TULCA extends the ULCA dimensionality reduction method to high-order tensors, unifying discriminant analysis and contrastive learning for flexible tensor group comparison.
Isometric dilations of commuting contractions and Brehmer positivity
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abstract
It is well-known that an $n$-tuple $(n\ge 3)$ of commuting contractions does not posses an isometric dilation, in general. Considering a class of $n$-tuple of commuting contractions satisfying certain positivity assumption, we construct their isometric dilations and consequently establish their von Neumann inequality. The positivity assumption is related to Brehmer positivity and motivated by the study of isometric dilations of operator tuples in [4].
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Visual Analytics Using Tensor Unified Linear Comparative Analysis
TULCA extends the ULCA dimensionality reduction method to high-order tensors, unifying discriminant analysis and contrastive learning for flexible tensor group comparison.