10,759 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
Parametric t-Distributed Stochastic Exemplar-centered Embedding
Parametric embedding methods such as parametric t-SNE (pt-SNE) have been
widely adopted for data visualization and out-of-sample data embedding without
further computationally expensive optimization or approximation. However, the
performance of pt-SNE is highly sensitive to the hyper-parameter batch size due
to conflicting optimization goals, and often produces dramatically different
embeddings with different choices of user-defined perplexities. To effectively
solve these issues, we present parametric t-distributed stochastic
exemplar-centered embedding methods. Our strategy learns embedding parameters
by comparing given data only with precomputed exemplars, resulting in a cost
function with linear computational and memory complexity, which is further
reduced by noise contrastive samples. Moreover, we propose a shallow embedding
network with high-order feature interactions for data visualization, which is
much easier to tune but produces comparable performance in contrast to a deep
neural network employed by pt-SNE. We empirically demonstrate, using several
benchmark datasets, that our proposed methods significantly outperform pt-SNE
in terms of robustness, visual effects, and quantitative evaluations.Comment: fixed typo
- …