1,458 research outputs found
Embedding based on function approximation for large scale image search
The objective of this paper is to design an embedding method that maps local
features describing an image (e.g. SIFT) to a higher dimensional representation
useful for the image retrieval problem. First, motivated by the relationship
between the linear approximation of a nonlinear function in high dimensional
space and the stateof-the-art feature representation used in image retrieval,
i.e., VLAD, we propose a new approach for the approximation. The embedded
vectors resulted by the function approximation process are then aggregated to
form a single representation for image retrieval. Second, in order to make the
proposed embedding method applicable to large scale problem, we further derive
its fast version in which the embedded vectors can be efficiently computed,
i.e., in the closed-form. We compare the proposed embedding methods with the
state of the art in the context of image search under various settings: when
the images are represented by medium length vectors, short vectors, or binary
vectors. The experimental results show that the proposed embedding methods
outperform existing the state of the art on the standard public image retrieval
benchmarks.Comment: Accepted to TPAMI 2017. The implementation and precomputed features
of the proposed F-FAemb are released at the following link:
http://tinyurl.com/F-FAem
Regularized principal manifolds
Many settings of unsupervised learning can be viewed as quantization problems - the minimization
of the expected quantization error subject to some restrictions. This allows the
use of tools such as regularization from the theory of (supervised) risk minimization for
unsupervised learning. This setting turns out to be closely related to principal curves, the
generative topographic map, and robust coding.
We explore this connection in two ways: (1) we propose an algorithm for nding principal
manifolds that can be regularized in a variety of ways; and (2) we derive uniform
convergence bounds and hence bounds on the learning rates of the algorithm. In particular,
we give bounds on the covering numbers which allows us to obtain nearly optimal
learning rates for certain types of regularization operators. Experimental results demonstrate
the feasibility of the approach
Covariance Eigenvector Sparsity for Compression and Denoising
Sparsity in the eigenvectors of signal covariance matrices is exploited in
this paper for compression and denoising. Dimensionality reduction (DR) and
quantization modules present in many practical compression schemes such as
transform codecs, are designed to capitalize on this form of sparsity and
achieve improved reconstruction performance compared to existing
sparsity-agnostic codecs. Using training data that may be noisy a novel
sparsity-aware linear DR scheme is developed to fully exploit sparsity in the
covariance eigenvectors and form noise-resilient estimates of the principal
covariance eigenbasis. Sparsity is effected via norm-one regularization, and
the associated minimization problems are solved using computationally efficient
coordinate descent iterations. The resulting eigenspace estimator is shown
capable of identifying a subset of the unknown support of the eigenspace basis
vectors even when the observation noise covariance matrix is unknown, as long
as the noise power is sufficiently low. It is proved that the sparsity-aware
estimator is asymptotically normal, and the probability to correctly identify
the signal subspace basis support approaches one, as the number of training
data grows large. Simulations using synthetic data and images, corroborate that
the proposed algorithms achieve improved reconstruction quality relative to
alternatives.Comment: IEEE Transcations on Signal Processing, 2012 (to appear
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