Constrained Nonnegative Tensor Factorization for Spectral Unmixing of Hyperspectral Images: A Case Study of Urban Impervious Surface Extraction
Bibliographic record
Abstract
In recent years, a new genre of hyperspectral unmixing methods based on nonnegative matrix factorization (NMF) have been proposed. Unlike traditional spectral unmixing methods, the NMF-based hyperspectral unmixing methods no longer depend on pure pixels in the original image. The NMF is based on linear algebra, which requires that the hyperspectral data cube is converted from 3-D cube to a 2-D matrix. Due to this conversion, the spatial information in the relative positions of the pixels is lost. With the emergence of multilinear algebra, the tensorial representation of hyperspectral imagery that preserves spectral and spatial information has become popular. The tensor-based spectral unmixing was first realized in 2017 using the matrix-vector nonnegative tensor factorization (MVNTF) decomposition. Using the construction of MVNTF spectral unmixing, this letter proposes to integrate three additional constraints (sparseness, volume, and nonlinearity) to the cost function. As we show in this letter, we found that the three constraints greatly improved the impervious surface area fraction/classification results. The constraints also shortened the processing time.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 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 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".