From tensors to novelties: Low-dimensional representations for anomaly detection in multispectral imagery

Anomaly detection in multispectral imagery must cope with high-dimensional inputs, scarce labeled anomalies and operational constraints. Tensor decompositions offer a structured way to compress such data, but their impact on anomaly detection performance and cost is not well quantified. This work studies how low-rank tensor representations affect one-class detectors on multispectral imagery. Two decomposition strategies are evaluated as feature extractors: a global CP (PARAFAC) model fitted on training tiles and a per-tile Tucker model. The resulting coefficients are used to train one-class support vector machines, autoencoders and isolation forests on typical examples only, and anomalies are identified through their detector scores. The study uses multispectral Mastcam images from the Mars Science Laboratory Curiosity rover, a dataset with rare labeled novelties. Experiments cover two evaluation regimes (randomized across subclasses and subclass-specific) and four training sizes n ∈ { 500 , 1000 , 1500 , 3000 } . Under randomized sampling, CP and Tucker improve ROC–AUC over PCA for OC-SVM by approximately 10 to 15 percent at n ≤ 1500 , while autoencoder gains span approximately 2 to 13 percent depending on decomposition and sample size. In subclass-specific tests for structured subclasses (drill-hole, DRT, dump-pile), CP and Tucker yield larger improvements at n ≤ 1500 , with absolute ROC–AUC increases over PCA ranging from approximately 14 to 56 percent, whereas for visually homogeneous subclasses (bedrock, broken rock, float, veins) decompositions rarely improve over PCA and can reduce performance. Computationally, CP can require peak RSS memory above 50 GB, whereas Tucker often remains below 10 GB (8.67 GB vs 52.53 GB in the reported runs, a 84% reduction), albeit with longer runtimes. Overall, the results indicate that tensor decompositions are most valuable as selective enhancements to PCA in multispectral anomaly detection pipelines when multiway structure is informative and training data are limited.