6,695 research outputs found
DIMAL: Deep Isometric Manifold Learning Using Sparse Geodesic Sampling
This paper explores a fully unsupervised deep learning approach for computing
distance-preserving maps that generate low-dimensional embeddings for a certain
class of manifolds. We use the Siamese configuration to train a neural network
to solve the problem of least squares multidimensional scaling for generating
maps that approximately preserve geodesic distances. By training with only a
few landmarks, we show a significantly improved local and nonlocal
generalization of the isometric mapping as compared to analogous non-parametric
counterparts. Importantly, the combination of a deep-learning framework with a
multidimensional scaling objective enables a numerical analysis of network
architectures to aid in understanding their representation power. This provides
a geometric perspective to the generalizability of deep learning.Comment: 10 pages, 11 Figure
Graph-Based Classification of Omnidirectional Images
Omnidirectional cameras are widely used in such areas as robotics and virtual
reality as they provide a wide field of view. Their images are often processed
with classical methods, which might unfortunately lead to non-optimal solutions
as these methods are designed for planar images that have different geometrical
properties than omnidirectional ones. In this paper we study image
classification task by taking into account the specific geometry of
omnidirectional cameras with graph-based representations. In particular, we
extend deep learning architectures to data on graphs; we propose a principled
way of graph construction such that convolutional filters respond similarly for
the same pattern on different positions of the image regardless of lens
distortions. Our experiments show that the proposed method outperforms current
techniques for the omnidirectional image classification problem
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