5,908 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
Geometric deep learning: going beyond Euclidean data
Many scientific fields study data with an underlying structure that is a
non-Euclidean space. Some examples include social networks in computational
social sciences, sensor networks in communications, functional networks in
brain imaging, regulatory networks in genetics, and meshed surfaces in computer
graphics. In many applications, such geometric data are large and complex (in
the case of social networks, on the scale of billions), and are natural targets
for machine learning techniques. In particular, we would like to use deep
neural networks, which have recently proven to be powerful tools for a broad
range of problems from computer vision, natural language processing, and audio
analysis. However, these tools have been most successful on data with an
underlying Euclidean or grid-like structure, and in cases where the invariances
of these structures are built into networks used to model them. Geometric deep
learning is an umbrella term for emerging techniques attempting to generalize
(structured) deep neural models to non-Euclidean domains such as graphs and
manifolds. The purpose of this paper is to overview different examples of
geometric deep learning problems and present available solutions, key
difficulties, applications, and future research directions in this nascent
field
Multi-view Convolutional Neural Networks for 3D Shape Recognition
A longstanding question in computer vision concerns the representation of 3D
shapes for recognition: should 3D shapes be represented with descriptors
operating on their native 3D formats, such as voxel grid or polygon mesh, or
can they be effectively represented with view-based descriptors? We address
this question in the context of learning to recognize 3D shapes from a
collection of their rendered views on 2D images. We first present a standard
CNN architecture trained to recognize the shapes' rendered views independently
of each other, and show that a 3D shape can be recognized even from a single
view at an accuracy far higher than using state-of-the-art 3D shape
descriptors. Recognition rates further increase when multiple views of the
shapes are provided. In addition, we present a novel CNN architecture that
combines information from multiple views of a 3D shape into a single and
compact shape descriptor offering even better recognition performance. The same
architecture can be applied to accurately recognize human hand-drawn sketches
of shapes. We conclude that a collection of 2D views can be highly informative
for 3D shape recognition and is amenable to emerging CNN architectures and
their derivatives.Comment: v1: Initial version. v2: An updated ModelNet40 training/test split is
used; results with low-rank Mahalanobis metric learning are added. v3 (ICCV
2015): A second camera setup without the upright orientation assumption is
added; some accuracy and mAP numbers are changed slightly because a small
issue in mesh rendering related to specularities is fixe
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