Bayesian non-negative matrix factorization with Student’s t-distribution for outlier removal and data clustering
Bibliographic record
Abstract
Non-negative Matrix Factorization (NMF) is an effective way to solve the redundancy of non-negative high-dimensional data. Most of the traditional probability-based NMF methods use Gaussian distribution to model the differences between the matrices before and after decomposition. However, the Gaussian distribution is strongly affected by outliers, and it may not fit all datasets accurately when there are no outliers in the data. In this article, we propose a novel Bayesian NMF with the Student’s t-distribution, i.e., TNMF. specifically, in order to reduce the impact of outliers on the algorithm, we use the Student’s t-distribution to fit the data points instead of the Gaussian distribution. In addition, it is possible to adjust the Degree of Freedom (DF) to make the Student’s t-distribution more flexible than the Gaussian distribution to fit data points when there are no outliers. Next, we combine the Automatic Relevance Determination (ARD) prior in our algorithm to simplify the model and allow for better performance of the algorithm. Finally, the article used 10 datasets to design two kinds of experiments, outlier removal and data clustering. The outlier removal results of this proposed algorithm are significantly better than the other methods, and it performs better in clustering compared to the other methods in the majority of cases.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".