1,619 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
Chaos and stability in a two-parameter family of convex billiard tables
We study, by numerical simulations and semi-rigorous arguments, a
two-parameter family of convex, two-dimensional billiard tables, generalizing
the one-parameter class of oval billiards of Benettin--Strelcyn [Phys. Rev. A
17, 773 (1978)]. We observe interesting dynamical phenomena when the billiard
tables are continuously deformed from the integrable circular billiard to
different versions of completely-chaotic stadia. In particular, we conjecture
that a new class of ergodic billiard tables is obtained in certain regions of
the two-dimensional parameter space, when the billiards are close to skewed
stadia. We provide heuristic arguments supporting this conjecture, and give
numerical confirmation using the powerful method of Lyapunov-weighted dynamics.Comment: 19 pages, 13 figures. Submitted for publication. Supplementary video
available at http://sistemas.fciencias.unam.mx/~dsanders
Multiclass latent locally linear support vector machines
Kernelized Support Vector Machines (SVM) have gained the status of off-the-shelf classifiers, able to deliver state of the art performance on almost any problem. Still, their practical use is constrained by their computational and memory complexity, which grows super-linearly with the number of training samples. In order to retain the low training and testing complexity of linear classifiers and the exibility of non linear ones, a growing, promising alternative is represented by methods that learn non-linear classifiers through local combinations of linear ones. In this paper we propose a new multi class local classifier, based on a latent SVM formulation. The proposed classifier makes use of a set of linear models that are linearly combined using sample and class specific weights. Thanks to the latent formulation, the combination coefficients are modeled as latent variables. We allow soft combinations and we provide a closed-form solution for their estimation, resulting in an efficient prediction rule. This novel formulation allows to learn in a principled way the sample specific weights and the linear classifiers, in a unique optimization problem, using a CCCP optimization procedure. Extensive experiments on ten standard UCI machine learning datasets, one large binary dataset, three character and digit recognition databases, and a visual place categorization dataset show the power of the proposed approach
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