24 research outputs found
A relaxation method for binary orthogonal optimization problems with its applications
This paper focuses on a class of binary orthogonal optimization problems
frequently arising in semantic hashing. Consider that this class of problems
may have an empty feasible set, rendering them not well-defined. We introduce
an equivalent model involving a restricted Stiefel manifold and a matrix box
set, and then investigate its penalty problems induced by the -distance
from the box set and its Moreau envelope. The two penalty problems are always
well-defined, and moreover, they serve as the global exact penalties provided
that the original model is well-defined. Notably, the penalty problem induced
by the Moreau envelope is a smooth optimization over an embedded submanifold
with a favorable structure. We develop a retraction-based nonmonotone
line-search Riemannian gradient method to address this penalty problem to
achieve a desirable solution for the original binary orthogonal problems.
Finally, the proposed method is applied to supervised and unsupervised hashing
tasks and is compared with several popular methods on the MNIST and CIFAR-10
datasets. The numerical comparisons reveal that our algorithm is significantly
superior to other solvers in terms of feasibility violation, and it is
comparable even superior to others in terms of evaluation metrics related to
the Hamming distance.Comment: Binary orthogonal optimization problems, global exact penalty,
relaxation methods, semantic hashin
SADIH: Semantic-Aware DIscrete Hashing
Due to its low storage cost and fast query speed, hashing has been recognized
to accomplish similarity search in large-scale multimedia retrieval
applications. Particularly supervised hashing has recently received
considerable research attention by leveraging the label information to preserve
the pairwise similarities of data points in the Hamming space. However, there
still remain two crucial bottlenecks: 1) the learning process of the full
pairwise similarity preservation is computationally unaffordable and unscalable
to deal with big data; 2) the available category information of data are not
well-explored to learn discriminative hash functions. To overcome these
challenges, we propose a unified Semantic-Aware DIscrete Hashing (SADIH)
framework, which aims to directly embed the transformed semantic information
into the asymmetric similarity approximation and discriminative hashing
function learning. Specifically, a semantic-aware latent embedding is
introduced to asymmetrically preserve the full pairwise similarities while
skillfully handle the cumbersome n times n pairwise similarity matrix.
Meanwhile, a semantic-aware autoencoder is developed to jointly preserve the
data structures in the discriminative latent semantic space and perform data
reconstruction. Moreover, an efficient alternating optimization algorithm is
proposed to solve the resulting discrete optimization problem. Extensive
experimental results on multiple large-scale datasets demonstrate that our
SADIH can clearly outperform the state-of-the-art baselines with the additional
benefit of lower computational costs.Comment: Accepted by The Thirty-Third AAAI Conference on Artificial
Intelligence (AAAI-19