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We propose a cross-modality manifold alignment procedure that leverages triplet loss to jointly learn consistent, multi-modal embeddings of language-based concepts of real-world items. Our approach learns these embeddings by sampling triples of anchor, positive, and negative data points from RGB-depth images and their natural language descriptions. We show that our approach can benefit from, but does not require, post-processing steps such as Procrustes analysis, in contrast to some of our baselines which require it for reasonable performance. We demonstrate the effectiveness of our approach on two datasets commonly used to develop robotic-based grounded language learning systems, where our approach outperforms four baselines, including a state-of-the-art approach, across five evaluation metrics.
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Orthogonal Procrustes and norm-dependent optimality
This note revisits the classical orthogonal Procrustes problem and investigates the norm-dependent geometric behavior underlying Procrustes alignment for subspaces. It presents generic, deterministic bounds quantifying the performance of a specified Procrustes-based choice of subspace alignment. Numerical examples illustrate the theoretical observations and offer additional, empirical findings which are discussed in detail. This note complements recent advances in statistics involving Procrustean matrix perturbation decompositions and eigenvector estimation.
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- Award ID(s):
- 1902755
- PAR ID:
- 10303825
- Date Published:
- Journal Name:
- The Electronic Journal of Linear Algebra
- Volume:
- 36
- Issue:
- 36
- ISSN:
- 1081-3810
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.13001/ela.2020.5009
