11,001 research outputs found
Geodesic Distance Function Learning via Heat Flow on Vector Fields
Learning a distance function or metric on a given data manifold is of great
importance in machine learning and pattern recognition. Many of the previous
works first embed the manifold to Euclidean space and then learn the distance
function. However, such a scheme might not faithfully preserve the distance
function if the original manifold is not Euclidean. Note that the distance
function on a manifold can always be well-defined. In this paper, we propose to
learn the distance function directly on the manifold without embedding. We
first provide a theoretical characterization of the distance function by its
gradient field. Based on our theoretical analysis, we propose to first learn
the gradient field of the distance function and then learn the distance
function itself. Specifically, we set the gradient field of a local distance
function as an initial vector field. Then we transport it to the whole manifold
via heat flow on vector fields. Finally, the geodesic distance function can be
obtained by requiring its gradient field to be close to the normalized vector
field. Experimental results on both synthetic and real data demonstrate the
effectiveness of our proposed algorithm
Deep Metric Learning via Lifted Structured Feature Embedding
Learning the distance metric between pairs of examples is of great importance
for learning and visual recognition. With the remarkable success from the state
of the art convolutional neural networks, recent works have shown promising
results on discriminatively training the networks to learn semantic feature
embeddings where similar examples are mapped close to each other and dissimilar
examples are mapped farther apart. In this paper, we describe an algorithm for
taking full advantage of the training batches in the neural network training by
lifting the vector of pairwise distances within the batch to the matrix of
pairwise distances. This step enables the algorithm to learn the state of the
art feature embedding by optimizing a novel structured prediction objective on
the lifted problem. Additionally, we collected Online Products dataset: 120k
images of 23k classes of online products for metric learning. Our experiments
on the CUB-200-2011, CARS196, and Online Products datasets demonstrate
significant improvement over existing deep feature embedding methods on all
experimented embedding sizes with the GoogLeNet network.Comment: 11 page
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