# Tag-Aware Ordinal Sparse Factor Analysis for Learning and Content Analytics

arXiv: https://arxiv.org/abs/1412.5967 · HTML: https://mlsanity.com/paper/1412.5967/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2014.

## Built on by (most cited first, 15 of 15)

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- [FlashSparse: Minimizing Computation Redundancy for Fast Sparse Matrix Multiplications on Tensor Cores](https://mlsanity.com/paper/2412.11007/) (2024)
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- [Transition-Aware Multi-Activity Knowledge Tracing](https://mlsanity.com/paper/2301.12916/) (2023)
- [Libra: Unleashing GPU Heterogeneity for High-Performance Sparse Matrix Multiplication](https://mlsanity.com/paper/2506.22714/) (2025)
- [CANINE: Coaching Visually Impaired Users for Interactive Navigation with a Robot Guide Dog](https://mlsanity.com/paper/2605.19501/) (2026)
- [Clustering Introductory Computer Science Exercises Using Topic Modeling Methods](https://mlsanity.com/paper/2104.10748/) (2021)
- [Multidimensional Item Response Theory in the Style of Collaborative Filtering](https://mlsanity.com/paper/2301.00909/) (2023)

## Abstract (arXiv)

Machine learning offers novel ways and means to design personalized learning systems wherein each student's educational experience is customized in real time depending on their background, learning goals, and performance to date. SPARse Factor Analysis (SPARFA) is a novel framework for machine learning-based learning analytics, which estimates a learner's knowledge of the concepts underlying a domain, and content analytics, which estimates the relationships among a collection of questions and those concepts. SPARFA jointly learns the associations among the questions and the concepts, learner concept knowledge profiles, and the underlying question difficulties, solely based on the correct/incorrect graded responses of a population of learners to a collection of questions. In this paper, we extend the SPARFA framework significantly to enable: (i) the analysis of graded responses on an ordinal scale (partial credit) rather than a binary scale (correct/incorrect); (ii) the exploitation of tags/labels for questions that partially describe the question{concept associations. The resulting Ordinal SPARFA-Tag framework greatly enhances the interpretability of the estimated concepts. We demonstrate using real educational data that Ordinal SPARFA-Tag outperforms both SPARFA and existing collaborative filtering techniques in predicting missing learner responses.