Uncorrelated Multilinear Principal Component Analysis for Unsupervised Multilinear Subspace Learning
Bibliographic record
Abstract
This paper proposes an uncorrelated multilinear principal component analysis (UMPCA) algorithm for unsupervised subspace learning of tensorial data. It should be viewed as a multilinear extension of the classical principal component analysis (PCA) framework. Through successive variance maximization, UMPCA seeks a tensor-to-vector projection (TVP) that captures most of the variation in the original tensorial input while producing uncorrelated features. The solution consists of sequential iterative steps based on the alternating projection method. In addition to deriving the UMPCA framework, this work offers a way to systematically determine the maximum number of uncorrelated multilinear features that can be extracted by the method. UMPCA is compared against the baseline PCA solution and its five state-of-the-art multilinear extensions, namely two-dimensional PCA (2DPCA), concurrent subspaces analysis (CSA), tensor rank-one decomposition (TROD), generalized PCA (GPCA), and multilinear PCA (MPCA), on the tasks of unsupervised face and gait recognition. Experimental results included in this paper suggest that UMPCA is particularly effective in determining the low-dimensional projection space needed in such recognition tasks.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.002 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
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 source (direct Gemma or distilled Codex), 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".