533 research outputs found
Weakly-Supervised Alignment of Video With Text
Suppose that we are given a set of videos, along with natural language
descriptions in the form of multiple sentences (e.g., manual annotations, movie
scripts, sport summaries etc.), and that these sentences appear in the same
temporal order as their visual counterparts. We propose in this paper a method
for aligning the two modalities, i.e., automatically providing a time stamp for
every sentence. Given vectorial features for both video and text, we propose to
cast this task as a temporal assignment problem, with an implicit linear
mapping between the two feature modalities. We formulate this problem as an
integer quadratic program, and solve its continuous convex relaxation using an
efficient conditional gradient algorithm. Several rounding procedures are
proposed to construct the final integer solution. After demonstrating
significant improvements over the state of the art on the related task of
aligning video with symbolic labels [7], we evaluate our method on a
challenging dataset of videos with associated textual descriptions [36], using
both bag-of-words and continuous representations for text.Comment: ICCV 2015 - IEEE International Conference on Computer Vision, Dec
2015, Santiago, Chil
Embedding multidimensional grids into optimal hypercubes
Let and be graphs, with , and a one to one map of their vertices. Let , where is the distance
between vertices and of . Now let = , over all such maps .
The parameter is a generalization of the classic and well studied
"bandwidth" of , defined as , where is the path on
points and . Let
be the -dimensional grid graph with integer values through in
the 'th coordinate. In this paper, we study in the case when and is the hypercube
of dimension , the hypercube of
smallest dimension having at least as many points as . Our main result is
that
provided for each . For such , the bound
improves on the previous best upper bound . Our methods include
an application of Knuth's result on two-way rounding and of the existence of
spanning regular cyclic caterpillars in the hypercube.Comment: 47 pages, 8 figure
Numerically optimized Markovian coupling and mixing in one-dimensional maps
Algorithms are introduced that produce optimal Markovian couplings for large finite-state-space discrete-time Markov chains with sparse transition matrices; these algorithms are applied to some toy models motivated by fluid-dynamical mixing problems at high Peclét number. An alternative definition of the time-scale of a mixing process is suggested. Finally, these algorithms are applied to the problem of coupling diffusion processes in an acute-angled triangle, and some of the simplifications that occur in continuum coupling problems are discussed
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