752992504764
MRR	0.18905935960684533	0.0954351717194279	0.2645136270923570	0.0748273483238209
NDCG	0.01855725520613782	0.006027635885299432	0.0311315445799227	0.00525156182861393
Map	0.09102503054552336	0.031691075934418146	0.1272435077566548	0.020370107270263175
Precision	0.12380611457273409	0.04852668083677559	0.1696978510621871	0.03421635529701036
Recall	0.00925958646390481	0.0029754989239676242	0.0149399014209997	0.0023486699132642124

TheMoviesDataset with 50% of features (the most frequent)

ICM: shape = (45433, 24551), sparcity: 0.9994530078838976

	KNN collaborative	KNN content based	SLIM ElasticNet	Structured SLIM
AUC	0.16328739386752908	0.10088097102584181	0.2263805145071017	0.07471752992504764
MRR	0.18905935960684533	0.10794440093970242	0.2645136270923570	0.07474540688286659
NDCG	0.01855725520613782	0.007064354060380539	0.0311315445799227	0.0051414034822329195
Map	0.09102503054552336	0.03703610893587213	0.1272435077566548	0.020058438644704992
Precision	0.12380611457273409	0.055847410224847426	0.1696978510621871	0.03371927822711188
Recall	0.00925958646390481	0.0034313059550974195	0.0149399014209997	0.002295724200388743

MovieLens 26M with GENRES

ICM: shape = (45843, 20), sparcity: 0.9061797875357197

	KNN collaborative	KNN content based	SLIM ElasticNet	Structured SLIM
AUC	0.16531220636270120	0.02413698599489908	0.2271634077587352	0.0792913926051874
MRR	0.19139018151447576	0.02351167837487133	0.2636167539188936	0.0787235073903345
NDCG	0.01897790003872984	0.00110770278659267	0.0310036592400856	0.0050223485920076
Map	0.09108725657623755	0.00595261532954509	0.1263267745014880	0.0206817543414812
Precision	0.12431652422927689	0.01177681328023700	0.1680321267170991	0.0339791489552076
Recall	0.00957347798587911	0.00061475823269545	0.0146979726141915	0.0021920817766374

MovieLens 26M with TAGS

ICM: shape = (45843, 53508), sparcity: 0.9998916544847266

	KNN collaborative	KNN content based	SLIM ElasticNet	Structured SLIM
AUC	0.16531220636270120	0.09306531239279914	0.2271456963025925	0.0320176517965009
MRR	0.19139018151447576	0.09721575909436314	0.2636120930093823	0.0309206601339358
NDCG	0.01897790003872984	0.00626021730383710	0.0310051664326851	0.0021933634099461
Map	0.09108725657623755	0.03198887534117678	0.1263297574835752	0.0075111395737320
Precision	0.12431652422927689	0.04987471475232986	0.1680433128999261	0.0148082688263470
Recall	0.00957347798587911	0.00310033025947884	0.0146982335097261	0.0011481825420549

Conclusions

As showed by the metrics, the algorithm we implemented is sensible to the sparcity of the ICM matrix it receives as input. In the case of the MovieLens 26M dataset, considering the ICM constructed with the genres with a sparcity near to 90%, the Structured SLIM trained a similarity matrix whose MAP is 4.5x better than the KNN Content Based algorithm.

Authors:

Alex Porciani, Luca Vavassori