Closed-Form Models of Accuracy Loss due to Subsampling in SVD Collaborative Filtering

We postulate and analyze a nonlinear subsampling accuracy loss (SSAL) model based on the root mean square error (RMSE) and two SSAL models based on the mean square error (MSE), suggested by extensive preliminary simulations. The SSAL models predict accuracy loss in terms of subsampling parameters li...

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Main Authors: Samin Poudel, Marwan Bikdash
Format: Article
Language:English
Published: Tsinghua University Press 2023-03-01
Series:Big Data Mining and Analytics
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Online Access:https://www.sciopen.com/article/10.26599/BDMA.2022.9020024
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author Samin Poudel
Marwan Bikdash
author_facet Samin Poudel
Marwan Bikdash
author_sort Samin Poudel
collection DOAJ
description We postulate and analyze a nonlinear subsampling accuracy loss (SSAL) model based on the root mean square error (RMSE) and two SSAL models based on the mean square error (MSE), suggested by extensive preliminary simulations. The SSAL models predict accuracy loss in terms of subsampling parameters like the fraction of users dropped (FUD) and the fraction of items dropped (FID). We seek to investigate whether the models depend on the characteristics of the dataset in a constant way across datasets when using the SVD collaborative filtering (CF) algorithm. The dataset characteristics considered include various densities of the rating matrix and the numbers of users and items. Extensive simulations and rigorous regression analysis led to empirical symmetrical SSAL models in terms of FID and FUD whose coefficients depend only on the data characteristics. The SSAL models came out to be multi-linear in terms of odds ratios of dropping a user (or an item) vs. not dropping it. Moreover, one MSE deterioration model turned out to be linear in the FID and FUD odds where their interaction term has a zero coefficient. Most importantly, the models are constant in the sense that they are written in closed-form using the considered data characteristics (densities and numbers of users and items). The models are validated through extensive simulations based on 850 synthetically generated primary (pre-subsampling) matrices derived from the 25M MovieLens dataset. Nearly 460 000 subsampled rating matrices were then simulated and subjected to the singular value decomposition (SVD) CF algorithm. Further validation was conducted using the 1M MovieLens and the Yahoo! Music Rating datasets. The models were constant and significant across all 3 datasets.
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spelling doaj-art-33ce6682ee824d5fb3454634dd238d602025-02-02T07:53:41ZengTsinghua University PressBig Data Mining and Analytics2096-06542023-03-0161728410.26599/BDMA.2022.9020024Closed-Form Models of Accuracy Loss due to Subsampling in SVD Collaborative FilteringSamin Poudel0Marwan Bikdash1Department of Computational Data Science and Engineering, North Carolina A & T State University, Greensboro, NC 27401, USADepartment of Computational Data Science and Engineering, North Carolina A & T State University, Greensboro, NC 27401, USAWe postulate and analyze a nonlinear subsampling accuracy loss (SSAL) model based on the root mean square error (RMSE) and two SSAL models based on the mean square error (MSE), suggested by extensive preliminary simulations. The SSAL models predict accuracy loss in terms of subsampling parameters like the fraction of users dropped (FUD) and the fraction of items dropped (FID). We seek to investigate whether the models depend on the characteristics of the dataset in a constant way across datasets when using the SVD collaborative filtering (CF) algorithm. The dataset characteristics considered include various densities of the rating matrix and the numbers of users and items. Extensive simulations and rigorous regression analysis led to empirical symmetrical SSAL models in terms of FID and FUD whose coefficients depend only on the data characteristics. The SSAL models came out to be multi-linear in terms of odds ratios of dropping a user (or an item) vs. not dropping it. Moreover, one MSE deterioration model turned out to be linear in the FID and FUD odds where their interaction term has a zero coefficient. Most importantly, the models are constant in the sense that they are written in closed-form using the considered data characteristics (densities and numbers of users and items). The models are validated through extensive simulations based on 850 synthetically generated primary (pre-subsampling) matrices derived from the 25M MovieLens dataset. Nearly 460 000 subsampled rating matrices were then simulated and subjected to the singular value decomposition (SVD) CF algorithm. Further validation was conducted using the 1M MovieLens and the Yahoo! Music Rating datasets. The models were constant and significant across all 3 datasets.https://www.sciopen.com/article/10.26599/BDMA.2022.9020024collaborative filteringsubsamplingaccuracy loss modelsperformance lossrecommendation systemsimulationrating matrixroot mean square error
spellingShingle Samin Poudel
Marwan Bikdash
Closed-Form Models of Accuracy Loss due to Subsampling in SVD Collaborative Filtering
Big Data Mining and Analytics
collaborative filtering
subsampling
accuracy loss models
performance loss
recommendation system
simulation
rating matrix
root mean square error
title Closed-Form Models of Accuracy Loss due to Subsampling in SVD Collaborative Filtering
title_full Closed-Form Models of Accuracy Loss due to Subsampling in SVD Collaborative Filtering
title_fullStr Closed-Form Models of Accuracy Loss due to Subsampling in SVD Collaborative Filtering
title_full_unstemmed Closed-Form Models of Accuracy Loss due to Subsampling in SVD Collaborative Filtering
title_short Closed-Form Models of Accuracy Loss due to Subsampling in SVD Collaborative Filtering
title_sort closed form models of accuracy loss due to subsampling in svd collaborative filtering
topic collaborative filtering
subsampling
accuracy loss models
performance loss
recommendation system
simulation
rating matrix
root mean square error
url https://www.sciopen.com/article/10.26599/BDMA.2022.9020024
work_keys_str_mv AT saminpoudel closedformmodelsofaccuracylossduetosubsamplinginsvdcollaborativefiltering
AT marwanbikdash closedformmodelsofaccuracylossduetosubsamplinginsvdcollaborativefiltering