10,878 research outputs found
Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds
Sparsity-based representations have recently led to notable results in
various visual recognition tasks. In a separate line of research, Riemannian
manifolds have been shown useful for dealing with features and models that do
not lie in Euclidean spaces. With the aim of building a bridge between the two
realms, we address the problem of sparse coding and dictionary learning over
the space of linear subspaces, which form Riemannian structures known as
Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into
the space of symmetric matrices by an isometric mapping. This in turn enables
us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we
propose closed-form solutions for learning a Grassmann dictionary, atom by
atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann
sparse coding and dictionary learning algorithms through embedding into Hilbert
spaces.
Experiments on several classification tasks (gender recognition, gesture
classification, scene analysis, face recognition, action recognition and
dynamic texture classification) show that the proposed approaches achieve
considerable improvements in discrimination accuracy, in comparison to
state-of-the-art methods such as kernelized Affine Hull Method and
graph-embedding Grassmann discriminant analysis.Comment: Appearing in International Journal of Computer Visio
Scalable Dense Non-rigid Structure-from-Motion: A Grassmannian Perspective
This paper addresses the task of dense non-rigid structure-from-motion
(NRSfM) using multiple images. State-of-the-art methods to this problem are
often hurdled by scalability, expensive computations, and noisy measurements.
Further, recent methods to NRSfM usually either assume a small number of sparse
feature points or ignore local non-linearities of shape deformations, and thus
cannot reliably model complex non-rigid deformations. To address these issues,
in this paper, we propose a new approach for dense NRSfM by modeling the
problem on a Grassmann manifold. Specifically, we assume the complex non-rigid
deformations lie on a union of local linear subspaces both spatially and
temporally. This naturally allows for a compact representation of the complex
non-rigid deformation over frames. We provide experimental results on several
synthetic and real benchmark datasets. The procured results clearly demonstrate
that our method, apart from being scalable and more accurate than
state-of-the-art methods, is also more robust to noise and generalizes to
highly non-linear deformations.Comment: 10 pages, 7 figure, 4 tables. Accepted for publication in Conference
on Computer Vision and Pattern Recognition (CVPR), 2018, typos fixed and
acknowledgement adde
Enhancing Domain Word Embedding via Latent Semantic Imputation
We present a novel method named Latent Semantic Imputation (LSI) to transfer
external knowledge into semantic space for enhancing word embedding. The method
integrates graph theory to extract the latent manifold structure of the
entities in the affinity space and leverages non-negative least squares with
standard simplex constraints and power iteration method to derive spectral
embeddings. It provides an effective and efficient approach to combining entity
representations defined in different Euclidean spaces. Specifically, our
approach generates and imputes reliable embedding vectors for low-frequency
words in the semantic space and benefits downstream language tasks that depend
on word embedding. We conduct comprehensive experiments on a carefully designed
classification problem and language modeling and demonstrate the superiority of
the enhanced embedding via LSI over several well-known benchmark embeddings. We
also confirm the consistency of the results under different parameter settings
of our method.Comment: ACM SIGKDD 201
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